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ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 1: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 2: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk
Page 3: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 4: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk
Page 5: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

R SOTVU @EBXWMB TZY @EB\[ T N]F^H%[ S F^_`[ SGT _XF^_)LEBXF^_ T _bacBX@Ede[ SGT @Ef^NgFIN T LEh�iE@EF^HOijDOL�klWm[n@-[ SOT @EBoFIi�FIHO_@Ea�kZ@EHO_\[nBopOk9[qFsr T f^@EiEF^kZhG[ S Lt[uL Y BX@�@EavFI_wacpOHONGLEd T Hq[nLEf^fxP�L]W�F^HONy@�a Y Bo@EiEBXL�d{z

|}a Y Bo@*@�ac_~kZLEH�D T kZ@�HO_XF^N T B T N�LE_ Y Bo@EiEBoLEd]_Xh�[ SOT H�@EH T d]F^i S [ T9��Y�T k9[][ S Lt[ Y Bo@*@Ea[ SOT @EB�P�_ S @EpOf^N S L�r T d�pGk S [n@�kZ@EHq[qBXF^DOpQ[ T [n@#[ SOT [ SGT @EB\P�@Ea Y Bo@EiEBoLEd]d{F^HOiEz R S FI_S LE_~F^HON TtT N�[npGBXH T N�@EpQ[�[q@�D T [ SOT kZLE_ T z��mLEBoFI@�pO_1[ T k S HO@Ef^@EiEF T _gN T r T fI@ Y�T N�F^H Y Bo@*@Ea[ SOT @EB�PKL�B T HO@ U0U F^N T fxPypO_ T N�FIH{kZ@�d Y pQ[ T B�_okZF T HOk T ac@EBbac@EBod�pOf^Lt[nF^HOiMLEHON{FIHqr T _�[qFIiEL�[nF^HOiY BX@�iEBXLEd]d]F^HOi!f^LEHOi�pOLEi T _mL�HON�fI@Ei�FIkt_1kt@EHOH T k9[ T N U Fx[ S [ SOT d]z� T [M[ SOT B T F^_�L]r`F^iE@EBo@EpO_uLEHONyr T H T BXLEDGf T�Y LEB�[7@Ea Y BX@�@Ea�[ SGT @EB\P UuS FIk S�S LE_�_o@�acLEB

S LEN~f^Fx[X[nf T F^d Y LEk'[ F^H�kZ@�d Y pQ[ T B�_XktF T HOk T h�HOLEd T fxP�@�BXNOF^HOLEfx��[ SOT @EB T [qFIk Y BX@�@Ea4[ SOT @�B�P�z R S FI_ac@*ktpO_ T _j@EH Y Bo@*@Eac_1@Ea U%T f^fIac@EpGHON T NGH T _o_Xh�pO_XpOL�fIfxP T'�`Y B T _o_ T N�F^H7[ SOT ac@�BXd�@Ea)L�_Xk SGT d]L@Ea�[nBoLEHO_X�GHOFs[ T FIHGNOpOk9[qFI@�H U Fx[ S B T _ Y�T k9[�[n@�L�B TZY B T _ T Hq[nLt[qFI@�H�@EabL�H#FIHOFx[nF^LEf�_ T iEd T Hn[{@�a[ SOT kt@EpOHq[nLEDGf T @EBoNOFIHGLEfI_oz��)BX@�@EaE[ SOT @EB�P�@Ea�[ S F^_bW�F^HON{FI_)kt@EHOk T BXH T N U Fx[ SjUuS Lt[mFx[mF^_�[ S Lt[fIF^d]Fs[q_)[ SOT kZL Y LEkZFx[}P�@Ea�L Y BX@�@Ea�_\P�_�[ T d�[n@]�^_ TZT F^Hn[q@�[ SOT [nBoLEHO_X�GHOFs[ TZ� z

|}a Y Bo@*@�ac_�kZLEH#D T kt@EHO_XF^N T B T N�LE_ Y Bo@EiEBoLEd]_Xh UuS L�[{W�F^HON�@Ea Y Bo@EiEBoLEd F^_jL Y Bo@*@Eab@�aU�T fIf^ac@EpOHGN T NOH T _X_o¡ ¢{P S P Y @t[ SOT _oFI_gF^_1[ S Lt[~[ SOT f^FId]Fx[nLt[qFI@EHG_~@Ea L�ac@EBod]LEf-_\P`_\[ T d£ac@EBU BXFx[nF^HOi Y BX@�@Eac_j@Ea U�T fIf^ac@EpOHGN T NOH T _X_�B TZ¤GT k9[!Fx[n_�f^FId]Fx[nLt[qFI@EHG_uL�_uL�_\P`_\[ T d¥FIH UuS F^k S [n@Y BX@�iEBXLEd¦_\[nBoLt[ T iEF T _7ac@EB]N T a T Lt[qFIHGi�@EH T _7@ YGY @EH T Hq[�F^H0L�k T B�[nL�FIH0W�F^HON§@�a�iELEd T z¨|}HB T k T Hq[{kt@Ed Y pQ[ T Bj_XktF T HOk T h�i�LEd T _ S L�r TgY BX@�r T N�F^Hqr*LEfIpGLEDOf T LE_�d]@�N T f^_jac@EB%N T _XktBXF^DOF^HOiY Lt[o[ T BoHO_m@Ea�F^Hq[ T BXLEk'[nF^@EHyD T [ U%TZT H�L]_�P�_�[ T d�LEHON�Fx[n_ T Hqr�F^BX@EHOd T Hn[qz

|-kZLEHOHG@t[~ktfIL�FId©[n@ S L�r T _XpODO_\[nLEHq[qFILt[ T N7[ S FI_ S P Y @t[ SOT _oFI_ohVDOpQ[~@EHOfxP�[n@ S L�r T [qLEW T HL]a T9U _\[ TtY _1F^Hg[ S Lt[uNGFIB T k9[qFI@�HOz R SOT�U @EBoW�B TtY @EB\[ T NKF^Hg[ SOT [ SGT _XF^_wfIF T _mF^Hg[ S B TtT LEB T LE_Xz

?VFIBo_�[nh`| Y B T _ T Hq[~L]acBXL�d T'U @�BXW�ac@EB N TtY�T HON T Hn[qfsP�[}P YAT N Y BX@EiEBoLEd]d]FIHOi]F^H][ SOT _�[}P�f TLENQrO@*ktLt[ T N§DqP�¢�LEB\[nF^HQ�lª�«@Eacz R SOT HO@�r T fs[qF T _ SOT B T LEB T kt@EHOH T k9[ T N U Fx[ S DOBXF^HOiEF^HOi�[ SOT[}P Y�T ��[ SGT @EB T [nF^k%L YOY BX@�LEk S [q@ Y BX@EiEBoLEd]d]FIHOi [ S Lt[mkZ@Ed T _-acBX@�d�[ SGT1¬ pOBoB�P��l­1@ U LEBoN7kt@EB��B T _ Y @EHON T HOk T kZf^@E_ T B�[q@1[ SOT kZLEf^kZpOf^Lt[qFI@EHGLEf�L YOY BX@�LEk S FIH�[ SOT ktLt[ T iE@EBoFIktLEf�[qBXLENOFx[nF^@EHM[ S Lt[kZ@Ed T _�acBX@Ed®ªvLEdMD T W]LEHON7ªvL U r T B T zm¯ Y LEB\[nF^kZpOf^LEB�k S LEf^f T HOi T F^_�[q@��OHGN7L�_od]@*@t[ S LEHONY BXL�k9[nF^kZL�f U L�P�@Ea T HOkt@*NGFIHOi{F^HONOpOk'[nFxr T L�HONykt@EF^HONOpOk'[nFxr T N T �OHOFx[nF^@EHO_oz

° T kZ@�HONOh`| S Llr T F^Hnr T _\[nF^iELt[ T N�L~H�pOd�D T B�@�a U L�P�_ @Ea�d]@�N T f^F^HOi~F^Hn[ T BoLEk9[qFsr T _�P�_�[ T d]_LEHONw[nBXL�HO_XFx[nF^@EH�_\P�_�[ T d]_bFIHML1kt@EHO_�[qBXpOk'[nFxr T kt@EHq[ T9� [qz R SOT ac@*ktpO_ SOT B T FI_�@EHud{@�N T fI_ U Fs[ SLMNGFIB T k9[1kt@Ed Y pQ[nL�[nF^@EHOLEf±F^Hn[ T B Y B T [nLt[qFI@EHGh�[ S Lt[1kZL�H!LEk'[npOL�fIfxPKD T pO_ T N!FIH Y BX@�iEBXLEd]d]F^HOiEzR SOT L YOY Bo@ELEk S F^_{F^HO_ Y FIB T N�DqP²L#kZ@EHG_�[nBopOk9[qFI@�H³NOp T [q@#� T [ T Bo_X_o@EH§LEHGN ° P`H T W�ze|´[KFI__ S @ U H S @ U @EH T d]L�P²B TtY B T _ T Hn[�iELEd T �µ[ SOT @EB T [nF^k�_�[nBoLt[ T iEF T _]@EabrGL�BXF^@EpO_]W�FIHONG_!pO_oFIHGi[ SOT _ T d]@*N T fI_oz

Page 6: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

?�F^HOLEf^fsPEh�|�iEFxr T L�kt@EHO_�[qBXpOk'[nF^@EH�@Ea Y BX@�r*LEDOf T @EBoNOF^HOLEf^_ U Fx[ S F^H�L�¢�LEB�[qFIHQ��ª�«@Ea-_\[}P`f T[}P YAT [ SOT @EB�P�[ S Lt[ S LE_7L�[}P YAT @Ea%HOLt[npGBXLEfmH�pOd�D T Bo_Xh�LEHON0L�H T9� [ T BXHOL�f%_ Tt¶ p T HOk T @EapOHGFsr T BX_ T _mkZf^@E_ T N�pOHON T B i T H T BXL�fIF^_ T N ¬ L�B�[ T _XF^LEH Y Bo@*NOpGk9[n_oz R SOT f^@*ktpO_ @EaG[ SGT FIN T LE_�ac@�B[ S FI_%kZ@EHO_\[nBopOk9[qFI@EH#f^F T d]@EB T FIH�kZ@EHqr T Hq[nF^@EHOLEf Y BX@�@Ea�[ SGT @EB\P�hVL�HON U%T B T [ SOT DGLE_XF^_�ac@EBmLkt@EHQ· T k'[npOB T d{L�N T DqP�d T LEf^d]@E_�[j[ S FIB\[}P�P T LEBo_uL�iE@�F^H U @EBoW{[ S Lt[]|�[ SOT H�LEDOLEHONG@EH T NGz¸ S L�[�F^_mH T9U¹SGT B T F^_)[ SOT kt@EHOk TZY [�@EaVL]�^f T HO_ � z R S F^_mFI_mL Y B T NGFIktLt[ T [nBoLEHO_Xac@�BXd T Bb[ S L�[S L�_ D TtT H�FId Y f^F^kZFx[uFIH~[ SGT kZ@EHG_�[nBopOk9[qFI@�Hy@Ea Y BX@�@Eac_�@Ea U%T f^fIac@EpGHON T NGH T _o_%_XF^HOk T J T Hn[qº T HOz| S @ Y�T [ S F^_7kt@EHOk TZY [�d{L�P»D T @Ea1_X@Ed T pG_ T F^H§LEH³LEf^i T DOBoLEF^kZhj_�P�_\[ T d]Lt[qFIk�L YOY Bo@ELEk S[q@�_ T [X[nF^HOi#f^@ U�T B~D�@�pOHONO_~@�H�[ SOT!Y BX@�@Ea¼��[ SOT @�B T [qFIk!_�[qB T HGit[ S @Ea d]@EB T7T'� [ T HO_oFsr T [}P YAT[ SOT @EBoF T _Xz

½

Page 7: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

¢�LEHqP�[ S LEHOW�_�[n@{dmP�_op Y�T B�r�F^_X@EBoh�Ju@EBXNG@EH��)fI@t[qW�FIHOhvac@EB S FI_�[nF^d T L�HON~[nBX@�pODOf T z|�LEklW�HO@ U f T NOi T iEBXL�[ T acpGfIfxP�[ SGT _op YOY @EB�[M@Ea�LEH °O¾ C ¬ C T _ T LEBok S ° [qpON T Hn[o�l_ S F Y z¢�LEHqP�[ S LEHOW�_�[n@�L�fIf�Lt[%[ SOT ªvLED�@�BXLt[q@EB�P�ac@EB)[ SOT ?±@EpGHONOLt[qFI@EHG_�@Ea ¬ @Ed Y pQ[ T B ° ktFs�

T HOk T NOpOBoFIHOi²dwP¨[nF^d T [ SOT B T h7ac@EB Y BX@�r�FINGFIHOi²LEH T'� [nBXL�@EBXNOF^HOLEBoFIfxP®_\[nF^d�pOf^Lt[qFIHOi�LEHONkZFxr�FIf^FI_ T N T Hqr�FIBo@EHOd T Hq[qzm��LEB�[qFIktpOf^LEB`[ S L�HOW�_`[n@jdmP�@E¿]k T �ld]Lt[ T _Xh�À�F^d�ªvLEF^BXNgLEHGN ¬ @EHO@EB¢�kZÁ-BXF^N T hvac@EBV[ SOT�Y f T LE_XpGB T @Ea±[ SOT F^BwkZ@Ed Y L�HnPEz

¢�LEHqPM[ S LEHOW�_�[q@*@)[n@�LEf^f�FIH1[ SOT �)BX@�iEBXLEd]d]F^HOi�ªv@EiEF^k-JuBX@Ep Y @EaOF^H1[ SGT�ÂjTZY L�B�[nd T Hn[@Ea ¬ @Ed Y p4[nF^HOi ° ktF T HOk T Lt[�[ SOT{à HOFxr T BX_oFs[}P0@Ea-J7«@t[ T D�@�BXiKLEHON ¬ S LEfId T BX_�|}HG_�[nFx[np4[ T @�aR�T k S HO@Ef^@EitP�ac@EB%LEBoBXLEHGiEFIHGi�ac@EB%d T [q@Mr�FI_oFs[{_ T r T BXL�f`[nF^d T _Xh�ac@�B�[ SGT F^Bjk S LEBXdÄLEHON S @E_��Y Fx[nLEf^Fs[}PEhvLEHON�ac@EB d]LEHqP�NOF^_XkZpG_X_XF^@EHO_1@EHKd{L�[X[ T BX_wB T fIL�[ T Ng[n@]dwP U @EBoW�z

|b@ U%T LgiEB T Lt[jN T LEf�[n@g¯%Hq[q@EH ° T [qº T B LEHON R S F T BoB�P ¬ @ ¶ pOLEHONGh�ac@EB T HOkZ@�pOBXLEi T d T Hq[nhFIHG_ Y F^BXLt[qFI@�HOh�LEHON][ S @�pOi S [nacpOf�B T d{L�BXW�_XzM| LEd T _ YAT ktFIL�fIfxP�iEBoLt[ T acpOf�[n@7¯1Hq[n@EH#ac@EBm_ S LEB��FIHGiy_o@Ed T{S L YOY P�LEHON�@*ktkZLE_oFI@�HOLEf^fsP S F^f^LEBXF^@EpO_ S @EpGBX_�kZ@�NOF^HOi T HO@EBod{@�pO_�@EBXNOF^HOLEf^_�FIHq[q@pOHO_opO_ YAT k'[nF^HOi�kZ@�d Y pQ[ T BX_Xz

Page 8: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

|%N T kZf^LEB T [ S Lt[�[ S F^_w[ SOT _oFI_ U LE_Mkt@Ed Y @�_ T N�DqP�dmP�_ T fIa LEHGN�[ S Lt[j[ SGT�U @EBXW#kt@EHq[nLEF^H T N[ SOT B T FIHyFI_wdmP�@ U HOh T'� k TZY [ UuSOT B TuT9��Y f^FIktFs[qfsP�_\[nLt[ T NK@t[ SOT B U F^_ T FIHg[ SGT [ T9� [nz

Å�Æ1ÇnÈ�ÇXÉ�Ê~ËZÌ�ÍlÎnÍXϱÐ

Page 9: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

Ñ]Ò�ÓOÔ�ÕZÖ�×#Ø Ù�Ú�Õq×ÜÛ�Ý�Þ�ß�Õqà\ÛAÚ áâ z â Á�LEklW�iEBo@EpOHON£zMzuzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ã

â z â z â ° @Ed T�S FI_\[n@EB\P zuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ãâ z â z ½ R SOT HO@t[qFI@�Hy@Ea Y Bo@EiEBXL�d zuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz â ã

â z ½ ¯%HK@�r T B�r�F T'U @Ea�[ SOT kZ@�Hn[ T Hq[n_m@Ea�[ SOT [ SOT _oFI_äz�zuzMzuzuzMzuzMzuzuzMz�zuz ½±ââ z ½ z â ?ABoLEd T9U @EBXW zuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ½±ââ z ½ z ½ ¢�@*N T f^FIHOi{F^Hn[ T BoLEk9[qFI@EH zuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ½±ââ z ½ z^å ª T HO_ T _¨zuzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ½E½â z ½ z^æ ¯ YOYAT HONOF ��ç kZ@EdMDOF^HOLt[n@�BXF^LEf�kZ@�d Y f T [ T H T _X_{@Ea�[ SGT LEBXFx[ S d T [nF^k

kZ@EdMDOFIHGLt[n@EBo_ zuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ½E½â z^å ¢�F^_XiEFxr�FIHGiE_�zuzMzuzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ½ å

Ñ]Ò�ÓOÔ�ÕZÖ�×7è év×4ÓGê�Ö�ë�Û±×Üì)í�îjï�ÔbÖ�ð�í�ñ�Ö�Õqð è±ò½ z â ?±BXLEd T'U @EBoW�f T r T fbzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ½Eó

½ z â z â ° P�Hn[qL � zuzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz åEô½ z â z ½ C1pOf T _-zMzuzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz å ½

½ z ½ R P YAT [ SOT @EB�P�f T r T f�zuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz åEã½ z ½ z â ° P�Hn[qL � zuzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz å ó½ z ½ z ½ C1pOf T _-zMzuzMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz æEô

½ z^å ° T [m[ SOT @�B�P�f T r T f�zMzuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz æEõ½ z^åEz â ¬ fI@E_opOB T pOHON T BwB Tt¤OT k'[nF^@EHO_m@EaVf^@EiEF^kZLEf`@ Y�T BXLt[qFI@�HO_¦zMzuzuzMz�zuz æEã½ z^åEz ½ |}HONOpGk9[nFxr T fsP�N T �OH T N�_ T [n_özuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz æE÷½ z^åEz^å Ã HGFsr T BX_ T _0zuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz ø ½

Ñ]Ò�ÓOÔ�ÕZÖ�×7ù î�×ÜÓOÚ�ðqà\Õqà\ÛAÚeðZï�ðqÕqÖ�ê�ð�í�à\Ú�ÕqÖ�×ÜÓOß�Õqà\ú±Ö�ðqï�ðZÕqÖ�ê�ð á±ûåEz â ��B T NOF^kZL�[ T _)r T BX_XpG_1acLEd]F^fIF T _�zMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz øE÷

åEz â z â ¾ ¶ pOLEf^Fs[}P zuzuzuzuzuzMzuzMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz øE÷åEz â z ½ ° TtY LEBXL�[nFxr T FI_m�^d{@�B T [ S L�H ��Y LEBoLEd T [qBXF^kZz±zMzuzuzMzuzMzuzuzMz�zuz õEååEz â z^å �)B T NOFIktLt[ T _ T HQ·9@�P�d]@EB T ktfI@E_opOB TuY Bo@ Y�T B�[qF T _ zMzuzMzuzuzMz�zuz õEååEz â z^æ |}HOktfIpO_oFI@�H�LEHON�@�r T BXf^L Y zMzuzuzMzuzMz�zuzMzuzuzMzuzMzuzuzMz�zuz õEæ

½

Page 10: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 12: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 13: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 14: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 15: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 17: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

R SOT BopOf T _vLEB T ktfILE_o_XF^� T NMFIHq[q@mf^@EiEF^kZL�f�BXpGf T _ YAT B\[nLEF^HOF^HOi�[n@�[ SGT rGL�BXF^@EpO_�f^@EiEF^kZLEfEkt@EHO_\[nLEHq[n_ohLEHGN�_�[qBXpOk'[npOBoLEf�BopOf T _Xz R SOT BXpOf T _�ac@EB T LEk S f^@EiEF^kZLEfAkZ@EHG_�[nL�Hn[�LEB T NOFxr`F^N T N�FIHq[n@�BXpOf T _�ac@�BF^Hq[nBX@�NOpOktFIHGi�[ S Lt[�kt@EHO_�[qLEHq[MFIHq[n@ Å L{ac@�BXd�pGfIL]@Ea Ð [ SGT L�Hn[ T k T N T Hn[�LEHON�ac@EB-FIHq[nBo@*NGpOkZF^HOiFx[%[q@u[ SGT _XpOktk T N T Hq[{@Ea�[ SOT kt@EHOkZf^pO_oFI@EH#_ TZ¶ p T Hn[qz R SOT _\[nBopOk9[qpOBXLEf�BXpGf T _ Å LE_o_XpOd Y [qFI@�HOh[ S FIHGHOFIHGiEh1kt@EHq[nBoLEk9[qFI@EHGh1LEHGN�F^Hq[ T BXk S LEHGi T Ð LEB T kt@EHOk T BXH T N U Fx[ S [ SOT DOpOB T LEpOktBXLEk'P²@Ea_ TZ¶ p T Hq[q_u[ SGT d]_ T fsr T _Xh UuS FIf T [ SOT B T d]LEF^HOF^HOi�_\[nBopOk9[qpOBXLEf-BXpOf T kZLEf^f T N��IktpQ[ � L�fIf^@ U _{ac@�B[ SOT�T f^FId]F^HOLt[nF^@EH�acBX@Ed [ SOT kt@EHOktfIpO_oFI@�H¨@EauLEH T Hq[nF^B T ac@EBod�pOf^L UuS F^k S @�kZkZpGBX_�FIH�[ SOTLEHq[ T k T N T Hq[�@Ea�@EH T @Ea�Fx[n_ Y B T d]F^_ T _XhgLEHONeacBo@Ed¥[ SOT _opOkZk T N T Hn[�@Ea�[ SGT @t[ SOT BXz R SOTkt@EHq[ T Hq[K@Ea J T Hq[qº T H � _ Ê�Ë:ë � È Ë4Ë�È�ò @EB�ktpQ[5T T f^F^d{F^HOLt[qFI@�H�[ SOT @EB T d FI_m[ S Lt[�[ SOT BopOf T @EaktpQ[MFI_wLEHKLENOd]F^_X_XF^DOf T BopOf T @�a±[ SOT _�P�_�[ T d�@Ea�BXpOf T _ U Fs[ S @EpQ[MktpQ[nzw?±BX@Ed [ S F^_Xh�L S @�_�[M@Eakt@EBX@Ef^f^LEBXF T _ ¤ @ U h�F^H�r`F^B�[qp T @Eav[ SOT kZBXpGkZF^LEf)_XpODOac@�BXd�pGfIL Y BX@ YAT B\[}P�@Eav[ SOT Å �GBX_�[7@EBoN T B Ð_\P`_\[ T d U Fs[ S @EpQ[1kZp4[nhE[ S L�[mFIH{LEHqP�N T BXFxrGL�[nF^@EH]@Ea�L�_ TZ¶ p T Hq[&�è ç]hE[ SGT @EHOfxP�ac@EBXdMpOf^LE_UuS F^k S @�kZktpOB]LEB T _opODOac@EBod�pOf^LE_{@Eag¨LEHON�ç]z Å ° TtT ac@EB T9� LEd Y f Ty¬ S L Y [ T BX_]æ�LEHON�ø@Ea&" â ôEø'$^z Ð R SOT [ T k S HO@Ef^@EitP�@Ea�HOLt[qpOBXLEfbN T NOpOk'[nF^@EH�_\P`_\[ T d{_MLEHON�_ Tt¶ p T Hq[�ktLEfIktpOf^F S LE_D T kt@Ed TMYAT B\rGL�_XFxr T [ S Bo@EpOi S @�pQ[ufI@�iEFIk�LEHGNykt@Ed Y pQ[ T Bw_XkZF T HGk T z� T [�LEHO@t[ SOT B�kZ@�Hn[qBXF^DOpQ[qFI@EH!@Ea�J T Hq[nº T H � _Xh�@Ea�d]@EB T NOF^B T k9[�B T f T r*LEHGk T [q@m[ SOT _opOD*· T k9[

@EaO[ S FI_V[ SOT _oFI_oh U LE_V[q@gfIL�pOHOk S [ SOT-UuS @�f T _opOD*· T k'[M@Eav@EBXNOF^HOLEfiT�[ SOT @EB T [nF^k Y BX@�@EaO[ SOT @EB�PEh@EB1�I@�BXNOF^HOLEf�LEHOLEfxP�_XF^_ � " ó ÷'$Ihs" ó ø%$Iz à HOf^F^W T J T Hq[nº T H � _j@t[ SOT B1kZ@EHq[nBoFIDGpQ[nF^@EHO_oh�[n@M[ SOT D T _\[@Ea�dmP�W�HO@ U f T NOi T [ S F^_�_XpOD*· T k9[ S LE_ S L�N�f^Fx[X[nf T F^d Y LEk9[{@EH�kt@Ed Y pQ[ T B�_XkZF T HGk T h�LEHON�F^_YAT B S L Y _!kZ@EHO_oFIN T B T N�[n@�D T Lt[yD T _�[�L S F^i S fxP�[ T k S HOFIktLEfm� T f^N U Fx[ S F^H0d]Lt[ SGT d]Lt[nF^kZL�ff^@EiEF^kZh�r T B�P�NOFI_\[nLEHq[]acBo@Ed�[ SGT d]@t[nFxr*Lt[nF^@EHO_1LEHONykZ@EHOk T BoHO_jacBX@Ed UuS FIk S Fx[~L�BX@E_ T zu­ T B T[ SOT ac@*ktpO_gFI_g@�H Y BX@�@Eac_g@EawL Y LEB�[qFIktpOf^LEBgW�FIHON�@Eaw_�[qLt[ T d T Hq[nh1HOLEd T fxP²_�[qLt[ T d T Hq[n_{@EaU%T f^fIac@�pOHON T NOH T _o_XzM|�_ S L�fIfvpO_opOLEf^fsP�B T _ T B�r T [ SOT [ T Bod � U%T f^f^ac@EpOHON T NOH T _X_ � ac@EB)[ SOTuY BX@ Y �T B�[}P�@Ea�L~DOF^HOLEB\P�B T f^Lt[nF^@EH�[ S Lt[jL�fIf Y @�FIHq[n_�FIH�[ SOT � T f^N�@EaG[ S L�[jB T fIL�[nF^@EH�LEB T LEktk T _o_XF^DOf T z¯1kZk T _X_oFIDOF^f^Fs[}P�@Ea`L Y @�FIHq[ È FI_�pO_XpGLEfIfxPyac@EBXdMpOf^Lt[ T N7_Xk SGT d]Lt[nF^kZL�fIfxP�F^Hu[ SOT ac@EBXd©@�a�[nBoLEHO_\��OHGFs[ T F^HONOpOk'[nF^@EH0@�r T B�[ SOT DOFIHGLEB�P�B T f^Lt[nF^@EH�óuh�p Y [n@�_X@�d TKY @EFIHq[ È FIH#[ SGT � T fIN³@Eaó�h U Fx[ S B T _ YAT k9[u[n@KLKacB TZT _ok SOT d]Lt[qFIk Y B T NOFIktLt[ T Æ z ü H T�U LlP#[q@ T'��Y B T _X_m[ S F^_MF^_�LE_ac@Ef^f^@ U _oz

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Á�P�L Y BX@�@Eab@Ea)_opOk S L�_�[nL�[ T d T Hn[!F^_jd T LEHq[{L Y Bo@*@�a�F^H7[ SGT fILEHGiEpOLEi T�T9� [ T HON T N U Fx[ SLgH T'U©Y B T NGFIktLt[ T kZ@�HO_�[qLEHq[ Æ h`pO_XF^HOi]HO@g_ YAT ktFIL�f�BXpOf T _ ac@�B Æ z ¯%kZk T _o_XF^DOFIf^Fx[}P�@�a�L Y @EF^Hq[F^_ Tt¶ pOFsr*LEf T Hq[1[n@ U�T fIf^ac@EpOHON T NOH T _X_j@Ea±[ SOT F^HOFx[nF^LEfv_ T i�d T Hq[g@Ea±[ SOT B T fIL�[nF^@EH�D T f^@ U [ S L�[Y @EF^Hn[-F^Hw[ SOT [qBXLEHG_XFx[nFxr T ktfI@�_XpOB T @EaÜ[ SOT B T fIL�[nF^@EH�øO_o@1|�d]L�P{_X@�d T [nF^d T _VB T a T B±[q@)[ SOT)Y @EF^Hq[Fx[n_ T f^a�LE_ U�T fIf^ac@EpOHGN T NOzy?±@EBji T H T BXL�f�B T LE_o@EHO_oh�LEHqP�_o@EpOHON�ac@EBXd]LEfb_\P�_�[ T d ac@EB U BXFx[nF^HOid]Lt[ SOT d]Lt[qFIktLEf Y Bo@*@�ac_ S LE_�L~_�[qBXF^k9[qfsP�fIF^d]Fs[ T N�kZL Y LEkZFx[}P{[n@~B T kZ@�iEHOF^_ T�U%T f^fIac@�pOHON T NOH T _o_XhF^H~[ SOT _ T HO_ T @�a YAT Bod]Fs[o[nF^HOi�[ SOT kt@EHO_\[nBXpGk9[nF^@EHK@Ea Y BX@�@Eac_�@�a�L�kZk T _X_oFIDOF^f^Fs[}P�ac@EB-HOLt[npGBXLEf^fsPLEBoFI_oFIHGi�HO@t[nL�[nF^@EHO_ Å _XpOk S LE_ ¬ LEHq[n@EB�HG@EBXd]LEf�ac@EBXd Ð ac@EB%kt@EpOHq[nLEDGf T @EBoNOF^HOLEf^_Xz~J T Hq[nº T H

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Page 18: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

_ S @ U%T N Å F^H|"xåEøl$ Ð [ S Lt[b[ SGT kZ@EHO_oFI_\[ T HOk9PK@Ea±�OBo_�[1@EBoN T B�L�BXFx[ S d T [qFIkwac@Ef^f^@ U%T N{DqP��OHGFs[qFI_\[nF^kB T LE_X@EHGFIHOiyacBX@Ed5[ SOT N T _ok T HGNOFIHGi�k S LEF^H Y BoFIHOktF Y f T ac@EB�[ SOT �OBX_\[�@�BXNOF^HOLEfbktfI@E_ T N�pGHON T B[ SOT @ YAT BoLt[nF^@EHO_]@Ea ¬ LEHq[n@EBd�1@EBXd]LEf ac@EBod]h%HOLEd T fsP ¬ LEHq[q@EB � _!�GBX_�[y� TZY _oFIf^@EH � H�pOdMD T B��� z�?ABo@Ed5[ S FI_MFs[�ac@EfIf^@ U�T N Å DqP³J�«@�N T f � _�_ T kt@EHON�F^HOkZ@�d Y f T [ T H T _X_%[ SOT @�B T d Ð [ S Lt[u[ SOTU�T fIf^ac@EpOHGN T NOH T _X_�@Ea ��� ktLEHOHO@�[{D TgY Bo@�r T N�F^H Å kZf^LE_X_oFIktLEfb@EBjF^Hn[qpOFx[nF^@EHOF^_�[nF^k Ð �OBo_�[!@EBoN T BH�pOd�D T B�[ SGT @EB\P�h±_X@�[ S Lt[�[ S FI_)@EBoNOFIHGLEf Å UuS @E_ T F^d Y @EB\[nLEHGk T S LEN]D TZT H!HO@�[nF^k T N]@�r T B S LEf^aL�k T Hn[qpOB�P Y B T r�FI@EpG_XfxP Ð B TZY B T _ T Hq[ T N�L�f^FId]Fx[]@EH7[ SGT LEDOF^fIFx[}P�@�ab_XpOk S L�_�P�_\[ T d [n@��^_ TtTFIHq[q@M[ SOT [nBoLEHO_o�OHOFx[ TZ� zr�%@t[�fI@�HOi7LEa¼[ T B U LEBoNO_ Å FIHù"så�õ%$ Ð J T Hq[nº T H�LEf^_X@ T _�[qLEDOf^FI_ SOT N7[ S Lt[[ S F^_�fIF^d]Fs[!F^_�D T _�[ Y @�_X_XF^DOf T h)F^H�[ SOT _ T HG_ T [ S Lt[j[ SOT�U�T fIf^ac@EpOHGN T NOH T _X_M@Ea�HO@t[nL�[nF^@EHO_jF^H¬ LEHq[n@EBmHO@EBod]LEf�ac@EBXd5kZLEHyD T _�P�_\[ T d]Lt[qFIktLEf^fsP T _\[nLEDOf^F^_ SOT N U Fs[ S�Y Bo@*@�ac_ T'��Y B T _X_XF^DOf T F^H�OBX_\[u@EBXN T B�LEBoFs[ S d T [qFIktz Å R S F^_ FI_ L~d]@�N T BoH~[nB T Lt[nd T Hn[uF^H�k S L Y [ T B â ôg@Eay" â ôEø%$^z Ð ° F^HOk T[ SOT HOh�@EBoNOF^HOLEf�[ SOT @EB T [nF^k Y BX@�@Ea�[ SOT @�B�P S LE_�D TZT H�kZ@EHGk T BoH T N U Fx[ S7UuS L�[]Fs[~FI_1LEDA@EpQ[gL_�P�_�[ T d ac@EB U BXFx[nF^HOimd]Lt[ SOT d]Lt[nF^kZLEf Y Bo@*@�ac_G[ S Lt[�N T [ T BXd]FIH T _VFx[n_�kZL Y LEkZFx[}P{ac@EB T'�`Y B T _o_XF^HOiY BX@�@Eac_!@Ea U%T f^fIac@EpGHON T NGH T _o_Xz¹­%LEHGNeFIH S LEHON U Fx[ S [ S FI_ S LE_�i�@EH T [ SOT F^Hqr T Hn[qFI@�H�@�a@EBXNGFIHOL�fbHO@t[nL�[nF^@EH�_�P�_�[ T d]_ U Fx[ S�UuS F^k S [q@KN T _XktBXF^D T{T r T Bud]@EB T acLEB`T ¤ pGHOi�B T i�FI@EHG_u@�a[ SOT _ T kt@EHON{H�pGd�D T B)kZf^LE_X_)F^H UuS FIk S [ SGT fIF^d]Fs[q_�@�aAd]@EB T Y @ U%T BoacpOf�_�P�_�[ T d]_�LEB T f^@�kZLt[ T NOz pOf^f U @EpGfIN SOT D T @Ea�_o@EpOf YAT B S L Y _Xh UuS @³NGFIN�HO@t[��OHGN»_o@Ed T [ S FIHOi³d]LEB�r T f^@EpO_ Å F^aNOF^¿{ktpOfx[~[n@ Y F^H�NO@ U H Ð L�D�@Ep4[M[ SOT kt@EHOH T k9[qFI@EHG_~D T [ U�TtT H�f^@EiEF^k7LEHGN�LEBoFs[ S d T [nF^ku[ S Lt[S L�r T _o@�acLEBuD TZT HK[nBXL�k T NGz ü H�[ SOT @t[ SOT B S LEHONOh�[ SOT{¶ p T _�[qFI@�H�kZLEH�D T BXLEF^_ T N çMUuS Lt[S LE_g[ S F^_g[n@�NO@ U Fx[ S�Y Bo@EiEBXL�d{d]F^HOiEh~@�BKkt@Ed Y pQ[ T BK_XkZF T HGk T ¡ R SOT�¶ p T _�[qFI@EH¨FI_�acLEBacBX@Ed B SOT [q@EBXF^kZLEf^h�F^H�r�F T'U @�a�[ SOT kZ@EHOH T k9[qFI@�H�D T [ U�TtT H Y BX@�@Eac_MLEHON Y Bo@EiEBoLEd]_�F^Hy[ SOTL YOY B T ktFILt[qFI@�H{@�a UuS FIk S J T Hq[nº T H � _�ac@�BXd�pGfILt[qFI@�Hg@Ea±HOLt[npGBXLEf*N T NOpGk9[nF^@EH Y f^L�P T N{LjkZBopOkZF^LEfBZú@Ef T z

J T Hq[qº T H � _~F^HO_\[nF^iELt[nF^@EH�@�a�@EBXNGFIHOL�fv[ SOT @EB T [qFIk Y BX@�@Ea�[ SOT @EB\P Å FIHK[ SOT _ T [o[nF^HOi�@Ea-_ T �¶ p T Hq[ukZL�fIktpOfIF`ac@EB-�OBo_�[�@�BXN T B�LEBXFx[ S d T [nF^k Ð U LE_ _o@*@EH7ac@EfIf^@ U�T N�DnP�LEHO@�[ SOT B�kZ@EHG_XF^_�[ T HOk9PY BX@�@Ea�ac@�B!ktfILE_o_XF^kZLEfm�OBo_�[#@�BXN T B7LEBoFs[ S d T [nF^k�i�Fsr T H0DqP¨¯%klW T BXd]LEHOHû" ½ $^hjDqP¨d T LEHO_7@�a[ SOT N T _Xk T HONOF^HOi�k S LEF^H Y BXF^HOkZF Y f T ac@EB�[ SGT _oLEd T @EBoNOF^HOLEf^z¨¯%klW T Bod{L�HOH � _�kZ@EHG_XF^_�[ T HOk9PY BX@�@Ea�pO_ T N�L�ac@EBXdMpOfIL�[nF^@EH²@Ea�kZf^LE_X_oFIktLEfjLEBXFx[ S d T [nF^k T9��Y f^@EFx[nF^HOi³­1FIf^D T B�[ � _�_o@�T�kZLEf^f T Nü Tu_\P`dMD�@�fIh�@�Bu�^k S @EF^k Tt� @ Y�T BXLt[q@EB ü�ýÿþ ü � ç ý Å � Ð h UuSGT B T ý Å � Ð F^_ML Y B T NOF^kZLt[ T!T'� �Y B T _X_oFI@EH U Fx[ S LMNOF^_�[nF^HOiEpGFI_ SOT N�LEBoiEpOd T Hq[jF^HONOF^kZL�[ T N�DqP{[ SOT r*LEBXF^LEDOf T � [ S Lt[�F^_�DA@EpOHONDqP�[ SOTjS F^i SOT B©T�@EBXN T Bm@ Y�T BXLt[q@EB ü z R SOT [ T BXd üOý _�[nL�HONO_mac@EB LEH�@ED*· T k9[M@Ea UuS FIk S [ SOTY B T NOF^kZLt[ T�S @Ef^NO_uFIa�Fx[ S @EfING_Mac@EBuLEHqP³@ED*· T k9[�L�[�LEf^f^z R S FI_M@ YAT BXL�[n@EBukZLEH�[nLEW T @EH�[ SOTBZú@Ef T�Y f^LlP T NyDnP�[ SOT �OBX_\[M@EBXN T B ¶ pOLEHq[nF^� T Bo_Xh�DqP�d T LEHO_m@Ea�[ SOT�Tt¶ pGFsr*LEf T HOk T _

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Page 19: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

[ S Lt[ UuS Lt[7B T d{L�FIHO_uLEB T [qBXp T{¶ pOLEHq[nF^� T BuacB TtT _\[nLt[ T d T Hq[q_ Å [ S pO_ T _�[nL�DOfIF^_ S FIHOi�kZ@EHO_oFI_\�[ T HOk'P Ð z ü BXNOF^HOLEf^_bLEB T pO_ T N�[q@ T _�[qLEDOf^FI_ S [ S Lt[�[ SOT Y Bo@*k T _X_)@Ea±B TZY f^LEk T d T Hq[)[ T Bod]FIHOL�[ T _oz¯1klW T Bod]LEHOH � _�d T [ S @�NO_ U�T B T _ ¶ pOLEB T fxP�F^H�[ SOT [nBoLENOFx[nF^@EH�@Ea)­%F^fID T B\[ � _ Í�Ç`ÎmÇ`�xË4È�ÇAÇlÎZÉ¡�9Ç z¯1klW T Bod]LEHOH � _ U @EBoW U LE_~_opODO_ Tt¶ p T Hq[nfxP�kZf^LEBoFI� T N�DnP R LEFs[ Å " â ôEå'$ Ð LEHGN�N T r T f^@ YAT N�DnP·�B T FI_ T f Å "xøEõ%$^h�"sø�ã%$ Ð FIHq[q@ S FI_ Ì�Î T ÍlÎ:ë�Ì�ȵÇXÉtÇ � Ë ÆÒ� È Ç��cÌ�È�ÇXÉ � ÉZÇnÈ�Ë�È �9ÎZÌ @Ea ktfILE_o_XF^kZLEf�LEBXFx[ S �d T [qFIktz»|}H�[ S F^_]FIHq[ T B Y B T [qLt[nF^@EHOh1BX@EpGi S fxP�_ YAT LEW�F^HOiEh%L Y Bo@*@Eam@Eam�OBX_\[y@EBXN T B]kZf^LE_X_oFIktLEfLEBoFs[ S d T [qFIkgF^_jFIHq[ T B Y B T [ T N�LE_jL�k T B�[qLEFIH T! �T k9[qFsr T acpOHGk9[nF^@EHOL�fVd]L YOY F^HOi��OHOFx[ T fsP�d{L�HnP�OBo_�[~@EBXN T B%H�pOd T BoFIktLEf�acpOHGk9[nF^@EHO_�[n@7H�pOdMD T BX_oz Å R S L�[gF^_XhA[ SOT acpGHOk9[qFI@EHGLEfVF^_%@EaV_ T kt@EHON@EBoN T Boz Ð |}H�Lyf^@*@�_ T _ T HG_ T h�[ S F^_�kt@EHO_�[qFs[qpQ[ T _�LEH�FIHq[ T B Y B T [qLt[nF^@EH�@�a-_XpGk S L Y Bo@*@�a-LE_uL[ T BXd]F^HOLt[qFIHOi Y BX@Ei�BXLEd®ac@EB�B T _ Y @EHONOF^HOi%[q@�L�_\[nB T LEd¹@Ea�kt@EHOktB T [ T NOLt[qLm[q@EW T HO_ U Fx[ S LEH4�@t[ SOT B)_opOk S [q@EW T HOh�d]@�NOpOf^@�_X@Ed T kZ@�NOFIHGiEz R S F^_�d{L�PKLEf^_X@�D T [ S @EpGi S [%@�a�LE_)L�_�[qBXLt[ T itPÅ UuS FIk S kZLEHKD T F^d Y f T d T Hq[ T NOhA[ S @EpOi S Fx[~d]L�P�HO@t[MD T a T LE_XF^DOf T [q@!pG_ T [ SOT F^d Y f T d T HQ�[qLt[nF^@EH Ð ac@EB U F^HOHOF^HOi�L�kt@EHq[ T _\[{LEiELEF^HO_\[g_X@�d T @EH T%UuS @7kZ@EHq[ T HONO_-[ S Lt[%[ SOT acpOHGk9[nF^@EHOL�fF^_1pGHON T �GH T Nyac@EBwL{k T B\[nLEF^H�LEBoiEpOd T Hq[M@Ea UuS FIk SySOT FI_ Y B TZY LEB T Ng[n@{_Xp YGY fsP�L�BXDOFx[nBoLEBXF^fsPf^@EHOiKFIHGFs[qFILEfV_ T i�d T Hq[n_Xzy|´[!d{L�P�D T�U @�B�[ S HO@t[qFIHGig[ S Lt[ Ë�ÈxÈ Y BX@�@Eac_j@Ea�kZf^LE_X_oFIktLEf)LEBXFx[ S �d T [qFIk L�B T F^Hn[ T B Y B T [ T N{F^H%[ S F^_ U L�PEhAHG@t[�·9pO_\[ Y BX@�@Eac_�@Ea U%T f^fIac@�pOHON T NOH T _o_Xzg�%@t[ @EHOfxP�LEB T[ SOT acpOHOk'[nF^@EHOLEf^_jkZ@�Hn[qFIH�pO@�pO_ Å kt@EHO_XF^N T B T N�LE_%acpOHOk9[qFI@�HO_�acBX@�d Á�L�FIB T _ Y L�k T [q@M[ SOT NOFI_\�ktB T [ T _ Y LEk T @Ea`HGLt[npOBoLEf±H�pOd�D T Bo_ Ð h�DOpQ[�[ SOT PKkZLEH!D T kZ@�N T N7DnP U%T f^fIac@�pOHON T NM[nB TZT _ Å [ SOTHO@�N T _1D T F^HOi7H T F^i S D�@EpGB S @�@*NG_)[ S BX@EpGi S @EpQ[ UuS F^k S [ SOT r*LEf^p T @EaVL{iEFxr T H�acpOHOk'[nF^@EHOLEfvF^_HO@�[�N T [ T BXd]F^H T N Ð UuS @E_ T N TZY [ S F^_wD�@EpGHON T NyDqP�[ SOT @EBoNOF^HOLEf ��� z

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Page 20: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

° k S «pQ[o[ T LEHGNgª�@�B T HGº T H]_oFId Y f^FI� T N�[ SOT Y BX@EDOf T d�@Ea�ktpQ[5T T f^FId]F^HOLt[qFI@EH{ac@EB�ac@EBXd]LEf Y BX@�@Eac_FIHqrO@Efsr�F^HOi�F^HONOpOk'[nF^@EH Y BoFIHGkZF Y f T _�DqP T: AT k'[nFxr T fsP§B TtY B T _ T Hq[qFIHOi#_opOk S�Y BX@�@Eac_�DnP³F^HO�OHOFx[ TU�T fIf^ac@EpOHGN T N![qB TtT _Xz R LEFs[MF^Hù" â ôEå'$�_ S @ U%T N S @ U @EH T d]FIi S [�pO_ T F^HO�OHOFx[ T È�ÇXÉ Æ Ë [q@!iEFxr TLEH�@EBoNOF^HOLEfiT [ SOT @EB T [qFIk1LEHOLEfxP�_XF^_�@Ea*[ SOT [ T BXd]_�@Ea�J7«@EN T f � _ R z R S FI_-FI_�LEH T LEBXfxP T9� LEd Y f T@Ea T'�`Y fI@EFx[nF^HOi![ SOT Å _X@�T�kZL�fIf T N Ð ¬ pOBXB\P§­1@ U LEBoN�kZ@�BXB T _ Y @EHON T HOk T [q@][qBXLEHG_Xa T BMLEH�F^N T LacBX@Ed�L�_�P�_\[ T d¹@Ea�BXpOf T _�ac@EB)F^HOa T BoBXF^HOi�_\[nLt[ T d T Hq[n_ Å U Fx[ S B T NGpOk9[qFI@EH7_�[ TtY _-ac@�B T f^FId]F^HOLt[X�FIHGijkZpQ[q_XhQ[q@�L�_�P�_\[ T d@Ea�BXpGf T _�ac@EBVkt@EHO_\[nBXpGk9[nF^HOijacpOHGk9[nF^@EHOL�fI_ Å U Fs[ S B T NOpOk9[qFI@�H{_\[ TtY _�ac@EBkZ@Ed Y p4[nF^HOi�[ SOT FIB)r*LEfIp T _ Ð z ° k S «p4[X[ Tt� _%FIHqr T Hq[nF^@EH�LEBX@E_ T F^H![ SGT kZ@�Hn[ T9� [{@Ea S FI_1LEHOLEfxP�_XF^_@Ea�_\P`_\[ T d{_ DGLE_ T N�@EHu[ SOT BXLEd]F^� T N�acBoLEiEd T Hq[�@Ea��)BXF^HOkZF Y F^L~¢�Lt[ SOT d]Lt[qFIktLEh`F^HOkt@EB Y @EBXL�[X�FIHGi�LKk T B\[nLEF^H Ë:ë`ȵÎZÌ�Î Æ Ì Y BXF^HOkZF Y f T7Y Bo@�r`F^NOF^HOi�ac@EB�[qBXLEHO_o�OHOFx[ T BXLEd]F^�OkZLt[qFI@�HO_`ø _oFId]F^fILEB_�[qpONOF T _ U%T B T pOHON T B�[qLEW T H#DqP�? T a T BXd]LEHGzj¯%H�F^d Y BX@�r T d T Hq[{@Ea�@Ea R LEFs[ � _md T [ S @*N U LE_iEFxr T H�DqP²¢�LEB\[nF^H�T�ª-«@�a1F^Hõ"xõEæl$Iz0¯1HO@t[ SOT B U L�P�@Ea T9��Y f^@EFs[qFIHGi�_ T d]F T�ac@EBod{L�f _�P�_�[ T d]_Å U Fx[ S F^HO�OHOFx[nL�B�PeBopOf T _ Ð [n@#LEHOL�fsP�_ T kZ@Ed Y pQ[qLt[nF^@EHO_g@�a J�«@EN T f � _1[ T Bod{_ S LEN�LEf^_X@#D TZT HN T d]@EHG_�[nBoLt[ T N�DqP ° L�HOk S F^_�"s÷�ø'$^z ° LEHOk S F^_ � L YOY Bo@ELEk SMU LE_�N T r T fI@ Y�T N�acpOB�[ SOT B�DnP  F^fIf T B" ½ ø%$bLEHON�­%@ U LEBXN�FIHâ"søEôl$Iz ° @Ed T d]@*N T BXH�N T r T f^@ Y d T Hq[n_�LEB T DqP ° k SqU FIk S [ T H�D T BXi#F^H"s÷�ã%$Iz|´[jd{L�P�D T acLEF^B�[q@{_oL�P7[ S Lt[�[ SGT FIN T L]Lt[ U @EBXW Å _XpODGfIF^d]FIHOL�fIfxP Ð F^H~[ SOT N T r T fI@ Y d T Hq[

@Ea�acpOHGk9[nF^@EHOL�fAF^Hq[ T B Y B T [nL�[nF^@EHO_Xh�LEHON!FIH�[ SOT LEHOLEfxP�_XF^_-@Ea*[ SOT kZ@Ed Y pQ[qLt[nF^@EHO_�@Ea�[ SOT acpGHOk9�[nF^@EHOLEf^_1[ S Lt[�LEBoFI_ T FI_m[ SOT F^N T L7[ S Lt[ Y BX@EiEBoLEd]_~LEB T FId Y f^F^kZFx[KFIH Y Bo@*@�ac_Xh DOpQ[ S L�r T [n@D TmT9� [qBXLEk'[ T N�acBo@Ed¨[ SGT d®DqPy_X@Ed T d]@EB T @�B�f T _o_�FIHGi T HOF^@EpO_�d T [nL%Tud]Lt[ SOT d]Lt[qFIktLEf Y BX@t�k T _X_Xh�HO@EH�T�_�[qLEHONOL�BXN�B T F^Hn[ T B Y B T [nLt[qFI@EHGhV@EBwpOH U F^HONOF^HOiEz R SOT BoLt[ SGT BmD�@Ef^N�_\[ TtY Å DOL�klW Ð[n@b[ SOT�Y Bo@ Y @�_XLEf Å @�ao·�@Ef^d{@�iE@EBX@ �� _ Ð [ S Lt[�@EH T kt@EpOf^N�LEk'[npOLEf^fxPj[ S F^HOW�@Ea Y BX@�@Eac_vLE_O[ SOT dj�_ T fsr T _ Å U Fx[ S @�pQ[�LEHqPeNGFI_ T d�DA@ U�T fIf^F^HOi Ð L�W�FIHGN�@�a Y BX@Ei�BXLEd]h U LE_%[nL�W T H�DqP0­%@ U L�BXNOhDOpQ[MLEBo@E_ T acBX@�d5LdÆ �2È �9Ç`ë0Å @Ea Y�T @ Y f T F^H�kZf^@E_ T kZ@�Hn[qLEk9[ Ð FIHqr�@�fsr�F^HOi7LEf^_X@ R LEFs[qh��)BXL U Fx[nºZh¢�LEB\[nF^H�Tuª�«@Each ° kt@t[X[qhw·�B T FI_ T f^hVJu@*@�NOd]LEHKLEHON�J7«@EN T fIz Å J�«@�N T fvLEHON�·�B T F^_ T f U%T B T r T B�P_Xk TZY [qFIktLEfIz Ð ­%@ U LEBXN]F^Hz"sæE÷'$GiEFxr T _�L Y B T _ T Hq[nL�[nF^@EH]@EaE[ SOT�Y BX@�@Eac_�F^HgFIHq[npGFs[qFI@EHGFI_\[nF^kmL�BXFx[ S �d T [nF^k{FIH�HOLt[qpOBXLEfVN T NOpGk9[nF^@EH�ac@EBXd L�_uL�_\P`_\[ T d @�av[}P YAT NK[ T Bod{_oh U Fx[ S kZ@�d Y pQ[nLt[qFI@�HBXpOf T _mac@EBV[ SOT [ T Bod]_1F^Hykt@EBXB T _ Y @EHGN T HOk TmU Fx[ S HO@EBod{L�fIF^_XLt[qFI@�H�BXpGf T _mac@�Bmac@�BXd]LEf Y Bo@*@�ac_XzR SOT F^d Y fIF^kZL�[nF^@EHO_�@Ea�[ SOT-¬ pGBXB�P7­%@ U LEBXNgL�HOLEf^@EitP{D T [ U%TZT H Y Bo@EiEBoLEd kZLEf^kZpOf^FGL�HON Y Bo@*@Ea_�P�_�[ T d]_~D T iEL�H�[q@yD T L YOY B T kZF^Lt[ T N�LEHGN T'�`Y fI@EFx[ T N�F^H Y Bo@*@�av[ SOT @EB\P�h�ac@EB T9� LEd Y f T DqP[nBoLEHO_Xa T BXBoFIHOiKLEHON T9� [ T HONOF^HOi R LEFx[ � _�HO@EBXd]LEf^F^_XLt[qFI@EH�B T _XpOfx[n_Mac@EB-[ SGT [ T Bod{_u@Ea�J�«@�N T f � _R [q@�_�P�_�[ T d]_�@Ea)iEB T Lt[ T B T'�`Y B T _o_XFxr T L�HON Y BX@�@Ea�[ SOT @EB T [nF^k]_�[nB T HOi�[ S z R SOT _opODO_�[qLEHOk T@Ea�[ SOTy¬ pGBXB�P.T�­%@ U LEBXNekt@EBXB T _ Y @EHON T HOk T#S LEN§L�fI_o@�D TZT H³NOF^_XkZ@�r T B T N²FIH³N T Á�BopOFx·9H � _¯%pQ[q@Ed]Lt[ S�Y Bo@Q· T k'[nh~F^HON TtY�T HON T Hq[qfsP�@Ea [ SOT�Y Bo@*@Ea [ SGT @EB T [nF^k�[nBoLENOFx[nF^@EH Å DOpQ[�HO@t[�@�a­ T P�[qFIHGi � _ T9��Y f^LEHOL�[nF^@EH�@Ea�[ SGT F^Hq[npOFx[nF^@EHOF^_�[qFIkud T LEHGFIHOi�_1@Ea�[ SGT f^@EiEF^kZL�f�kZ@EHG_�[nL�Hn[q_ Ð z

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Page 21: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 22: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 23: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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° F^HOk T [ SOT ãEô � _Xh`[ SOT~Y Bo@*@Ea�[ SOT @EB T [qFIktLEf�LEHOL�fsP�_XF^_�@Ea)¢�LEB\[nF^H�Tuª�«@Ea�[}P Y�T [ SOT @�B�P S LE_D TZT H Y pO_ SOT N!kt@EHO_oFIN T BXLEDGfsP�acpGB�[ SGT BbF^Hjr*LEBoFI@�pO_ Y pODGfIF^kZLt[qFI@�HO_)DnP ° T [qº T BÒ"x÷ ó $Ih�" â ôEôl$\"s÷�÷'$^hCmLt[ S · T H�"s÷�ô'$\" óEó $^h��VL�fId]iEB T H�" ó�½ $Ih�L�HONgJMBoF @EBQ"x÷ â $Iz�?±@EB±[ SOT d]@E_\[ Y LEB\[nhQ[ S FI_ S LE_bkZ@EH4�_oFI_\[ T N!FIH�[ SOT [nB T Lt[nd T Hn[1@EaA_�[qBX@EHGi T B)ac@EBod{_b@�a�pOHGFsr T BX_ T kt@EHO_�[qBXpOk'[nF^@EHj[ S LEHj[ S @E_ T @EBoFIit�F^HOLEf^fsP�F^Hq[nBo@*NOpGk T N�DnP�¢�LEB�[qFIH�T�ª�«@Eacz�Cm@EpOi S fsP�_ Y�T LEW�FIHOi�h±[ SOT d T [ S @�NO_ T d Y f^@lP T N#pO_ TdMpQ[npOL�f*F^Hq[ T B Y B T [nLt[qFI@�HO_V@Ea4[}P YAT [ SOT @�BXF T _VF^H Å kZf^LE_X_oFIktLEf Ð _�P�_\[ T d]_b@Eaq·�BXF Y W T Tu�)f^Lt[ T W�_ T [[ SOT @EB\P T'� [ T HGN T N]DqP�L � F^@Ed]_�LE_o_ T B\[nF^HOi-[ SGT�T9� F^_�[ T HOk T @Ea�f^LEBoi T ktLEBXNOF^HOLEf^_Xz R SOT _�P�_\[ T d]_@Ea�·�BXF Y W T Tu�)f^Lt[ T Wg_ T [�[ SOT @�B�P�LEB T LEHOLEfxP�_ T N!DqP�@t[ SOT Bbd T LEHO_Xh±pO_oFIHGiM_o@ YOS F^_�[qFIktLt[ T N7N T �r T f^@ Y d T Hq[n_wF^HM[ SGT%Y Bo@*@Ea�[ SOT @EB�P�@Ea�F^HO�OHOFx[nL�B�P�_�P�_�[ T d]_ NOp T [q@�Á�«pOk S @Efs[qº%LEHGN��V@ S f T BX_Å fI@�kZLEf Y B T NOFIktLt[nFxr�Fs[}P Ð h�L�HON�FIH~[ SGTuY BXF^HOkZF Y f T _wpOHON T BXfxP�FIHOi�[ SOT kt@EHO_\[nBXpGk9[nF^@EHK@Ea�@EBXNOF^HOLEfHO@�[nLt[qFI@EH�_\P`_\[ T d{_oz

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Page 24: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

FIkt_ kZ@EpGfIN�D T kZ@�HO_XF^N T B T NKLE_�[}P YAT _�P�_�[ T d]_wac@EB Y Bo@EiEBoLEd]d{F^HOigf^LEHOiEpGLEi T _oz R SOT r�F T'U @�a[}P Y�T _�P�_�[ T d]_�LEN4rGL�HOk T N�FIH�[ S FI_ Y L YAT B�FI_uBXL�NOFIktLEf^fsP�NOF AT B T Hq[�acBX@�dÿ[ S @�_ T{Y B T rGL�FIf^FIHGiFIH�kt@Ed Y pQ[ T Bj_XktF T HOk T z R SOT]Y B T r*LEFIf^F^HOi~r`F T9U F^_ Y�T B S L Y _ [ S Lt[�[ SOTgY pOB Y @�_ T @Ea)L�[}P Y�T_�P�_�[ T d¹F^_�[q@ Y B T r T Hq[ Y BX@EiEBoLEd]_)�IiE@�FIHOi U Bo@EHOi � " ât½ $^z�|}H{kZ@EHq[nBoLE_�[qh±¢�LEB�[qFIH�Tuª�«@Ea � _�[}P Y�T_�P�_�[ T d]_ U%T B T N T _XF^iEH T N0_X@�[ S L�[ Å HO@t[y@EHOfxP�_ S @EpOf^N Y Bo@EiEBXL�d{_]HO@�[��^iE@ U BX@�HOi � h%DOpQ[LEf^_X@ Ð LEHqP�kZ@Ed Y pQ[qLt[nF^@EH T r�@EW T N�DqP�L U%T f^f T�[}P Y�T N Y BX@EiEBoLEd _ S @EpOf^N![ T BXd]FIHGLt[ T hV@EBwF^H@t[ SGT B U @�BXNO_b[n@ T HG_XpOB T [ S Lt[ Y Bo@EiEBXL�d{_w_ S @EpOf^Ny�^iE@{BXF^i S [ � z

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Page 25: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 28: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 29: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 30: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 31: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 32: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 33: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

ªvLt[ T Bbk S L Y [ T Bo_)LEB T kt@EHOk T BXH T N U Fx[ S [qBXLEHO_oFs[qFI@�H{_\[nBopOk9[qpOB T _�L�HON]FIHq[ T BXLEk'[nFxr T _�[qBXpOk'[npOB T _@EH�L�_ T [nhV@�BXNOF^HOLEf�HO@t[qLt[nF^@EH�_\P`_\[ T d{_ohbLEHON Y BX@�@Eac_%@EaVLEkZk T _X_oFIDGFIf^Fs[}P�@Ea`[ S @�_ T HO@�[nLt[qFI@EHG_F^H�L Y LEB\[nF^kZpOf^LEBv[}P YAT [ SGT @EB\P�z R SOT _ T LEB T @EBoNOFIHGLEB�P�d]Lt[ SOT d]Lt[nF^kZLEf�HO@t[qFI@EHG_�@Ea�HO@~i�B T L�[_o@ YOS F^_�[qFIktLt[nF^@EHOz²­%@ U%T r T BXhj| S L�r T LEF^d T N�Lt[KkZ@EHG_�[nBopOk9[qFI@�HO_ U Fx[ S L�kZf T LEB]kt@Ed Y pQ[nL��[qFI@EHGLEfIh�LEHON#pOfx[nF^d]Lt[ T fsP Y BXL�k9[nF^kZL�fVd T LEHGFIHOi�z~|}H Y pOBo_XpOFx[{@Ea`[ S Lt[nh�| S L�r T pO_ T N�@EH![ SOTd T [qL7f T r T f Y BXF^HOkZF Y f T _%@�a�d]@EB T @EBwf T _X_)[ SOT _XLEd T W�F^HON�L�_1LEB T ac@�BXd]LEf^FI_ T N�F^H{[ SOT [}P YAT[ SOT @EB\P�D T FIHGi7kZ@�HO_XF^N T B T NOzj?±Bo@Ed5L!d{L�[ SOT d{L�[nF^kZLEf Y @EFIHq[M@Ea±r`F T9U [ S F^_1d]L�P�D TuT ktk T HQ�[qBXF^kZh�kZ@�d Y LEB T N U Fx[ S pO_oFIHGiM_ T [5T�[ SGT @EB T [nF^kwLEDO_\[nBXL�k9[nF^@EHO_oz�|´[m_ TtT d]_ ¶ pOFs[ T HOLt[npGBXLEf*acBX@EdL Y Bo@EiEBXL�d{d]F^HOi Y @EF^Hq[M@Ea±r�F T9U z

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Page 34: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 35: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

B�«Zª �|²~­�� F�J ³�²~° � FKDGFG�

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ý ç��?�f ¢¡ Ë ç ãè ý

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Page 36: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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ü [ SOT B)k S @EF^k T _-ac@EB)LupOHOFxr T BX_XL�f�ktLt[ T iE@EB�PKL�B TwY @�_X_XF^DOf T�UuS F^k S d]L�PyD T _oFId Y f T B Å LEHONf T _X_1_ T HG_XFx[nFxr T [n@j[ SGT _opODQ[nf T F^_X_op T _ Y�T kZpOf^FIL�B�[n@j[}P Y�T [ SOT @EB�P�_opOBXBo@EpOHONGFIHOiu[ SOT HO@t[qFI@EH@Ea TZ¶ pOLEf^Fs[}P�F^H�Fs[q_ r*LEBoFI@�pO_�d{L�HOFIa T _�[qLt[nF^@EHO_ Ð z�|}H Y LEB�[qFIktpOfIL�BXh)FIHG_�[ T LEN�@Eav[ SOT kZLt[ T iE@�B�P@Ea�acLEd]FIf^F T _ ( Å ¯ ç 9 ÇnÈ Ð�¯ è 9 ÇnÈ h U�T d]L�P�[nLEW T Å [n@]L]�OBX_\[ML YOY Bo@ � F^d]Lt[nF^@EH Ð

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Page 37: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

R SOT _ T _XpOiEi T _�[qFI@�HO_vac@EB�L �IpGHOFsr T Bo_XLEf � kZLt[ T iE@EB\PgN T [ T BXd]FIH T Æ ÇnÈ�Ë Æ Ë�È�ÇAÇ Æ Ë�È �9ÍlË�È d]@*N4�T fI_oh�F^H UuS F^k S [ SOT ·9pONOiEd T Hq[q_-LEB T F^Hq[ T B Y B T [ T N�LE_ Y BX@ Y @E_oFs[qFI@�HO_�L�D�@Ep4[%Lud]Lt[ SGT d]Lt[nF^kZL�f_\[nBXpGk9[npGB T z R SOT _ T d]LlP�ac@EB T9� LEd Y f T D TMT9��Y B T _X_ T N�F^H![ SOT fILEHGiEpOLEi T @EañÉ�?ñT�_�[}P�f T _ T [[ SOT @EB\P�hw_ T B�r�F^HOi�LE_~L��^H T p4[nBXL�f � È �cÌ ² ë`Ë < ÉZËZÌ�ÍlË z�Á T _oFIN T _]d{@�N T fI_~@�ab[ S F^_~W�FIHONGhb[ SOT B TLEB T d]@�N T f^_~F^H UuS F^k S [ SGT pOHON T �OH T N�kZ@EHG_�[nL�Hn[q_~LEHON Y BXF^d]Fs[qFsr T BXpGf T _�@Ea�@�H T _\P`_\[ T dLEB T [qBXLEHO_ofIL�[ T N�F^Hq[n@![ SOT�T'�`Y B T _o_XF^@EHO_gLEHGN�N T BoFsr T N�BXpGf T _g@Ea�L�d T [qLEf^LEHOiEpOL�i T h UuS FIk Sd]L�P S L�r T [}P YAT [ SOT @EB T [nF^kZLEf�·9pGNOi T d T Hn[!ac@EBod]_XhbBXL�[ SOT B-[ S LEH7[qBXpQ[ S @Ea)L Y BX@ Y @E_oFs[qFI@EHGhLE_ U Fx[ S É�?�_ T [1[ SOT @�B�P�z R SOT [qLEBXi T [Mac@EB�[ SOT [nBoLEHO_ofILt[qFI@�H�d]L�P�D T L�[}P YAT [ SOT @EB\P�[ S L�[@EH T L�k9[npGLEfIfxPKpO_ T _�LEHON{NOFIB T k'[nfxPKpOHON T BX_�[qLEHONO_oz ü aAkZ@�pOBX_ T hAH T Fx[ SOT B�W�F^HON{@Ea`d T [qLEd]Lt[ S �T d{L�[nF^kZLEf�d]@�N T f�kZLEH�_ T B\r T [n@gDOBoFIHGigLED�@�pQ[j_opOk S L�NOFIB T k'[upOHON T BX_�[qLEHONOF^HOiEh�DGpQ[�@EH�[ SOTkt@EHq[nBXL�B�P Y B T _op YOY @E_ T _%_XpGk S L{NOFIB T k'[nfxP�pOHON T BX_�[q@*@�N�d T [nL�fILEHGiEpOLEi T z

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Page 38: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

Å\Ð h Å �æ ý Ð kZ@EHq[ T9� [n_Å\Ð � h Å ¬ æ Ë�ÐÀ¿ �nÁ ¹à _XpODG_�[nFx[np4[nF^@EHO_Ä · �$¬ h â � kZLt[ T iE@�BXF^kZLEf�_\[nBXpGk9[npGB Tý · �$¬ h Ë · �Q¬ h acpOHOk'[n@EBoFILEf�_\[nBopOk9[qpOB T

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[ SOT @EB�P Å UuS FIk S @*ktkZpOB�FIH ý LEHON Ë Y @E_oFs[qFI@�H Ð pO_oFIHGi [ SOT _ T F^HOiEB T NOF T Hq[n_oz R SOT T9��Y B T _X_oFI@�HO_DOpOF^fs[mp Y F^H�[ S F^_ U LlP�LEB T kt@EHO_�[qFs[qp T Hq[q_�@�a�·9pGNOiEd T Hq[n_ozV¸ T S Llr T HO@ U L�P�P T [1@Ea±d]LEW�FIHGiý � _mLEHON Ë � _Xz

¯1_wd T Hq[nF^@EH T NyLEf^B T L�NQP�hG[ SOT ·9pONOiEd T Hq[q_ S L�r T [ SOT ac@EfIf^@ U FIHGi!_oF � ac@�BXd]_Xz ç�¦0§�¨;©ª¡�«V©¬�ç çÿè

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Page 39: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

LE_ U%T f^fvLE_�[ SOT _ T r T BXLEfvBXF^i S [5T�[n@%Tuf T a¼[MBXpGf T _

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Page 45: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 46: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

T9��Y B T _X_oFI@�HO_]LEB T DOpOF^fs[�p Y LEf^_X@�acBo@Ed d]H T d]@EHOF^k�HOLEd T _ Å F^N T Hq[qFI� T BX_ Ð UuS F^k S B T a T Bm[n@N T �GH T N»@EB�d T B T fxP�N T ktfILEB T N�r*LEfIp T _Xz R SGT B T _ S @EpOf^N»L�H�pGHOfIF^d]Fs[ T N»_Xp YOY fsP @�aMH T'UHOLEd T _oz R SOT _ T HGLEd T _�LEB T pG_ T N�[n@�_ S @ U UuSOT B T FIH�[ SOT D�@�NQPä@EaML ¶ pOLEHq[qFI� T B Å F^aLEHqP UuSOT B T Ð [ SOT�¶ pOLEHq[nF^� T NyLEBXi�pOd T Hq[M@*ktkZpOBo_Xz

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Page 47: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 48: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Å ýúù Í~Ð · ¬ þ Å ý · ¬ Ð ù Å�Í · ¬ Ð ç��?�f £¡ çæ â

Page 49: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

� |}H4· T k9[qFI@�HOzF ç Å �æ ý Ð è Å ýúù Í~Ð ·  · ç Å wæ Í~Ð è Å ý ù Í�Ð ·  

� Á-FIHOL�B�P³kZLE_ T _ Y fIFx[nh-@EBMktLE_ T ac@EBXd]z R S F^_�BopOf T LEf^fI@ U _M@EH T [q@�N T �OH T L�acpOHOk'[nF^@EHU Fx[ S L�NGFI_\·9@EFIHq[mpOHGFI@EHgL�BXiEpOd T Hn[mDqP7N T �GHOFIHGiuF^HO_\[ T L�Nj[ U @�acpOHOk'[nF^@EHO_�_ TZY LEBoLt[ T fsPEh@�H T ac@EB LEBXi�pOd T Hq[n_m@Ea�F�ac@EBXd]h�LEHGNg[ SOT @t[ SGT Bwac@EBV·9z

ü ç��?�f ¢¡ Å �æ ý ù Í~Ð æË ç Å �æ ý Ð è ü · Å   æZF Ð æ¤ ç Å wæ Í~Ð è ü · Å   æ9· Ð" Ë æ ¤ $ ç Å �æ ý�ù Í~Ð è ü

� ¬ BoFs[ T BoFI@EH�ac@EB Tt¶ pOLEf^Fs[}P U Fs[ S d]@EB YGS FI_od]_j@Ea�kZL�_ T ac@�BXd]z R S FI_%BXpOf T LEf^f^@ U _1pO_�[q@T'��Y B T _X_�LEHqPKd]@EB YOS F^_Xd UuS @E_ T @EpQ[ T Bod{@�_�[%LEBXiEpGd T Hq[ S LE_�LuNOFI_\·9@EF^Hn[�pOHOF^@EHu[}P YATF^HKkZLE_ T ac@�BXd]z

ü ç��?�f ¢¡ Å �æ ý ù Í~Ð æË ç Å �æ ý Ð è ü · Å   æZF Ð æ¤ ç Å wæ Í~Ð è ü · Å   æ9· ÐÄ ç Å �æ ý ù Í~Ð è ü

" Ë æ ¤ $ þ Ä ç Å �æ ý ù Í~Ð è üÆ Ä · Å   æZF Ð þ Ë ç Å �æ ý Ð è ü · Å   æZF Ð

Ä · Å   æ9· Ð þ ¤ ç Å �æ Í~Ð è ü · Å   æ9· Ð

è�Å è�Å è�Å � � ÓGà�×!Õ ï�ÔbÖ�ð¬ @EHq[ T9� [n_jLEB T ktfI@E_ T N�pOHON T B T'� [ T HO_oFI@�H�DqP�acB T _ S N T kZf^LEBXLt[qFI@�HO_Xz1¸�Fx[ S#Y LEFIB)[}P Y�T _Xh�[ SOT[}P YAT _mFIHKL]iEFsr T HykZ@EHq[ T'� [~LEB T kZf^@E_ T N�pOHGN T BmL]_XF^d{F^f^LEBwW�F^HONy@Ea�kt@Ed Y B TtSOT HG_XF^@EHOz

R SOT ac@Ef^fI@ U F^HOi!BopOf T _wLEB T LEf^f�F^Hg[ SOT iEf^@EDOLEf�kt@EHq[ T9� [

ç?¦�§0¨;©ª¡;«V© æý ç����f ¢¡ �æÍ ç��?�f £¡ Å �æ ý Ð

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� ��LEF^BXF^HOiEzY L�FIB ç Å wæ ý æ Í�Ð è Å ý Í~Ð ·  ¡�

æ ½

Page 50: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

� ° Y f^Fx[X[nF^HOi�LEH�LEBoiEpOd T Hq[{@Ea Y LEF^B-[}P Y�T z R S F^_jBXpOf T LEf^fI@ U _j@EH T [q@�N T �GH T LKacpGHOk9�[nF^@EH U Fs[ S L Y LEF^B-[}P Y�T LEBoiEpOd T Hq[!DqP�N T �OHGFIHOiyFIHG_�[ T LEN�LyL�acpOHOk'[nF^@EH U Fx[ S [ U @LEBoiEpOd T Hq[n_mkZ@�BXB T _ Y @EHONOF^HOij[n@j[ SOT kt@Ed Y @EH T Hq[n_m@Ea�[ SOT�Y LEF^BXz

ü ç��?�f £¡ Å wæ ý Í~Ð æÍ ç Å �æ ý æ Í~Ð è ü · Å   �Zæ Y LEFIB а Y f^Fs[�"sk!$ ç Å �æ ý Í~Ð è ü

� ¬ BXFx[ T BXF^@EH0ac@EB TZ¶ pOL�fIFx[}P U Fs[ S d]@EB YOS FI_od{_7@Ea ° Y fIFx[�" $wac@EBod{z R S FI_!BXpOf T LEf^f^@ U _pO_�[n@#DGBXF^HOi�LEHqP²d]@EB YOS FI_od UuS @E_ T @�pQ[ T BXd]@E_�[yLEBoiEpOd T Hq[ S L�_ Y LEFIB%[}P YAT FIHq[q@° Y f^Fx[�" $�ac@EBod]z

ü ç��?�f ¢¡ Å �æ ý Í~Ð æÍ ç Å �æ ý æ Í~Ð è ü · Å  ¡� æ Y LEF^B Ð æÄ ç Å �æ ý Í~Ð è ü

° Y fIFx[�"xk:$ þ Ä ç Å wæ ý Í~Ð è üÆ Ä · Å  ¡� æ Y LEFIB Ð þ Í ç Å wæ ý æ Í�Ð è ü · Å  ¡� æ Y LEF^B Ð

è�Å è�Å è�Å á �J�\ÕqÖ�×ÜÚ�ÓOÕqà\ú±Ö��%Ý�à\ð�ÿlÞ�Ú�ß�Õqà\ú±Ö#Ú�Û±×Üê�Ó��s� Û±×4êR SOT [}P Y�T _Göõ÷Eh^öløý÷Eh-kZ@EHOH T k9[qFsr T _ ù h LEHON ¶ pOL�Hn[qFI� T BX_��®F^Hq[nBX@�NOpOk T N�_X@#acL�B�kZL�H�D T@EDQ[qLEFIH T N§L�_!F^HO_�[qLEHOk T _7@�a%L�k T B\[nLEF^H§_ok SOT d]LEh-[ S Lt[y|�_ S LEf^fwkZLEf^fwNOFI_\·9pOHOk'[nFxr T HO@�BXd]LEfac@EBXd]h UuS F^k S F^_�F^HONOF^_ YAT HO_oLEDOf T F^H Y BoLEk9[qFIk T z R S FI_�_ok SOT d]L�LEf^fI@ U _�pO_�[q@�FIHq[qBX@�NOpOk TFIH³L�iEFsr T H0kt@EHq[ T'� [|äL�H T9U [}P YATgUuS FIk S FI_j[ SGT NOF^_�·9@�FIHq[ypOHOF^@EH§@�a%L��OHOFx[ T acLEd]FIfxPö|ç��� � þ â æ ����� æ Ì ÷!@Ea ÍlÎZÌ�鵂 � È ¤ È ÎnÍXÏZË h�@�B Ç � ȵÇXÌ�ËL�9ÎZÌ�Ë @�awvz ° pOk S LEH T9� [ T HO_XF^@EH|ç��d]LlP³D T!T d Y [}P�h�@�Bu_\[nLEB\[ U Fx[ S L{[}P YAT ý ç��?�f £¡ eF^HK[ SOT kZ@EHq[ T'� [Jvh�L�HON�kt@EHq[nF^H�p TU Fs[ S L�H T'� [ T HO_oFI@�H�@Ea�[ SOT kt@EHq[ T9� [ Å �æ ý Ð z

|´[�FI_�L�fId]@E_\[ T _o_ T Hn[qFIL�fjFIH Y BoLEk9[qFIk T [n@�L�fIf^@ U [ SOT DOBoLEHOk SOT _�@EajL�NOF^_�·9pOHGk9[nF^@EH�[n@D T fIL�D T fIf T N�pG_XF^HOi#�Id T LEHOF^HOiEacpOf�HOLEd T _ ��U Fx[ S Lyd]H T d]@EHOF^k�B)ú@Ef T z Å ?±@EB T9� LEd Y f T h ac@EB@EH T d{F^i S [�pG_ T Ì��2È L�HON ÍlÎZÌ�Ë LE_�f^LED T f^_ Ð z ¾ LEk S DGBXLEHOk S @Ea�L�NOF^_�·9pGHOk9[qFI@EH�FI_MFIH�i T HQ�T BoLEfbLyN TZYAT HON T Hq[ Å��2åcÇZå @EBXN T B�_ T HO_XFx[nFxr T Ð kZ@EH4·9pOHOk9[qFI@�HOh�L�HON UuSGT B T kZ@�HQ·9pOHOk'[nF^@EHO_uLEB THO@EH�T T d Y [}P Å LE_ U Fs[ S ÍlÎZÌ�Ë�Ð h�@EH T _X@�d T [nF^d T _ U LEHq[n_�[q@7B T a T B�[q@u[ SOT kt@Ed Y @EH T Hq[n_jDqPHOLEd T _ Å L�_ U Fx[ S � ÇAÇlË�ê LEHON � È�Ë:�2È´Ð z

R SGT pO_ T @�ab_XpOk S L�d T k S L�HOFI_od BXL�FI_ T _j_X@�d T NOFI¿]ktpOfs[{F^_X_op T _�@Eab_ Y�T kZF^�OkZL�[nF^@EH Å ac@EBT9� LEd Y f T hb[n@#NO@ U Fx[ S�Tt¶ pOLEf^Fs[}P Ð hm@�r T B UuS FIk S |�_ S L�fIf�_XWÜLt[ T z�¸ S Lt[�d]Lt[X[ T Bo_~FI_%[ S Lt[FIH�[ SOT]T HON U%T ktLEH��Ikt@Ed Y FIf TZ� LEH�LEBXDGFs[qBXLEB\P�FIHG_�[nL�HOk T @Ea�[ SOT _Xk SOT d]L�pO_XF^HOiy@EHOfxP�[ SOTY LEB\[nF^kZpOf^LEB�F^HO_�[qLEHOk T _`öQ÷EhSö�øZ÷Eh ù h�LEHON� z ü abkZ@EpOBo_ T [ SOT B T d]L�P�D T d]@EB T [ S LEH�@EH TU L�P�@EabkZ@�d Y FIf^FIHGi�L7d�pGfs[qF T U L�P�NGFI_\·9pOHOk9[qFI@�H#�IF^Hq[n@�DOF^HOLEB\P � hVL�HON�@t[ SOT B SOT LENGLEk SOT _j@�aFId Y f T d T Hn[qLt[nF^@EHOz

R SGT HG@t[nLt[qFI@�HK|�_ S L�fIf�pO_ T F^_wLE_wac@Ef^fI@ U _ çæ�å

Page 51: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

� Â F^_�·9pGHOk9[qFI@EHGh�@EBwNOLt[nL�[}P YAT z

Ý�ÓOÕZÓ Í ( ç ç (���;�Í è ç ç è

­ T B T Í ( æ ����� æ Í è _\[nLEHON�ac@EBjDOBoLEHOk S f^LED T f^_Xh UuS F^k S _ S @�pOfIN�LEf^fbD T NOF^_�[qFIHOk'[nz R SOTf^LED T f^_ U FIf^fvD T ktLEfIf T N ÍlÎZÌ�Ë4È É¡ë`ÍnȵÎZÉ¡Ë z

� ¬ L�_ TgT9��Y B T _o_XF^@EHO_Xh�ac@EB�L�HOLEfxP`_oFI_�@EabNGLt[nL�[}P YAT _Xz�¸ T ktLEH�LE_XWKL��^NOLt[npGd � Å r*LEf^p T@�a�L]NOLt[qL�[}P YAT Ð LEDA@EpQ[uFx[n_wkZ@�HO_�[qBXpOk'[n@EBmac@EBXd]h�L�HONyFx[n_ Y L�B�[n_oz

ß�ÓGðqÖ ê Û��Í (��è Ç (���;�

Í è �è Ç èR SGT ktLE_ T�T9��Y B T _o_XF^@EH�kZ@�d Y FIf T _mFIHq[q@�r*LEBoFI@EpG_mW�F^HONO_m@Ea�_ Y f^Fs[qz

R @�ac@EBXdMpOf^Lt[ T [ SOT BXpGf T _�ac@EBuNOF^_�·9pOHOk'[nFxr T HG@EBXd]LEf)ac@EBod{h�@EH TjU @�pOfIN�FIHq[nBo@*NGpOk T LEHLEp � F^f^FILEB\P�·9pONOiEd T Hn[qh U BXFx[X[ T H�L�_ ac@EfIf^@ U _Xz

ç ç?¦0§�¨;©ª¡�«V©

R SOT d]LEFIHKBXpGf T _ YAT ktpOf^FILEBb[n@�[ S FI_�·9pONGi T d T Hq[�ac@EBXdÿLEB T LE_wac@Ef^f^@ U _oz

Å�Ð ç?¦0§�¨;©ª¡;«V©

ç�¦�§0¨;©ª¡;«V©ý ç����f ¢¡ ç ç?¦�§�¨;©ª¡�«V© Å �æ ý ÐÅ ý æ!ç Ð ç?¦0§�¨;©ª¡;«V©

�1@t[ T [ S L�[1[ SOT HG@t[nLt[qFI@�H Å �;��� æ �;��� Ð F^_1D T F^HOi!pO_ T N SOT B T F^H�L!H T9U�U L�P.ø±[ SOT �OBo_�[�LEBXiEp4�d T Hq[ Y f^LEk T F^_mac@�B Lj[}P YAT hvLEHONg[ SGT _ T kt@EHON�ac@�B L{kt@EHq[ T'� [qz

ü H TMU @EpOf^Ny[ SGT H�F^Hq[nBX@�NOpOk T [ SGT _ T d]FIkt@EfI@�H��iø � L�_�L�kt@EHOktLt[ T HOLt[nF^@EH�@ YAT BoLt[n@�BXh�_X@[ S Lt[

çl¦�§�¨;©ª¡�«V©ç ç?¦0§�¨;©ª¡�«V© \ø)ç ç?¦0§�¨;©ª¡;«V©

­1@ U%T r T B�[n@7NO@M[ S FI_ Y BX@ YAT BofsP�@EH T dMpO_�[gFIHq[nBo@*NGpOk T~Tt¶ pOLEf^Fs[}P�D T [ U�TtT H�kZ@EHq[ T'� [n_XhbL�HONL Y f T [ S @EBXL{@Ea�LE_X_o@*ktFIL�[ T NyBXpOf T _,ø�_X@{|-kt@EHq[ T Hq[�dmP�_ T fIa U Fs[ S [ S FI_mF^HONOF^kZLt[qFI@EHGz

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Page 52: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

|}a� _�[qLEHONO_%ac@EB)[ SOT [}P Y F^kZL�fVNOLt[qLM[}P Y�T iEFsr T H#LEDA@�r T hA[ SGT H![ SOT ac@EBod{L�[nF^@EH�BopOf T FI_LE_wac@Ef^fI@ U _Xz

\ø)ç ( ç?¦�§0¨;©ª¡;«V©�;���\ø)ç è ç?¦�§0¨;©ª¡;«V© çf�?�f £¡

R SOT [}P Y FIHOi{BXpGf T _1ac@EB NGLt[nL]kZ@�HO_�[qBXpOk'[n@EBo_1LEB T LE_ ac@Ef^fI@ U _Xz

Í ( ç Å \ø)ç ( Ð è ·���� ������Í è ç Å \ø)ç è Ð è ·�� ���

|}a�LENONGFs[qFI@EHGLEfIfxP ü _�[qLEHONO_!ac@EBj[ SOT [}P Y FIktLEf1ktLE_ TyT9��Y B T _X_oFI@�H�i�Fsr T H0LEDA@�r T h-[ SOT H�[ SOT[}P Y FIHGi7BXpGf T ac@EB ktLE_ T�T9��Y B T _o_XF^@EHO_�F^_wLE_wac@EfIf^@ U _Xz

Ç ( ç Å \ø)ç ( Ð è � · Å ��� � æ Í ( Ð�����Ç � ç Å \ø)ç è Ð è � · Å �����Zæ Í è Ð

ü ç Å �æ� Ð è �

è�Å è�Å è�Å ò évÞ�Ú�ß�Õqà\Û±ÚeÕ�ï`ÔbÖ�ð

R SOT acpOHOk9[qFI@�H][}P YAT BopOf T _mLEB T LEf^f�F^H][ SOT iEfI@�DOLEf�kt@EHq[ T9� [

ç?¦0§�¨;©ª¡�«V© æý ç��?�f £¡ �æÍ ç��?�f ¢¡ Å �æ ý Ð

� ?±@EBXd]Lt[qFI@�HK@�a�acpOHGk9[nF^@EHg[}P Y�T _Xz

ý Í ç��?�f ¢¡

ç ç?¦�§�¨;©ª¡�«V© æ¬�ç çÿè

Å ý Í�Ð · ¬ þ Å ý · ¬ ÐnÅ�Í · ¬ Ì Ð çf�?�f ¢¡ ç

� ?±@EBXd]Lt[qFI@�HK@�a�acpOHGk9[nF^@EHO_oz¤ ç Å �æ ý Ð è Í� ¤ ç ãè ý Í

� ¯ YGY fIF^kZL�[nF^@EHOz< ç �è ý Í

< Å Ð ç Å �æ ý Ð è Íæ�ø

Page 53: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

� ¬ BoFs[ T BoFI@EH�ac@EB Tt¶ pGLEfIFx[}P U Fx[ S L�d]@EB YOS F^_Xd UuS @E_ T f T a¼[nd]@E_�[�kZ@�d Y @EH T Hq[�F^_�@EaacpGHOk9[qFI@EHKac@EBod{z

ç ç?¦�§�¨;©ª¡�«V© æ¬�ç çÿè �æ¤ ç Å �æ ý Ð è Í æÄ ç çÿè Å ý Í~Ð · ¬

Å � ¤ Ð · ¬ þ Ä ç çÿè Å ý Í~Ð · ¬Æ Ä Å Ð þ ¤ · ¬SÌ ç Å çSæ ý · ¬ Ð è Í · ¬SÌ

è�Å è�Å è�Å û �y×4Û±Þ�Ú�ÝeÕ ï�ÔbÖ�ðR SOT ac@Ef^fI@ U F^HOi{BXpOf T _w_ S LEB T [ SGT ac@�fIf^@ U FIHOi{iEf^@EDOLEf�kt@EHq[ T'� [qz

ç�¦�§0¨;©ª¡;«V©R SOT P�LEB T BopOf T _w@Ea±[}P YAT ac@�BXd]Lt[nF^@EHOh`LEHON TZ¶ pOLEf^Fs[}P�D T [ U%TZT H![}P Y�T _Xz

° T [ ç��?�f £¡ ç ç?¦�§�¨;©ª¡�«V© æ¬�ç çÿè

° T [S· ¬ þ ° T [ çn�?�f ¢¡ ç¾ f ç��?�f ¢¡ Å �æ ° T [ Ð ç ç?¦0§�¨;©ª¡�«V© æ

¬#ç çÿè ¾ f£· ¬ Ì þ ¾ f çn�?�f ¢¡ Å çbæ ° T [ Ð

|vkZL�fIf*pO_ T [ SOT�U @EBXNO_b�^_Xd]LEf^f � LEHONg�^f^LEBXi Tt� F^HgkZ@EHGH T k'[nF^@EH U Fs[ S iEBX@EpGHON%[}P Y�T _b_X@-[ S Lt[ ° T [F^_)[ SOT @EHOfxP È ËZÉ ² Ç i�BX@EpOHGN{[}P Y�T _Xh�LEHONyLEfIf�@�[ SOT B1iEBo@EpOHONg[}P Y�T _ Å HOLEd T fxP�[ S @E_ TMS Llr�F^HOiL!ac@EBXd ¾ f5· Å ¬ æ Ë�Ð hýöQ÷Eh�@EB�öløZ÷ Ð L�B T Ë Æ Ë�ÈxÈ zj|}HGac@EBXd]LEf^fsPEh�| ktLEf^f�L�[}P Y�T @�a�_X@Ed T ac@EBXdf^LEBXi T FIa�L�HnP�@EavFx[n_�kt@Ed Y @EH T Hq[n_ F^_�f^LEBXi T h`LEHGN�L~acpOHOk'[nF^@EH�fIL�BXi T FIavFx[n_�[}P YAT @EaOr*LEfIp T _�F^_f^LEBXi T z

R SOT ac@Ef^fI@ U F^HOi!BopOf T BopOf T F^_ U @�B�[ S HO@t[qFIHGiEz

Ë ç |è ° T [¾ f¢· Ë ç��?�f £¡

|}H�i T H T BXLEf^h)|�_ S LEfIfbL�fIf^@ U dmP�_ T fIa�[n@ U BXFx[ T ¾ f Ë · ¬ FIHO_\[ T LEN�@Ea ¾ f�· Å ¬ æ Ë�Ð h)LEHON ¾ f ËF^HO_�[ T LENy@Ea ¾ fV· Ë z

B�« � ��FKN N$P�F&³�²?ì � F�DêFé�

° @�acL�BXh U Fx[ S L�H T d Y [}P�acL�d{F^fxP�@Eab_ T [q_Xh�[ SOT [}P Y�T _\P�_�[ T d F^_ T d Y [}PEz R SGT B T F^_�@EHGfsP�Li T H T BoLEf�acBXL�d T'U @�BXW�F^H UuS F^k S [q@]fIL�P�@Ep4[ Y LEB�[qFIktpOfIL�B Ë4ÇnÈ T È�ÇAÇlÎZÉ¡�9Ç`Ë z

R SOT N T _okZBoF Y [qFI@�HM[nLEW T _�[ SOT ac@EBod©@EaAkZf^@E_XpGB T kZ@EHONGFs[qFI@EHG_�@EH Å ° T [5æ ¾ f Ð h T'�`Y B T _o_ T N�DnP[}P Y F^HOi ·9pONOiEd T Hq[q_�LEHGN Tt¶ pGLt[nF^@EHO_oz R SOT kZf^@E_XpOB T kZ@EHONGFs[qFI@EHG_�LEB T @Ea�[ S B TZT DOBX@�LEN]W�F^HONO_oz

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Page 54: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

� ¬ f^@E_XpOB T pOHON T BbB TZ¤GT k9[qFI@�HO_�@�a�[ SOT f^@EiEF^kZLEfO@ Y�T BXLt[qFI@EHG_ Å öQ÷�æ;ö�øZ÷�æ ù æ æ Ð @EaE[ SOTacBXL�d T'U @�BXW�[}P Y�T _\P`_\[ T d{z

� ¬ f^@E_XpOB T pOHON T B Y BXF^HOktF Y f T _ @�a�F^HONOpGk9[nFxr T N T �OHOFx[nF^@EH�@Ea Y B T _XktBXF^D T N�ac@EBXd]h`@�B-d]@EB Ti T H T BoLEfIfxP Y BXF^HOkZF Y f T _biEpGLEBXLEHq[ TZT F^HOi-[ SOT�T9� F^_�[ T HOk T @Ea T9� [nB T d T _X@�fIpQ[qFI@�HO_�[n@ TZ¶ pOLt�[nF^@EHO_w@Ea�r*LEBXF^@EpO_wW�F^HONO_Xz

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Page 55: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 56: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 57: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 58: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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H ç ° T [H þ Å Ë ç ý Ð~Í�ÅoË�Ð è H

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Í'K $ Å ý ç ° T [ ÐmÅ ¾ f ý è ° T [ Ð è ° T [¾ f Í'K�Å ý æ Í�Ð þ Å Ë ç ¾ f ý Ð ¾ f Í�ÅXË�Ð è ¾ f Í'K�Å ý æ Í~Ð

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7 ç Æ%Î:Î!Å H Å ý æ Í~ÐXÐ è Æ1Î:Î7Å H Å ý æ Í~ÐoÐü87 Å�ò ç Í'KKÅ ý æ Í�ÐXÐ þ ß�ÓOðZÖ ò Û�� Y LEF^B Ë <#è Å ¤ ç Í�ÅoË�Ð�Ð ü Å < Å ¤ ÐXÐ

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Page 59: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

¯ Y B T NOF^kZL�[ T ü ç Æ1Î:Î7Å H Å ý æ Í~ÐoÐ F^_y� ÉtÎ ² ÉtÇ`ËLËL���Ç F^a Å � ç H Å ý æ Í~Ð�Ð ü87 Å � Ð èü Å � Ð h UuS F^k S kZL�H{D T�U BXFx[X[ T H{d{@�B T kZ@�d Y LEk9[qfsPKLE_ ü873Bóü z-¯1H T f T d T Hq[%@EaNH Å ý æ Í�ÐF^_ Ë�ÍlÍlÇ`ËLËL� ¤ È Ç FIa Å [q@ Y pQ[1Fs[1F^d Y B T NGFIktLt[nFxr T fsP Ð Fx[mFI_�F^H�[ SOT FIHq[ T BX_ T k9[qFI@�H�@EaALEfIf Y BX@EiEB T _o_XFxr TY B T NOF^kZL�[ T _oz R SGT B T kZpOBo_XF^@EH Y BoFIHOktF Y f T B TZ¶ pOF^B T _M[ S L�[�LEf^f T f T d T Hq[q_�@EaOH Å ý æ Í~Ð LEB TLEktk T _X_XF^DOf T h�LEHON T9��Y B T _X_ T _�[ SOT �If T L�_�[nH T _X_ � @�aPH Å ý æ Í�Ð z

êQK $ Å ý ç ° T [�æ Í ç Æ1Î:Î!Å ¾ f ý Ðü ç Æ1Î:Î!Å H Å ý æ Í~ÐoÐ æ Í ç ü 7 B ü� ç H Å ý æ Í~ÐXÐ

è ü Å � ÐêQK�Å ý æ Í æ ü æ Í æ � Ð þ �\Ö�Õ � þ ß�ÓOðqÖ � Û�� Y LEF^B Ë <#è � ¤ � êQK�Å ý æ Í æ ü æ Í æ < Å ¤ ÐoÐ

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'y¹ vÒ¹v R )?Á-,y½�Ä�Âq½\Â

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ü H T%Y pOB Y @E_ T acpOfI�GfIf T N�DqP{[ SOT FIHq[qBX@�NOpOk9[qFI@�H�@Ea�LMpOHOFxr T Bo_ T F^_�[q@ YAT BXd]Fx[-[ SOT N T �OHOFx�[qFI@EH�@Ea�acLEd]F^fIF T _1@Ea�_ T [n_�DqP�B T kZpOBo_XF^@EHOh�DqP Y Bo@lr�F^NOF^HOi�L7_ T [g@�B1acLEd]F^fsP�@EaV_ T [q_�ac@EBb[ S L�[B T kZpGBX_XF^@EHg[n@g� S L YOYAT H�F^Hq[n@ � z ?±@EB T9� LEd Y f T h�@�H T d]LlP U FI_ S Å LE_�F^H~[ SOT kt@EHO_�[qBXpOk'[nF^@EH�@Ea° kt@t[X[ � _N TS�d]@*N T f�@Ea�[ SOT pOHq[}P YAT N ��T�kZLEf^kZpOf^pO_ Ð h�[n@]N T �GH T L]_ T [ ç

Å Ì ç 2 ÐVU!Å = Ðë]Ò�Ö�×ÜÖ W Å ô Ð þ 2

W Å 9 Ì�Ð þ W Å\Ì�Ð è W Å\Ì�Ð

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¯%HG@t[ SOT B T'� L�d Y f T @EaA[ SOT N T �OHOFx[nF^@EHy@EaV_ T [5T�r*LEf^p T N#acpOHGk9[nF^@EHyDnP�B T ktpOBX_oFI@EH�FIHq[n@!LpOHGFsr T BX_ T FI_�L @EBXN T N�DqP][ SOT N T �OHGFs[qFI@EH7@Ea*[ SGT 2yTMF^HON T'��T N#acLEd]FIfxPy@Ea��^_�[nL�HONOLEBoN � �GHOFs[ T

ø ½

Page 60: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

_ T [n_Xh UuS F^k S ktLEHKD T D T U BoFs[o[ T HyLE_wac@Ef^f^@ U _oz

2 Å ô Ð þ öQ÷2 Å\[ = Ð þ 2 Å = Ð ù â

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|}H�[ SOT B T d{L�FIHON T Bj@Ea�[ S F^_jk S L Y [ T B U%T FIHq[qBX@�NOpOk T kt@EHO_�[qLEHq[n_�LEHON Tt¶ pGLt[nF^@EHO_�ac@EB�Lr*LEBXF T [}P�@Ea�pOHGFsr T BX_ T _oz%?�F^BX_\[ Í'c&d h Í'e�d ac@�B�LEH T d Y [}P#pGHOFsr T Bo_ T h`LEHON�kt@EHO_�[qLEHq[n_ ac@EB�_X@�d T@t[ SGT Bj�^d{F^kZBo@E_Xkt@ Y F^k � pOHOFxr T BX_ T _`ø�H T9� [ Í'c h Í'e ac@EB�L��IH T9� [!pOHOFxr T Bo_ Tt� @ Y�T BXLt[q@EB`øb�OHGLEfIfxPÍ'f h Í�g ac@EB�L��^_Xp Y�T BXpOHOFxr T BX_ TZ� kZf^@E_ T N�HG@t[�@EHOfxPäpGHON T B~[ SOT @EBoNOFIHGLEB�PäkZ@EHO_\[nBopOk9[qFI@EHG_DOpQ[7LEf^_X@�pGHON T B [ SGT H T'� [�pOHOFxr T BX_ T @ YAT BXL�[n@EBozy­1Llr�F^HOi�_opOk S LK_Xp YAT BopOHOFxr T Bo_ T LEf^f^@ U _@EH T [n@]N T �OH T Å F^Hq[ T BoHOLEf^fsP Ð L!_ TZ¶ p T HOk T @Ea�ktpOd�pGfILt[qFsr T pOHGFsr T BX_ T _1DnP�B T ktpOBX_oFI@EHy@EH~[ SOT_�[qBXpOk'[npOB T @Ea�@Ea�HOLt[qpOBXLEf�H�pOdMD T BX_oz

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Page 61: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

BopOf T _mLEB T B T NOpOHGNOLEHq[nz

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Í'c'l þ Í Ì ÅXÍ ���'� æ Í ��� � ÐÍ'e l ÅoÍnÐ þ ß�ÓOðqÖ Í Û�� F�øOè Í����·!øè Í ���'�

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Page 62: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

[ SGT ac@�fIf^@ U FIHOij[}P Y�T ·9pONGi T d T Hq[q_�[ SGT H S @Ef^NOz

¾ f Í'c l þ ö�øZ÷ ù öløý÷¾ f Í'ehlqÅ [^[ Ð þ ö�øZ÷ ç��?�f ¢¡¾ f Í'ehlqÅ Ð þ öQ÷ ç����f ¢¡

� R SOT H T9� [�pOHGFsr T BX_ T @ YAT BXL�[n@EBoz R S FI_�@ Y�T BXLt[q@EB�d]L Y _�L³acLEd]FIfxP@Ea~_ T [n_{[n@§Ld]@EB T%T9� [ T HO_XFxr T acLEd]F^fsP UuS F^k S kt@EHq[nLEF^HO_�Fx[jL�HON�F^_�LEf^_X@gkZf^@E_ T N�pOHON T B��x[ SOT pO_XpOL�f �_ T [5T�ac@EBXd]F^HOi7@ Y�T BXLt[qFI@EHG_Xz

Í'c ç Å ý ç ° T [ Ð1Å ¾ f ý è ° T [ Ð è ° T [Í'e ç Å ý ç ° T [�æ Í ç ¾ f ý è ° T [ Ð ¾ f Í'c)Å ý æ Í~Ð è ° T [

|}Hu[ SOT ac@EfIf^@ U FIHGi�|�_ S LEf^f�B TZY f^LEk T ¾ f Í'c DqPnmjh ¾ f Í'e DnPno§LEHON!_X@M@EHOz�¢�@�B T @�r T BXh|-@�d{Fx[ [ SGTuY LEBXLEd T [ T B Å ý æ Í~Ð acBo@Ed5L�fIf�@�kZktpOBXB T HOk T _m@EaPmLEHGNpo�z

m þ Ý�ÓOÕqÓ úë ç Å�Ðú È`Ë ç ÅXË ç ¾ f ý Ðúù Ë ¤ ç ÅXË ç m?æ ¤ ç m ÐúÌ � ç Å�Ðúq Ë ¤ ç ÅXË ç m?æ ¤ ç o ÅXË�Ð è m ÐúÌ ( ç Å�Ðúr Ë ¤ ç ÅXË ç m?æ ¤ ç o ÅXË�Ð è m ÐúÌ ç Å�Ð

çf�?�f £¡o ÅoÍnÐ þ ß�ÓOðqÖ Í Û�� úë è ¾ f ýú È�Ë è ¾ f Í�ÅoË�Ð

úù Ë ¤ è o ÅXË�Ð ù o Å ¤ ÐúÌ � è öQ÷úq Ë ¤ è Å � ç o ÅoË�Ð�Ð o Å ¤ Å � ÐXÐúÌ ( è öløý÷úr Ë ¤ è Å � ç o ÅXË�Ð�Ð o Å ¤ Å � ÐoÐúÌ è 2

çf�?�f £¡ ÅoÍ ç m Ð

� R SOT _op Y�T B�pOHOFxr T BX_ T " óE½ $^z R SOT _op YAT B©T�pOHOFxr T BX_ T F^_M[ SOT f T LE_�[�acL�d{F^fxPä@Ea�_ T [n_kZf^@E_ T N�pOHON T B1[ SOT H T'� [�pOHOFxr T Bo_ T @ YAT BoLt[n@�B Å LE_ U%T f^f�LE_MLEfIf�[ SGT _�[qLEHONOL�BXN�[}P Y�Tac@EBod{F^HOi{@ YAT BXL�[nF^@EHO_Xh UuS FIk S ac@EBw_XF^d Y fIF^kZFx[}P�|-@�d{Fx[ Ð z

Í'f ç ° T [Í�g ç ¾ f Í'f è ° T [

|}HK[ SOT ac@EfIf^@ U FIHGi�|%_ S LEf^f�B TZY f^LEk T ¾ f Í'c DqPsmjh ¾ f Í'e DqPsoLEHON�_X@�@�HOz�C T kZL�fIfø�ø

Page 63: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

[ S Lt[ Í'c LEHON Í'e LEB T [ SOT _ T [mac@EBod{F^HOijkt@EHO_�[qLEHq[n_)ac@EB�[ SOT H T'� [mpGHOFsr T Bo_ T @ Y�T BXLt[q@EBXz

t þ Ý�ÓGÕqÓ úë!Ë ¤ ç ÅoË ç t�æ ¤ ç 9 ÅXË�Ð è t Ðú È`Ë ¤ Í ç ÅoË ç t�æ ¤ ç 9 ÅXË�Ð è tæ Í ç m Å 9 ÅXË�Ð æ�9�· ¤ ÐXÐ

ç����f ¢¡9 ÅoÍqÐ þ ß�ÓGðqÖ Í Û�� úë�Ë ¤ è m Å 9 ÅXË�Ð æ�9 · ¤ Ðú È Ë ¤ Í è o Å 9 ÅXË�Ð æ�9�· ¤ æ ÍqÐ

ç��?�f ¢¡ ÅXÍ ç t ÐR SGT B T FI_1L7_Xd]LEf^f�LEDOpO_ T @Ea�[ SOT kt@Ed Y @E_oFs[qFI@�H�@ YAT BXL�[n@EBmLEDA@lr T z}9-· ¤ F^_%pG_ T N�LE_L]_opOiEi T _�[nFxr T HO@t[qLt[nF^@EH�ac@EB^� ��� 9 Å ¤ Å � ÐoÐ z

� ¯ r`F^_�[qL�@Ea�pOHOFxr T Bo_ T _Xz R SGT _Xp YAT BopOHOFxr T Bo_ T kZ@EHO_\[nBopOk9[qFI@EH²ktLEHeD T#T fIL�D�@EBoLt[ T Np Y @EH�_o@{L�_V[n@]@EDQ[qLEFIH�LEH�@ YAT BoLt[n@�B�@EH�acLEd]FIf^F T _Xh UuS FIk S LE_X_oFIi�HO_�[n@]L]acLEd]FIfxP7[ SOTH T9� [ d]@EB T-T9� [ T HO_oFsr T acLEd]FIfxP UuS FIk S F^_�kZf^@E_ T NgpOHON T BA[ SGT H T'� [wpOHOFxr T BX_ T @ Y�T BXLt[q@EBXzR S FI_mi T H T BXL�fIF^_XLt[qFI@�HyktLEHyD T [nLEW T HKFIHKL]H�pOd�D T Bm@Ea�NOFIB T k'[nF^@EHO_Xz|}Hy@EH T NOF^B T k9[nF^@EHOh�@EH T ktLEH�Fx[ T BXLt[ T [ SOT _�[ TtY acBo@Ed[ SGT H T'� [5T�pOHOFxr T Bo_ T @ YAT BoLt[n@�B[q@M[ SGT H T9� [5T�_Xp Y�T B©T�pOHOFxr T Bo_ T @ Y�T BXLt[q@EBXzg¯1_�B T d]LEBXW T N�DqP�� T [ T B  P`D�· T BXhA[ S F^__\[ TtY�S LE_jkZf^@E_ T _oFId]F^fIL�BXFx[nF T _ U Fs[ S L�W T P Y LEB\[]@Ea`[ SGT @EBXNOF^HOLEfiT�[ SOT @EB T [nF^k%� T DOf T HN T BXFxr*Lt[nFxr T @ YAT BoLt[n@�BXh�HOLEd T fxP§[ SOT kZ@�HO_�[qBXpOk'[nF^@EH»@�a-[ SOT H T'� [�FIHO�GHOFs[ T @EBXNOF^HOLEfL�D�@�r T L{iEFxr T HK@EBoNOFIHGLEf UuS F^k S F^_mktfI@�_ T NypOHON T BwL!iEFxr T HyHG@EBXd]LEf�acpOHGk9[nF^@EHOz|}H§LEHO@t[ SOT B!NOFIB T k'[nF^@EHOh�@EH T kZLEH0L�NON§L�k T B\[nLEF^H0� ��T N�T Y @EF^Hn[�@ Y�T BXLt[q@EB�[q@K[ SOT@ Y�T BXLt[qFI@EHG_-pOHON T B UuS F^k S L~pOHOFxr T BX_ T F^_�ktfI@E_ T NOh UuS FIk S LEDG_�[nBoLEk9[q_�L U L�P�acBX@Edä[ SOT@ Y�T BXLt[qFI@EH!pOHON T B UuS F^k S [ SGT pOHGFsr T BX_ T d�pO_\[jD T ktfI@E_ T NOz �)pOBo_XpOF^HOi%[ S FI_�NOF^B T k'[nF^@EHU%T LEBXBoFsr T Lt[�k T B�[qLEF^H�ac@�BXd]_�@Ea�¢�L S f^@�pOHOFxr T BX_ T hgNOp T [q@ ° T [qº T BÜ" â ôEôl$Iz R SOT¢�L S f^@�pOHOFxr T BX_ T F^_�F^Hq[ T B T _\[nF^HOi~D T kZL�pO_ T LEfIf�[ SOT pOHOFxr T Bo_ T _�Fs[%kZ@�Hn[qLEF^HO_�F^Hq[ T BXHOLEf^fxPL�NOd]Fs[1L Y BXF^HOkZF Y f T @Ea�_�[qBXpOk'[npOBoLEf±B T ktpOBX_oFI@�HOh�L�fs[ S @EpOi S [ SGT ¢�L S fI@upOHOFxr T BX_ T Fs[q_ T fIaL�NOd]Fs[q_~HO@�_opOk S _Xk SOT d T z�|´[�F^_�@�HOfsP§L�� ��T N Y @EF^Hq[nh�HG@t[�@EH TuUuS F^k S FI_�FIH�L�HnP_ T HO_ T �^f T LE_\[ � z

øEõ

Page 64: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

R SOT�Y B T r�FI@�pO_~k S L Y [ T Bg_ T [�@�pQ[�L�acBoLEd T9U @EBXW�ac@EBMkZ@EHO_\[nBopOk9[qFsr T _ T [~[ SOT @�BXF T _Xh L�HON�F^H[ S L�[~acBoLEd T9U @EBXW�N T _XkZBoFID T N#L Y LEB\[nF^kZpOf^LEBmfIF^d]Fs[ T N#_ T [1[ SOT @�B�P�z R SOT k S L Y [ T B1LEa¼[ T B)[ S FI_@EH TjT'�`Y fI@EFx[n_V[ SOT kZf^@E_opOB TjY Bo@ YAT B�[qF T _ @EaO[ SOT _ T [q_ FIH�[ S FI_V[ SOT @�B�P7[q@gN T [ T Bod{F^H T Lgf^@ U%T BD�@�pOHONK@EHyFx[n_ Y Bo@*@�a�[ SOT @�B T [qFIktLEfv_�[qB T HGit[ S z

R S FI_uk S L Y [ T BukZ@EHGk T BoHO_m[ U @�W�F^HONO_u@Ea-_\P�_�[ T d]_ UuS F^k S LEB T{YAT B\r*LE_XFxr T HO@t[!@EHOfxP�F^HkZ@Ed Y p4[ T Bj_okZF T HOk T h�DOpQ[]L�fI_o@�FIH�HOLt[qpOB T h�HOLEd T fsPy[nBXL�HO_XFx[nF^@EH�_�P�_�[ T d]_�LEHON�F^Hn[ T BoLEk9[qFsr T_�P�_�[ T d]_Xz ü BXNOF^HOLEf±HO@�[nLt[qFI@EH!_�P�_�[ T d]_ LEB T L Y LEB�[qFIktpOf^LEB-W�F^HON�@Ea*[qBXLEHG_XFx[nF^@EH7_\P`_\[ T d{zm|}HQ�[ T BXLEk'[nFxr T _�P�_�[ T d]_�L�B T pO_ T acpOf�ac@EB`d{@�N T fIf^FIHGi1F^Hq[ T BoLEk9[qFsr T _\P�_�[ T d]_±[}P Y F^� T NMDqP ½ T Y�T BX_X@�HiELEd T _1@EabL7k T B\[nLEF^H�W�FIHGNOz�|�N T _XktBXF^D T L�H�L YOY BX@ELEk S [n@7B TZY B T _ T Hq[nF^HOi~[ SOT _ T1U Fx[ S NOLt[nL_�[qBXpOk'[npOB T _%F^H�N TZYAT HGN T Hq[%[}P YAT [ SOT @EB�PEh�_o@�[ S Lt[M@EH T d{L�P Y Bo@EiEBoLEd U Fx[ S [ SOT d]z

° @Ed T LE_ Y�T k9[q_�@Ea`dmPKL YOY BX@ELEk S d]LlPKD T HO@�r T f^zw?±@EB T9� LEd Y f T h`L [nBoLEHO_oFs[qFI@EH!_�P�_�[ T dFI_�pO_opOLEf^fsPj[qLEW T Hm[n@wD T _XF^d Y fsP{LmDOF^HOLEB�PgB T f^Lt[qFI@EHu@EHuL1_ T [qh*LEHGNMd]@�N T f^f T N U Fx[ S LmDGFIHOL�B�PY BX@ Y @E_oFs[qFI@�HOLEf�acpOHOk'[nF^@EHOzm|´[ML YOYAT LEBo_b[ S @EpOi S [ S Lt[w[ SOT B T F^_m@�a¼[ T HKd]@EB T [ S LEHK@EH T�U L�P[n@m_XW�F^H~L1ktLt[nh Y LEB\[nF^kZpOf^LEBofsP{F^Hm[}P YAT [ SOT @EB\P�z ¾ r T H~_opOk S L�H�L YOY LEB T Hn[qfsP{_\[nBoLEFIi S [qac@EB U LEBoNHO@t[qFI@EHKLE_wL{DOFIHGLEB�P�B T f^Lt[nF^@EHKFI_w_XpG_Xk TtY [nF^DOf T [n@{NOF �T BXF^HOi{FIHq[ T B Y B T [qLt[nF^@EHO_oh�LEHGNyLENGd{Fx[n_Lt[wf T LE_\[m@EH T B TZY B T _ T Hq[nLt[qFI@EH{_XpGDQ[nfxP�NOF �T B T Hn[1acBo@Ed�x[ SGT @EDqr`F^@EpO_ � @EH T z�|}HgLj_ T HO_ T h�[ S FI_B TtY B T _ T Hq[qLt[nF^@EH7F^_)d]@EB T kt@Ed Y pQ[nL�[nF^@EHOLEf^h±LEHON]f T _X_ Y BX@ Y @E_oFs[qFI@�HOLEf^z R SOT B T FI_ YAT B S L Y _)Lt[f T LE_�[�L{d{@�BXLEf SOT B T h�[ S Lt[MF^H�L YOY BX@ELEk S FIHOi{L Y BX@EDGf T d FIH][}P YAT [ SOT @EB�P�@EH T dMpO_�[~_�[qLEB�[[ S F^HOW�F^HOi�BoFIi S [!acBX@�d [ SGT D T i�FIHOHGFIHOi�zy?±BX@�d @EH T]Y @EF^Hn[!@Ea�r�F T'U [ S FI_uFI_�_oLENOh)DOpQ[!@EH Td]LlP�L�fI_o@{f^@�@EW�@EH�Fx[�d]@EB T�Y @E_oFs[qFsr T fxP�LE_wLEH�@ YOY @EB�[qpOHOFx[}P�z

R SGT DOF^acpOBXktLt[nF^@EH�D T [ U%TZT H�[ SOT kZ@Ed Y pQ[qLt[nF^@EHOL�f�LEHGN Y BX@ Y @E_oFs[qFI@�HOLEf�B TZY B T _ T Hq[nL�[nF^@EH@Ea�B T f^Lt[nF^@EHO_mkZLEHyD T [nBoLEk T N�DOLEklW~[q@u[ SGTM¶ p T _�[nF^@EHO_%@EaVB TZY B T _ T Hq[nF^HOi��I_opODO_ T [n_ � F^H{[}P Y�T[ SOT @EB�PEz R SOT B T LEB T B T LEf^fsP�[ U @�HO@�[nF^@EHO_ ç acLEd]FIfxP Å iEFxr T H Y LEBoLEd T [qBXF^kZLEf^fsPEhjDqP¨L�H T'� �S LEpO_\[nFxr T�T H�pGd T BXLt[qFI@�H Ð h LEHGN Y B T NOF^kZLt[ T Å iEFxr T H�DqP0L Y BX@ Y @E_XFx[nF^@EHOL�f�acpOHGk9[nF^@EH Ð z R SOTB T fILt[qFI@�HO_ S F Y D T [ U%TZT H�[ SOT _ T NOF AT B T Hq[�HO@�[nF^@EHO_7F^_�HO@�[#Lt[�LEf^f1_\[nBXL�FIi S [qac@EB U LEBXNoø~Fs[�FI_

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Page 65: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

F^Hq[nF^d{L�[ T fxP²kt@EHOH T k9[ T N U Fx[ S [ SOT�T9� [qBXLE@EBoNOF^HOLEBXF^fxP�r T'� Lt[nF^@EpO_]F^_X_Xp T @�a pOHON T BX_�[qLEHONOF^HOi� TZ¶ pOLEf^Fx[}P � F^H�[}P Y�T [ SOT @EB\P ( z{?±Bo@Ed¹[ SOT D T iEF^HOHOF^HOiEhbFx[ S LE_%D TtT H�kZf T LEB-[ S Lt[]@�H T d�pG_�[NOF^_�[qFIHGiEpOF^_ S D T [ U�TtT H TZ¶ pOL�[nF^@EHOLEf�u ë�ê ² Ç Æ ÇXÌ�È Ë LEHGN�� ÉtÎ � Î:ËL�9È��9ÎZÌ ø DOpQ[~[ S F^_~FI_M@EHOfxP�[q@NO@�pODOf T [ SOTMY BX@EDOf T d]_b[ S L�[�L�BXF^_ T z R SOT kt@EpOBo_ T | S L�r T LENO@ Y [ T N SOT B T F^_w_XF^d Y fsP�[q@!LED4�_\[nLEF^H�acBX@�d L YOYAT LEfO[n@!LEHqP�i T H T BXL�f�HO@�[nF^@EH�@Ea Y BX@ Y @E_oFs[qFI@EHGLEf TZ¶ pOLEf^Fs[}PEhV@EBmac@EBod @EaA[ SOTF^N T Hq[qFs[}P�[}P Y�T h UuSOT [ SOT B T'� [ T HO_oFI@�HOLEf�@EBjFIHq[ T HO_oFI@EHGLEfIz R SOT �OBo_�[�[ U @�_ T k9[qFI@EHG_�@Eav[ S F^_k S L Y [ T B�NOF^_XkZpG_X_-[ SGT HO@t[qFI@�HO_%@EaV�I_opODO_ T [ � FIH![}P YAT [ SGT @EB\P�acBo@Ed©[ S F^_ YAT Bo_ YAT k'[nFxr T hbL�HON[ SOT B TZYAT BokZpO_o_XF^@EHO_1@Ea±[qLEW�FIHGi�[ S FI_wLEDG_�[ T Hq[nF^@EHOF^_�[ Y @EF^Hq[u@Ea±r�F T9U z

R SOT B T LEB T [ U @�d]LEF^H#_ T k'[nF^@EHO_�F^H�[ S F^_jk S L Y [ T BXz R SOT �OBo_�[{åEz ½ F^_jkZ@EHGk T BoH T N U Fx[ S[qBXLEHO_oFs[qFI@�H7_�P�_\[ T d]_ozm|´[1iEFxr T _�[ SOT N T �OHGFs[qFI@EHGh�[ SGT N T �OHOFx[nF^@EHO_�@EaA_X@Ed T B T f^Lt[ T N7HG@t[nF^@EHO_ohLEHGN�FIf^fIpG_�[nBoLt[ T _%[ SOT FIB�L YOY f^FIktLt[nF^@EH U Fx[ S L�H�pOdMD T Bg@Ea T9� LEd Y f T _]LEHON�kt@EHO_\[nBXpGk9[nF^@EHO_ozR SOT @t[ SOT BuåEz^åyF^_Mkt@EHOk T BXH T N U Fx[ S FIHq[ T BXLEk'[nFxr T _�P�_�[ T d]_Xh UuS F^k S L�B T _X@Ed T9UuS Lt[�d]@EB Tkt@Ed Y f T'� [ S LEHw[nBXL�HO_XFx[nF^@EH~_\P`_\[ T d{_oz ¯%iEL�FIHOh*|�iEFxr T [ SOT N T �OHGFs[qFI@EHGh4[ S Lt[�@�aO_X@Ed T B T f^Lt[ T NHO@�[nF^@EHO_b[ S Lt[ YAT B�[qLEF^H{[n@{F^Hn[ T BoLEk9[qFsr T~Y BX@�iEBXLEd]d]F^HOi Å LEHONy_�[nBoLt[ T iEF T _%ac@�Bmi�LEd T _ Ð h�L�HONY B T _ T Hq[~_o@Ed T F^f^fIpO_\[nBoLt[nFxr TuT9� LEd Y f T _1LEHON�kZ@EHG_�[nBopOk9[qFI@�HO_Xz

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Page 66: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 67: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 68: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 69: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 70: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 71: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 72: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 73: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 74: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 75: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

R SOT H U%TMS Llr TÛ ý Å�Æ�Ð þ Û ý( Å\ÆuÐ�Ü Û ý� Å�Æ�Ð

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Page 76: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

R SGT [nBoLEHO_XFx[nFxr T ktfI@�_XpOB T kZ@EHG_�[nBopOk9[qFI@�H Y B T _ T B\r T _ U%T f^fIac@�pOHON T NOH T _o_Xz R @7_ S @ U [ S F^_XhU�T H TtT Nu[q@�_ S @ U [ S Lt[1ac@EBbLEH]LEBoDOFs[qBXLEB\P�_�[qLt[ T Ë LEHGN Y B T NOF^kZL�[ T Y�h±FIa�Y�FI_ Y Bo@EiEB T _X_oFsr TU Fs[ S B T _ Y�T k9[u[n@ Å [ SGT kt@Ed Y @�_XFx[ T [nBoLEHO_XFx[nF^@EHO_u@Ea Ð Û Ì [ SOT H�Fx[{FI_ Y Bo@EiEB T _X_oFsr T LEf^B T LENQPU Fs[ S B T _ YAT k'[�[n@ Å [ SGT Lt[q@Ed]FIk)[nBoLEHO_XFx[nF^@EHO_�@Ea Ð Û z R S FI_�F^_-@�Dnr�F^@EpO_�D T kZLEpO_ T [ SGT Lt[q@Ed]FIk[nBoLEHO_XFx[nF^@EHO_mLEB T Ë Æ ÎZÌ ²�[ SOT kZ@�d Y @E_oFs[ T [qBXLEHO_oFs[qFI@�HO_w@EaÁÛ Ì z

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Page 77: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 78: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 79: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

|}H�[ S F^_�kZ@EHO_\[nBopOk9[qFI@EH U�T{Y pQ[ Í �ILEDA@�r Tt� ý z�¯ä[qBXLEHO_oFs[qFI@�H�acBo@Ed LEH T f T d T Hq[�@Ea ý F^_[ SOT _XL�d T LE_-L1[qBXLEHG_XFx[nF^@EH�FIH ý h UuS FIf T-U%T LENONM[q@1[ SGT [nBoLEHO_XFx[nF^@EHO_-acBX@Ed¹LEH T f T d T Hq[u@EaÍ _ T r T BoLEfVH T'U [nBoLEHO_XFx[nF^@EHO_oh�@�H T ac@EB T LEk S�T f T d T Hn[g@Ea ý zj|}Hn[qpOFx[nFxr T fxP�hbFx[�FI_mkZf T LEB)[ S L�[[ S FI_wkt@EHO_�[qBXpOk'[nF^@EH Y B T _ T B\r T _�[nBXL�HO_XFx[nFxr�Fs[}PEz

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Page 80: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 81: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 82: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

FIHg[ T BXd]_m@Ea Y B T NGFIktLt[ T [nBoLEHO_oac@EBXd T Bo_1F^HONOpGk T NyDqP�LEHKFIHq[ T BXLEk'[nFxr T _�P�_�[ T d]z¯1H �cÌ�ȵÇXÉtË�ÍnÈ ���ÇÒËLÌlË4È�Ç Æ¥kZ@EHG_XF^_�[n_m@Ea�[ SOT ac@Ef^f^@ U F^HOi{NOLt[qLn1 ç

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Page 83: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 84: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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Page 85: ECS LFCS-00-421.pdf Sequence - era.ed.ac.uk

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