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Introduction toFormal Languages
Martin Franzle
Informatics and Mathematical Modelling
The Technical University of Denmark
02140 Languages and Parsing, MF, Fall 2003 – p.1/16
Formal Languages
What is it?
02140 Languages and Parsing, MF, Fall 2003 – p.2/16
(Formal) Languages
� A language is a set of “legal” sentences.
A sentence is a sequence of symbols.
The symbols can be characters, words punctuation,hieroglyphs, dots and dashes (Morse code),
A formal language is a language defined by a finite set ofunambiguous rules delimiting the legal sentences from theillegal ones.
02140 Languages and Parsing, MF, Fall 2003 – p.3/16
(Formal) Languages
� A language is a set of “legal” sentences.
� A sentence is a sequence of symbols.
� The symbols can be characters, words
�
punctuation,hieroglyphs, dots and dashes (Morse code), � � �
A formal language is a language defined by a finite set ofunambiguous rules delimiting the legal sentences from theillegal ones.
02140 Languages and Parsing, MF, Fall 2003 – p.3/16
(Formal) Languages
� A language is a set of “legal” sentences.
� A sentence is a sequence of symbols.
� The symbols can be characters, words
�
punctuation,hieroglyphs, dots and dashes (Morse code), � � �
� A formal language is a language defined by a finite set ofunambiguous rules delimiting the legal sentences from theillegal ones.
02140 Languages and Parsing, MF, Fall 2003 – p.3/16
Why are they interesting?
Because formal languages arise everywhere in computing:
� Programming languages, query languages, etc.
� The inputs expected by programs:
� inputs to be keyed in, e.g. numbers in certain format, names,etc.
� sequences of button clicks in a GUI.
� Protocols for data exchange between computers (e.g. SMTP)
Knowledge of their algorithmic properties permits auto-matic generation of programs for their manipulation.
02140 Languages and Parsing, MF, Fall 2003 – p.4/16
Why are they interesting?
Because formal languages arise everywhere in computing:
� Programming languages, query languages, etc.
� The inputs expected by programs:
� inputs to be keyed in, e.g. numbers in certain format, names,etc.
� sequences of button clicks in a GUI.
� Protocols for data exchange between computers (e.g. SMTP)
Knowledge of their algorithmic properties permits auto-matic generation of programs for their manipulation.
02140 Languages and Parsing, MF, Fall 2003 – p.4/16
Some means of defining formal languages
A finite and unambiguous set of rules can be given by
1. a “computer” with finite memory such that the whole machinecan be described finitely,
“Regular languages”
2. a finite set of recursive definitions of the formif is a natural number then is an arithmetic expression,
,if and are arithmetic expressions then is anarithmetic expression,
“Context-free languages”
3.
02140 Languages and Parsing, MF, Fall 2003 – p.5/16
Some means of defining formal languages
A finite and unambiguous set of rules can be given by
1. a “computer” with finite memory such that the whole machinecan be described finitely,
“Regular languages”
2. a finite set of recursive definitions of the form
� if � is a natural number then � is an arithmetic expression,
�
� � � ,
� if ��� and ��� are arithmetic expressions then � � � ��� is anarithmetic expression,
�
� � �
“Context-free languages”
3.
02140 Languages and Parsing, MF, Fall 2003 – p.5/16
Some means of defining formal languages
A finite and unambiguous set of rules can be given by
1. a “computer” with finite memory such that the whole machinecan be described finitely,
“Regular languages”
2. a finite set of recursive definitions of the form
� if � is a natural number then � is an arithmetic expression,
�
� � � ,
� if ��� and ��� are arithmetic expressions then � � � ��� is anarithmetic expression,
�
� � �
“Context-free languages”
3. � � �
02140 Languages and Parsing, MF, Fall 2003 – p.5/16
Some means of defining formal languages
A finite and unambiguous set of rules can be given by
1. a “computer” with finite memory such that the whole machinecan be described finitely,
“Regular languages”
2. a finite set of recursive definitions of the form
� if � is a natural number then � is an arithmetic expression,
�
� � � ,
� if ��� and ��� are arithmetic expressions then � � � ��� is anarithmetic expression,
�
� � �
“Context-free languages”
3. � � �
02140 Languages and Parsing, MF, Fall 2003 – p.5/16
Regular languages:
Application domains
02140 Languages and Parsing, MF, Fall 2003 – p.6/16
Regular languages
arise naturally in
� descriptions of hardware components,
because these are computational devices with finite memory,
� descriptions of communication protocols,
because these engage into an alternation of finitely many differentphases,
� word classification problems, e.g.:is the next word a hyperlink, or is it to be rendered as text?
� descriptions of embedded computer systems,
because these are computers with finite memory.
02140 Languages and Parsing, MF, Fall 2003 – p.7/16
Regular languages
arise naturally in
� descriptions of hardware components,
�
because these are computational devices with finite memory,
� descriptions of communication protocols,
�
because these engage into an alternation of finitely many differentphases,
� word classification problems, e.g.:is the next word a hyperlink, or is it to be rendered as text?
� descriptions of embedded computer systems,
�
because these are computers with finite memory.
02140 Languages and Parsing, MF, Fall 2003 – p.7/16
Finite automata as models:
Embedded computer systems
02140 Languages and Parsing, MF, Fall 2003 – p.8/16
The coffee vending machine — architecture
Vending machine
cout
Financialadministr.
Brewercontrol
caf
canccoin req
02140 Languages and Parsing, MF, Fall 2003 – p.9/16
The coffee vending machine — dynamics
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.10/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
An example run
brewidle wait
no payno pay
(*, *, *, req, −caf)(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid(cin, *, −cout, *, *)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, −canc, −cout, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, canc, *, −req, −caf)
Brewer control
paid
(*, canc, cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, −cout, *, caf)
(*, *, *, *, caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
brewidle wait
no payno pay
(*, *, *, req, −caf)
(*, −canc, *, −req, −caf)
(*, canc, *, −req, −caf)
(*, *, *, *, caf)
Brewer control
paid
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, −canc, −cout, *, −caf)
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
brewidle wait
no payno pay
Brewer control
paid
Financial administration
(−cin, *, −cout, *, *)
(−cin, *, *, *, −caf)
(cin, *, −cout, *, *)
(cin, *, *, *, −caf)
(*, −canc, *, −req, −caf)
(*, *, *, req, −caf)
(*, −canc, −cout, *, −caf)
(*, *, *, *, caf)
(*, *, −cout, *, caf)
(*, canc, cout, *, −caf)
(*, canc, *, −req, −caf)
02140 Languages and Parsing, MF, Fall 2003 – p.11/16
The coffee vending machineProduct automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, *, caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(*, canc,
cout, r
eq, −
caf)
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, *, caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(*, canc,
cout, r
eq, −
caf)
Unreachable states!
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, canc,
cout, r
eq, −
caf)
(−cin, *, −cout, *, caf)
Free coffee!
02140 Languages and Parsing, MF, Fall 2003 – p.12/16
The coffee vending machine
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, *, caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(*, canc,
cout, r
eq, −
caf)
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, *, caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(*, canc,
cout, r
eq, −
caf)
Unreachable states!
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, canc,
cout, r
eq, −
caf)
(−cin, *, −cout, *, caf)
Free coffee!
02140 Languages and Parsing, MF, Fall 2003 – p.12/16
The coffee vending machine
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, *, caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(*, canc,
cout, r
eq, −
caf)
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, *, caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(*, canc,
cout, r
eq, −
caf)
Unreachable states!
Product automaton: Financial admin. * Brewer ctrl.
(*, −canc, −cout, req, −caf)
no pay no pay no pay
paid paid paid
(*, −canc, −cout, −req, −caf)
(−cin, *, −cout, req, −caf)
(−cin, −canc, −cout, −req, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(−cin, *, −cout, *, −caf)
(−cin, −can, −cout, *, −caf)
(*, canc, cout, −req, −caf)
(*, *, −cout, *, caf)
brew
idle wait brew
idle wait(−cin, canc, −cout, −req, −caf)
(cin, *, −cout, *, −caf)
(*, canc,
cout, r
eq, −
caf)
(−cin, *, −cout, *, caf)
Free coffee!
02140 Languages and Parsing, MF, Fall 2003 – p.12/16
What you’ll learn
1. The model of finite automata,
2. methods for expressing properties like “free coffee”, namelyregular expressions,
3. algorithms for manipulating regular languages,
4. how to plug these algorithms together such that theyautomatically check properties like “free coffee”.
I.e., you will build programs which analyze programs!
02140 Languages and Parsing, MF, Fall 2003 – p.13/16
What you’ll learn
1. The model of finite automata,
2. methods for expressing properties like “free coffee”, namelyregular expressions,
3. algorithms for manipulating regular languages,
4. how to plug these algorithms together such that theyautomatically check properties like “free coffee”.
I.e., you will build programs which analyze programs!
02140 Languages and Parsing, MF, Fall 2003 – p.13/16
Embedded systems in-the-large
02140 Languages and Parsing, MF, Fall 2003 – p.14/16
Context-free languages:
Application domains
02140 Languages and Parsing, MF, Fall 2003 – p.15/16
Context-free languages
arise naturally in
� in the definition of programming languages, query lang., etc.:
�
if � is a natural number then � is an arithmetic expression,
�
if ��� and ��� are arithmetic expressions then � � � ��� is an arithmeticexpression,
�
� � �
formal definition permits tool support by compiler-compilers,
� descriptions of expected document structures, e.g. DTDs in XML
formal def. facilitates conformance check and automatic decomposition.
You’ll learn
to formally define context-free languages,
to use compiler-compilers based on CFLs.
02140 Languages and Parsing, MF, Fall 2003 – p.16/16
Context-free languages
arise naturally in
� in the definition of programming languages, query lang., etc.:
�
if � is a natural number then � is an arithmetic expression,
�
if ��� and ��� are arithmetic expressions then � � � ��� is an arithmeticexpression,
�
� � �
formal definition permits tool support by compiler-compilers,
� descriptions of expected document structures, e.g. DTDs in XML
formal def. facilitates conformance check and automatic decomposition.
You’ll learn
to formally define context-free languages,
to use compiler-compilers based on CFLs.
02140 Languages and Parsing, MF, Fall 2003 – p.16/16
Context-free languages
arise naturally in
� in the definition of programming languages, query lang., etc.:
�
if � is a natural number then � is an arithmetic expression,
�
if ��� and ��� are arithmetic expressions then � � � ��� is an arithmeticexpression,
�
� � �
formal definition permits tool support by compiler-compilers,
� descriptions of expected document structures, e.g. DTDs in XML
formal def. facilitates conformance check and automatic decomposition.
You’ll learn
� to formally define context-free languages,
� to use compiler-compilers based on CFLs.
02140 Languages and Parsing, MF, Fall 2003 – p.16/16
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