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procedureWorklist :=

Simulate;

null;

while Worklist not empty loopq := first element on Worklist;

/* Push initial state on list and enter initial state in Unique State Table (UST) */

/* States on the worklist are unexamined elements of the UST */

for in loop i 1 . . T

/* Check current node in task i to se if it is possible to generate

Create a new state z , reflecting task i’s movement, as well as other

/* z is checked against the UST */

if unique (z) then

if moveable (i) then

Enter z in UST;

elseenter z in duplicate state table;

Push z onto Worklist;

tasks as required ( such as in the case of a rendezvous occuring);

* a successor state on the basis of task i’s performing a rendezvous,

* task activation, or the like

*/

end Simulate;

end loop;end loop;

end if;

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entry / begin

entry / beginentry / begin

entry / begin

lock(l_last)

lock(l_last)lock(l_first)

release(l_last)

return

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return

release(l_first)

lock(l_first)

release(l_first)

release(l_last)

buf1.get(item) buf1.put(item)

buf.get()buf.put()

produce()consume()

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return

return return

buf.get(item)

l_last

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0 b 0

closed open

A a

B b

A a

b

B b

C Y c

D

Deadlock

LAP_hiding(prod()) LAP_hiding(cons())

LAP_hiding(put()) LAP_hiding(get()) Partial global RG for the program

GAP_hiding(put()) GAP_hiding(get()) Partial local RG for class Buffer

C c

D d

D d

B b

C c

Y y

X x

open B

put() get()

closed B,last b,0 l_first

C,last c,firstclosed

X

prod() put() cons()

ax

XB x a A X x

xX

y

Y y d

begin

lock(l_last)

lock(l_first)

return

begin

return

begin

begin

lock(l_first)

lock(l_last)

return

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buf.put(item)

begin

l_first

A

open

closed

open B,0

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1. Number of classes, their id’s and objectsint Number_Of_Classes

Class_Name_1 Thread/Not_A_Thread Number_Of_Objects obj_1 obj_2 ... obj_n

Class_Name_2 Thread/Not_A_Thread Number_Of_Objects obj_1 obj_2 ... obj_n

Class_Name_n Thread/Not_A_Thread Number_Of_Objects obj_1 obj_2 ... obj_n

2. Depiction of a class and its methodsClass_Name_i

Number_Of_Locks Lock_1 Lock_2 . . . Lock_n

Number_Of_Methods Method_1 Method_2 . . . Method_n

Method_1

Node_1

Node-2

Node_n

Method_2

Method_n

3. Structure of a nodeint Node_Id

int Type

union {

char* LockName

char* FunctionName

int Successors []

}

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1. Number of local reachability graphsint Number_Of_Graphs

2. Depiction of a reachability graph

Class_Id class_id

Node_1

Node_2

Node_n

End of reachability graph

3. Structure of a nodeint Node_Id

int Position [ Number_Of_Threads ]

int LockStatus [ Number_Of_Locks ]

.

.

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r_next.insert()

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dbase.delete()

release(l_key) r_next=EOF

r_key=Null

lock(l_key)

begin

user.access() record.insert()

create()

release(l_key)

return

release(l_key) release(l_key)

r_next.read()

r_key=key

record.read()

return

Yes Yes NoNo

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lock(l_dir)

begin

dir = my_dir

lock(l_num)

num <= MAX

release(l_dir)

release(l_num)

lock(l_dir)

return

release(l_num)

release(l_dir)

car.start()bridge.cross()

lock(l_num)

YesNo

YesNo

bridge.cross()

return

begin

release(l_num)

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g$TMR��?= �];3=?>/Y�geF?T�> C��DC�@�=?[���@�=?[�� KM=?>/O?[GN(>A@ ge>bO?>AT^RWKM>bNn§ZR$T�>7 =?>� :!$>bN\d[$T��cBC[$VURWK^BC[eO?@��Q: O?[cN?>�BL@B =?>� :!$>AN£\d[eT��$RWVCBCN(BLK��ªH$� R$N?N?BLO?g F�� K^=?>VL[� :!`@�KMRWKMF(@^>A@+6 R�\�KM>AT K^=?>3>���>. K,[$\�> R� =uKM=?T�> R$N�9S[$\ >AR� =uKM=?T�> R$Nu@�KMRWKM>���"O$�WR$VLBCN @�K R�KM>A@�[� � AF?T�T^BLO?g�N?F(> KM[��GBL[eVUR�KMBC[$O [$\�KM=?>`IyF(K^F�R$V�>)(� AVLF?@^BL[eO b[eO?N?B KMBL[eOQR$T^>hRWVC@^[u@�=?[���O'�:�O{>AT^T�[eT [ . AF(T^T^BLO?g N?F?>yK^[/�GBL[eVUR�KMBC[$O�[$\�KM=(>JN(> R$N?VL[� :! A[eO(N?BLK^BC[eO BL@@�=?[���O BLOªY�geF?T�>:C��DE��¨¤�>bT^>$§�H�[$KM=ªK^=?> �?T^[cN?F� b>AThR$O?N{KM=(>0 A[eO?@�F?IJ>ATK^=?T^>AR$N?@hR$T�>¨T^>bVC> RW@^BCO(gQRQVL[� :!2��=?B" ={K^=?>�� A[eF?VLN{O?[$K =�R��$>�R� Aa�F?BCT�>AN6dBI� >���R�@!K RWK^>�R�\�KM>ATpRQN?> R$N(VC[ :!#9 ��;3=?>�>AT�T^[eThBC@ AR$F?ge=ZKpH �< =(>. :!�BCO?g

Lock states before

effect of AP

Lock states after

effect of AP

Thread State

(Producer)

Lock states before

effect of AP

Lock states after

effect of AP

Thread State

(Consumer)

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+

1 0 <- valid status

+

+ +

2 2 <- invalid status 1 2 <- invalid status

1 1 <- valid status

0 0

1 0

5 4

0 0

0 0

1 0

0 0

5 5

0 0

0 11 0

0 0

1 0

0 1

1 0

1 1

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1 0

Prod_1 Cons_1

7 7

0 1

1 11 1

Status before effect of1 1 <- release(l_first) :Prod_1

Status after effect of0 1 <- +release(l_last) :Cons_1

2 1 <- Invalid Status 2 1 <- Invalid Status

Status after effect ofrelease(l_first) :Prod_1

1 0 <-

Status before effect ofrelease(l_last) :Cons_1

1 1 <- +

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