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Checking (Bi)Simulation Relations of Kripke Structures -- Examples from Previous Exams
Exam of 2013, October 7; Problem 4
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b,c; init 1; labels 0:; 1:a; 2:; 3:; 4:b; 5:c; transitions 1->2; 1->3; 2->4; 3->4; 3->5;
K2
vars a,b,c; init 1; labels 0:; 1:a; 2:; 3:b; 4:c; transitions 1->2; 2->3; 2->4;
Exam of 2013, July 22; Problem 5
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars p,q; init 0; labels 0:p; 1:p; 2:q; 3:p; transitions 0->1; 1->2; 1->3; 2->2; 3->3;
K2
vars p,q; init 0; labels 0:p; 1:p; 2:p; 3:p; 4:q; 5:p; transitions 0->1; 0->2; 1->3; 2->4; 2->5; 3->3; 4->4; 5->5;
Exam of 2012, March 19; Problem 2
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b; init 0; labels 0:; 1:a; 2:b; 3:a,b; transitions 0->1; 1->2; 1->3; 2->0; 3->0;
K2
vars a,b; init 0; labels 0:; 1:a; 2:a; 3:b; 4:a; 5:a,b; transitions 0->1; 0->2; 0->4; 1->3; 2->5; 3->0; 4->3; 4->5; 5->0;
Exam of 2012, February 13; Problem 2
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b; init 1; labels 0:; 1:a; 2:b; 3:b; 4:a; transitions 1->2; 2->3; 3->3; 3->4; 4->1;
K2
vars a,b; init 1; labels 0:; 1:a; 2:a; 3:b; 4:b; 5:a; transitions 1->3; 2->1; 3->2; 3->3; 3->4; 4->5; 5->1;
Exam of 2012, February 13; Problem 3
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b; init 1; labels 0:; 1:a; 2:b; 3:b; 4:a; transitions 1->2; 2->3; 3->3; 3->4; 4->1;
K2
vars a,b; init 1; labels 0:; 1:a; 2:b; 3:b; 4:a; transitions 1->2; 2->3; 2->4; 3->3; 3->4; 4->1;
Exam of 2010, December 8; Problem 3
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b; init 0; labels 0:a; 1:a,b; 2:b; transitions 0->0; 0->1; 0->2; 1->1; 2->0;
K2
vars a,b; init 0; labels 0:a; 1:b; transitions 0->1; 0->0; 1->1;
Exam of 2010, September 23; Problem 7
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b; init 0; labels 0:a; 1:b; 2:b; transitions 0->0; 0->1; 0->2; 1->1; 2->0;
K2
vars a,b; init 0; labels 0:a; 1:b; transitions 0->1; 0->0; 1->1;
Exam of 2010, September 23; Problem 3(a)-(b)
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b; init 1; labels 0:b; 1:a; 2:a,b; transitions 0->0; 1->0; 1->1; 1->2; 1->0;
K2
vars a; init 0; labels 0:a; 1:; transitions 0->1; 0->0; 1->1;
Exam of 2010, July 23; Problem 3(c)-(d)
K1xK2
K1≤K2
K2≤K1
K1≈K2
K1≈K1
K2≈K2
print all simulation diagrams
K1
vars a,b,c; init 0; labels 0:a; 1:c; 2:b; transitions 0->2; 1->0; 2->0; 2->1;
K2
vars a,b,c; init 0; labels 0:a; 1:c; 2:b; 3:b; transitions 0->2; 0->3; 1->0; 2->1; 3->0;
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