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# l3 - CS 267 Automated Verification Lecture 3 CTL model...

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CS 267: Automated Verification Lecture 3: CTL model checking algorithm, counter-example generation Instructor: Tevfik Bultan

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Automated Verification of Finite State Systems [Clarke and Emerson 81], [Queille and Sifakis 82] CTL Model checking problem: Given a transition system T = (S, I, R), and a CTL formula f, does the transition system satisfy the property? CTL model checking problem can be solved in O(|f| × (|S|+|R|)) Note that the complexity is linear in the size of the formula and the transition system Recall that the size of the transition system is exponential in the number of variables and concurrent components (this is called the state space explosion problem)
CTL Model Checking Algorithm Translate the formula to a formula which uses the basis EX p, EG p, p EU q Start from the innermost subformulas Label the states in the transition system with the subformulas that hold in that state Initially states are labeled with atomic properties Each (temporal or boolean) operator has to be processed once Processing of each operator takes O(|S|+|R|)

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CTL Model Checking Algorithm Boolean operators are easy ¬ p : Each state which is not labeled with p should be labeled with ¬ p p q : Each state which is labeled with both p and q should be labeled with p q p q : Each state which is labeled with p or q should be labeled with p q
CTL Model Checking Algorithm: EX p EX p is easy to do in O(|S|+|R|) All the nodes which have a next state labeled with p should be labeled with EX p s2 s1 s4 s3 p p p, EX p p, EX p EX p s2 s1 s4 s3

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