Download Automated Technology for Verification and Analysis: 6th by Sriram K. Rajamani (auth.), Sungdeok (Steve) Cha, Jin-Young PDF

By Sriram K. Rajamani (auth.), Sungdeok (Steve) Cha, Jin-Young Choi, Moonzoo Kim, Insup Lee, Mahesh Viswanathan (eds.)

This e-book constitutes the refereed lawsuits of the sixth overseas Symposium on computerized expertise for Verification and research, ATVA 2008, held in Seoul, Korea, in October 2008.

The 21 revised complete papers five brief papers and seven device papers provided including three invited talks have been conscientiously reviewed and chosen from eighty two submissions. The focos lies on theoretical the right way to in achieving right software program or structures, together with either practical and non useful facets; in addition to on functions of concept in engineering tools and specific domain names and dealing with of sensible difficulties taking place in instruments. The papers are equipped in topical sections on version checking, software program verification, determination systems, linear-time research, device demonstration papers, timed and stochastic platforms, concept, and brief papers.

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Extra resources for Automated Technology for Verification and Analysis: 6th International Symposium, ATVA 2008, Seoul, Korea, October 20-23, 2008. Proceedings

Example text

We introduce the relation |=R which differs from the finer relation |=ed only ed for the formulas of the type E >k Gψ1 and E >k ψ1 Uψ2 . In particular, we require ˆ the existence of k + 1 pairwise R-edge-disjoint paths satisfying Gψ1 or ψ1 Uψ2 . Then, the subset-edge-disjoint graded-CTL model-checking requires to ˆ ˆ verify whether (K, sin ) |=R ed ϕ, for a Kripke structure K, a set R ⊆ R, and a graded-CTL formula ϕ. The lower bound to this problem obviously matches the lower bound of the edge-disjoint graded-CTL model-checking problem.

K belongs to Sψ . Finally let us now prove Claim 2. (if ): Let s ∈ Sψ and C = v0 , . . , vh−1 be a non-sink-cycle, reachable from s via a finite path s, u0 , . . , ui , v0 . Let vj , for 0 ≤ j ≤ h − 1, be an exitnode of C connected to a node w0 ∈ Sψ such that w0 = v(j+1) mod h and (vj , w0 ) ∈ Rψ . Since (K, w0 ) |= E >0 ψ1 Uψ2 , then in Gψ there is a finite path w0 , . . , wr starting from w0 and ending in a wr such that (K, wr ) |= ψ2 . Consider the k + 1 pairwise distinct finite paths πl , 0 ≤ l ≤ k, defined as πl = s, u0 , .

Therefore we obtain the following theorem. Theorem 4. There is an algorithm to solve the edge-disjoint graded-CTL modelchecking problem in space O(|R| · |S| + |ϕ|). 2 A Fragment One question that naturally arises from Theorem 3 is whether it is possible to define interesting fragments of graded-CTL for which the edge-disjoint gradedCTL model-checking problem can be solved in polynomial-time. In particular, the proof of Theorem 3 suggests that only formulas of the type E >k Gϕ, with k > 0, are “hard” to verify.

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