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By Edmund M. Clarke, Paolo Zuliani (auth.), Tevfik Bultan, Pao-Ann Hsiung (eds.)

This publication constitutes the refereed court cases of the ninth foreign Symposium on computerized expertise for Verification and research, ATVA 2011, held in Taipei, Taiwan, in October 2011.
The 23 revised normal papers provided including five invited papers, eleven brief papers, and a couple of device papers, have been conscientiously reviewed and chosen from seventy five submissions. The papers handle all theoretical and sensible points of automatic research, verification and synthesis; therefore supplying a discussion board for interplay among the local and the foreign learn groups and within the field.

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Additional resources for Automated Technology for Verification and Analysis: 9th International Symposium, ATVA 2011, Taipei, Taiwan, October 11-14, 2011. Proceedings

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Supported by the Engineering and Physical Sciences Research Council (EPSRC) under grants no. EP/G051100/1 and EP/H017585/1. T. -A. ): ATVA 2011, LNCS 6996, pp. 28–42, 2011. c Springer-Verlag Berlin Heidelberg 2011 Making Software Verification Tools Really Work 29 We believe that a long-term vision for the field is to produce verification tools that are a necessary component of any serious development environment. Despite current success stories, formal verification using model checking based techniques is a long way from such mainstream adoption.

A path π of a tree T is a prefix-closed set π ⊆ T such that ε ∈ π and for every x ∈ π, either x is a leaf or there exists a unique c ∈ such that x · c ∈ π. A path is full if it contains a leaf. An edge in T is a pair x, x · c ∈ T × T . The set of edges in T is denoted Edge(T ). We sometimes refer to a path π as a sequence of edges. Then, we say that an edge x, x · c is in π iff both x and x · c are in π. Given an alphabet Σ, a weighted Σ-labeled tree is a triple T, V, C , where T is a tree, V : T → Σ maps each node of T to a letter in Σ, and C : Edge(T ) → maps each edge of T to a cost in .

For every word w, we have that max{La (w), Lb (w)} = |w| − min{La (w), Lb (w)}. It is easy to construct an automaton B the recognizes the language L(w) = |w|. By Lemma 3, NWAs are closed under addition. By adding A and B we obtain an NWA C such that LC (w) = |w| − min{La (w), Lb (w)} = max{La (w), Lb (w)}. So, C is an NWA that recognizes max{La , Lb }, contradicting the fact that no such NWA exists. The proof for max-UWAs is dual. 22 4 S. Almagor and O. Kupferman The Sum Semantics Recall that in a sum-AWA A, the value of a run is the sum of all the costs in the run tree.

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