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Automated Technology for Verification and Analysis: 8th by Krishnendu Chatterjee, Thomas A. Henzinger (auth.), Ahmed

By Krishnendu Chatterjee, Thomas A. Henzinger (auth.), Ahmed Bouajjani, Wei-Ngan Chin (eds.)

This booklet constitutes the refereed court cases of the eighth foreign Symposium on automatic expertise for Verification and research, ATVA 2010, held in Singapore, in September 2010. The publication comprises three invited talks, 21 ordinary papers and nine software papers.

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Extra resources for Automated Technology for Verification and Analysis: 8th International Symposium, ATVA 2010, Singapore, September 21-24, 2010. Proceedings

Sample text

We say that a language L is in a class γ if L is γ-recognizable; that is, L can be recognized by an automaton in the class γ. Given two classes γ and η we say that γ is more expressive than η if every η-recognizable language is also γ-recognizable. If γ is not more expressive than η and η is not more expressive than γ, we say that γ and η are incomparable. Different classes of automata have different expressive power. In particular, NBWs recognize all ω-regular languages, while NCWs are strictly less expressive [18].

Theorem 3. NPBW are NBW-type: if A is an automaton such that L(AP ) is ω-regular, then L(AP ) = L(AB ). Proof. Since both L(AP ) and L(AB ) are ω-regular, so is their difference, and thus there is an NBW A such that L(A ) = L(AB ) \ L(AP ). We prove that L(A ) = ∅. Assume by way of contradiction that L(A ) = ∅. Then A accepts also a periodic word, thus there are u, v ∈ Σ ∗ such that u · v ω ∈ L(AB ) \ L(AP ). Let r be an accepting run of AB on u · v ω . Thus, inf (r) ∩ α = ∅. Hence, there are indices i < j such that r visits α between reading u · v i and u · v j , and such that r(uv i ) = r(uv j ).

Lemma 1. The relation ≡A is an equivalence relation with at most 3(|Q| alence classes. 2 ) equiv- Lemma 2. Consider an NPBW A. Let m denote the number of equivalence classes of ≡A . Consider a word w ∈ Σ m . There exist s ∈ Σ ∗ and z ∈ Σ + such that s ≺ z w, and s ≡A z. Promptness in ω-Regular Automata 31 Proof. Since ≡A has m equivalence classes, every set of m + 1 words must contain at least two ≡A -equivalent words. 2], . . m]}. Theorem 6. Consider an automaton A. Let m denote the number of equivalence classes of ≡A .

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