Automated Technology for Verification and Analysis: 13th by Bernd Finkbeiner, Geguang Pu, Lijun Zhang

By Bernd Finkbeiner, Geguang Pu, Lijun Zhang

This ebook constitutes the lawsuits of the thirteenth overseas Symposium on computerized know-how for Verification and research, ATVA 2015, held in Shanghai, China, in October 2015.

The 27 revised papers offered including 6 instrument papers during this quantity have been rigorously reviewed and chosen from ninety five submissions. They exhibit present learn on theoretical and sensible facets of automatic research, verification and synthesis through supplying a global discussion board for interplay one of the researchers in academia and industry.

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Extra info for Automated Technology for Verification and Analysis: 13th International Symposium, ATVA 2015 Shanghai, China, October 12–15, 2015, Proceedings

Example text

E. is not a SP folding equivalence. It can be observed that bd is ∼1 . Whenever two events are merged, their preconditions need not fireable in βL,◇ to be merged to preserved sequential executions. The equivalence relation ∼2 does not only merge events labeled by b, but it also sets p1 ∼2 p2 and is a SP ∼2 can replay every trace in the log L, but folding equivalence. The folded net βL,◇ it also adds new traces of the form a∗ , a∗ b, a∗ bc, a∗ bd, a∗ bcd and a∗ bdc. Given an unfolding, every SP folding equivalence generates a net that preserves its sequential executions.

We start by translating L into a collection of partial orders whose shape depends on the specific definition of ◇. Definition 1. Given a sequence σ ∈ A∗ and an independence relation ◇ ⊆ A×A, we associate to σ a labeled partial order lpo◇ (σ) inductively defined by: 1. If σ = ε, then let ∶= ⟨τ, ∅⟩ and set lpo◇ (σ) ∶= ({ }, ∅). 2. If σ = σ ′ a, then let lpo◇ (σ ′ ) ∶= (E ′ , ≤′ ) and let e ∶= ⟨a, H⟩ be the single event such that H is the unique ⊆-minimal, causally-closed set of events in E ′ satisfying that for any event e′ ∈ E ′ , if λ(e′ ) a, then e′ ∈ H.

We will be needing a few additional notions before we can define the notion of a proof graph. The signature of E, denoted sig(E), is the set {(X, v) | X ∈ bnd(E), v ∈ D}. For given set S ⊆ sig(E), we write Strue (X) for the predicate environment induced by S as follows: Strue (X) = {v ∈ D | (X, v) ∈ S}. We furthermore assume a mapping rankE ( ) which assigns to every bound predicate variable of E a unique natural number that satisfies: – rankE (X) ≤ rankE (Y ) iff the equation for X precedes Y ’s equation in E; – rankE (X) is even iff σX = ν.

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