Stubborn Sets for Simple Linear Time Properties
- Cite this paper as:
- Lehmann A., Lohmann N., Wolf K. (2012) Stubborn Sets for Simple Linear Time Properties. In: Haddad S., Pomello L. (eds) Application and Theory of Petri Nets. PETRI NETS 2012. Lecture Notes in Computer Science, vol 7347. Springer, Berlin, Heidelberg
We call a linear time property simple if counterexamples are accepted by a Büchi automaton that has only singleton strongly connected components. This class contains interesting properties such as LTL formulas \(G(\varphi \implies F \psi)\) or ϕU ψ which have not yet received support beyond general LTL preserving approaches.
We contribute a stubborn set approach to simple properties with the following ingredients. First, we decompose the verification problem into finitely many simpler problems that can be independently executed. Second, we propose a stubborn set method for the resulting problems that does neither require cycle detection, nor stuttering invariance, nor existence of transitions that are invisible to all atomic propositions. This means that our approach is applicable in cases where traditional approaches fail. Third, we show that sufficient potential is left in existing implementations of the proposed conditions by exploiting all the available nondeterminism in these procedures. We employ a translation to integer linear programming (ILP) for supporting this claim.
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