An approximation-based incremental SMT approach for diagnosability analysis of real-time systems
Abstract In this article, we focus on improving the efficiency of diagnosability checking for real-time systems modeled as timed automata. Inspired by a recently introduced extension of the classic CEGAR (CounterExample-Guided Abstraction Refinement) algorithm, namely the RECAR (Recursive Explore and Check Abstraction Refinement) algorithm, we propose new RECAR-like algorithms that combine over-approximation and under-approximation techniques. We use CEGAR to quickly terminate the refinement loop by over-approximation and under-approximation, in the case where the original formula is respectively satisfiable or unsatisfiable, and then show the soundness of our RECAR-like approach applied to an arbitrary formula. We define then several types of parameterized over- and under-approximations along with refinement strategies for the diagnosability problem. Finally, we evaluate the effectiveness of our method and its implementation with the Z3 SMT solver on different benchmarks by comparing it to the direct method without approximation shortcuts.
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Recently, it has been proposed to use approximation techniques in the context of decision procedures for the quantifier-free theory of fixed-size bit-vectors. We discuss existing and novel variants of under-approximation techniques. Under-approximations produce smaller models and may reduce solving time significantly. We propose a new technique that allows early termination of an under-approximation refinement loop, although the original formula is unsatisfiable. Moreover, we show how over-approximation and under-approximation techniques can be combined. Finally, we evaluate the effectiveness of our approach on array and bit-vector benchmarks of the SMT library.KeywordsModel CheckDecision ProcedureSmall ModelTest Case GenerationOriginal FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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