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تسجيل مستخدم جديدProving Non-Inclusion of Buchi Automata based on Monte Carlo Sampling
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The search for a proof of correctness and the search for counterexamples (bugs) are complementary aspects of verification. In order to maximize the practical use of verification tools it is better to pursue them at the same time. While this is well-understood in the termination analysis of programs, this is not the case for the language inclusion analysis of Buchi automata, where research mainly focused on improving algorithms for proving language inclusion, with the search for counterexamples left to the expensive complementation operation. In this paper, we present $mathsf{IMC}^2$, a specific algorithm for proving Buchi automata non-inclusion $mathcal{L}(mathcal{A}) otsubseteq mathcal{L}(mathcal{B})$, based on Grosu and Smolkas algorithm $mathsf{MC}^2$ developed for Monte Carlo model checking against LTL formulas. The algorithm we propose takes $M = lceil ln delta / ln (1-epsilon) rceil$ random lasso-shaped samples from $mathcal{A}$ to decide whether to reject the hypothesis $mathcal{L}(mathcal{A}) otsubseteq mathcal{L}(mathcal{B})$, for given error probability $epsilon$ and confidence level $1 - delta$. With such a number of samples, $mathsf{IMC}^2$ ensures that the probability of witnessing $mathcal{L}(mathcal{A}) otsubseteq mathcal{L}(mathcal{B})$ via further sampling is less than $delta$, under the assumption that the probability of finding a lasso counterexample is larger than $epsilon$. Extensive experimental evaluation shows that $mathsf{IMC}^2$ is a fast and reliable way to find counterexamples to Buchi automata inclusion.
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