Abstract
Checking language inclusion between two nondeterministic Büchi automata \(\mathcal A\) and \(\mathcal B\) is computationally hard (PSPACE-complete). However, several approaches which are efficient in many practical cases have been proposed. We build on one of these, which is known as the Ramsey-based approach. It has recently been shown that the basic Ramsey-based approach can be drastically optimized by using powerful subsumption techniques, which allow one to prune the search-space when looking for counterexamples to inclusion. While previous works only used subsumption based on set inclusion or forward simulation on \(\mathcal A\) and \(\mathcal B\), we propose the following new techniques: (1) A larger subsumption relation based on a combination of backward and forward simulations on \(\mathcal A\) and \(\mathcal B\). (2) A method to additionally use forward simulation between \(\mathcal A\) and \(\mathcal B\). (3) Abstraction techniques that can speed up the computation and lead to early detection of counterexamples. The new algorithm was implemented and tested on automata derived from real-world model checking benchmarks, and on the Tabakov-Vardi random model, thus showing the usefulness of the proposed techniques.
This work was supported by Royal Society grant JP080268, the UPMARC project, the CONNECT project, National Science Council of Taiwan project no. 99-2218-E-001-002-MY3, the Czech Science Foundation (projects P103/10/0306 and 102/09/H042), the Czech Ministry of Education (projects COST OC10009 and MSM 0021630528), and the BUT FIT project FIT-S-11-1.
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Abdulla, P.A. et al. (2011). Advanced Ramsey-Based Büchi Automata Inclusion Testing. In: Katoen, JP., König, B. (eds) CONCUR 2011 – Concurrency Theory. CONCUR 2011. Lecture Notes in Computer Science, vol 6901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23217-6_13
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DOI: https://doi.org/10.1007/978-3-642-23217-6_13
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