Computing Bottom SCCs Symbolically Using Transition Guided Reduction

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Authors

BENEŠ Nikola BRIM Luboš PASTVA Samuel ŠAFRÁNEK David

Year of publication 2021
Type Article in Proceedings
Conference Computer Aided Verification - 33rd International Conference, CAV 2021
MU Faculty or unit

Faculty of Informatics

Citation
Web https://link.springer.com/chapter/10.1007/978-3-030-81685-8_24
Doi http://dx.doi.org/10.1007/978-3-030-81685-8_24
Keywords Bottom SCC; Symbolic algorithm; Boolean network
Description Detection of bottom strongly connected components (BSCC) in state-transition graphs is an important problem with many applications, such as detecting recurrent states in Markov chains or attractors in dynamical systems. However, these graphs’ size is often entirely out of reach for algorithms using explicit state-space exploration, necessitating alternative approaches such as the symbolic one. Symbolic methods for BSCC detection often show impressive performance, but can sometimes take a long time to converge in large graphs. In this paper, we provide a symbolic state-space reduction method for labelled transition systems, called interleaved transition guided reduction (ITGR), which aims to alleviate current problems of BSCC detection by efficiently identifying large portions of the non-BSCC states. We evaluate the suggested heuristic on an extensive collection of 125 real-world biologically motivated systems. We show that ITGR can easily handle all these models while being either the only method to finish, or providing at least an order-of-magnitude speedup over existing state-of-the-art methods. We then use a set of synthetic benchmarks to demonstrate that the technique also consistently scales to graphs with more than 2^1000 vertices, which was not possible using previous methods.
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