Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2017) 10168 LNCS 223-235

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We present a minimization algorithm for finite state automata that finds and merges bisimulation-equivalent states, identified through partition aggregation. We show the algorithm to be correct and run in time O(n2d2 |Σ|), where n is the number of states of the input automaton M, d is the maximal outdegree in the transition graph for any combination of state and input symbol, and |Σ| is the size of the input alphabet. The algorithm is slower than those based on partition refinement, but has the advantage that intermediate solutions are also language equivalent to M. As a result, the algorithm can be interrupted or put on hold as needed, and the derived automaton is still useful. Furthermore, the algorithm essentially searches for the maximal model of a characteristic formula for M, so many of the optimisation techniques used to gain efficiency in SAT solvers are likely to apply.

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Björklund, J., & Cleophas, L. (2017). Minimization of finite state automata through partition aggregation. In *Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)* (Vol. 10168 LNCS, pp. 223–235). Springer Verlag. https://doi.org/10.1007/978-3-319-53733-7_16

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