Abstract
In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties and transformations of Muller automata. We present the first practical implementation of the ACD in two different tools, Owl and Spot, and adapt it to the framework of Emerson-Lei automata, i.e., \(\omega \)-automata whose acceptance conditions are defined by Boolean formulas. The ACD provides a transformation of Emerson-Lei automata into parity automata with strong optimality guarantees: the resulting parity automaton is minimal among those automata that can be obtained by duplication of states. Our empirical results show that this transformation is usable in practice. Further, we show how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for \(\omega \)-automata.
Salomon Sickert is supported in part by the Deutsche Forschungsgemeinschaft (DFG) under project number 436811179, and in part funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 787367 (PaVeS)
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Casares, A., Duret-Lutz, A., Meyer, K.J., Renkin, F., Sickert, S. (2022). Practical Applications of the Alternating Cycle Decomposition. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13244. Springer, Cham. https://doi.org/10.1007/978-3-030-99527-0_6
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