Practical Applications of the Alternating Cycle Decomposition

Abstract In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties transformations of Muller automata. We present first practical implementation ACD in two different tools, Owl Spot, adapt it framework Emerson-Lei automata, i.e., $$\omega $$ ω -automata whose acceptance conditions are defined by Boolean formulas. The provides a transformation automata into parity with strong optimality guarantees: resulting automaton is minimal among those that can be obtained duplication states. Our empirical results show this usable practice. Further, we how generalize many other specialized constructions such as deciding typeness degeneralization generalized Büchi providing algorithms for -automata.