# Büchi Automata Optimisations Formalised in Isabelle/HOL

Abstract : In applications of automata theory, one is interested in reductions in the size of automata that preserve the recognised language. For Büchi automata, two optimisations have been proposed: bisimulation reduction, which computes equivalence classes of states and collapses them, and $a$-balls reduction, which collapses strongly connected components (SCCs) of an automaton that only contain one single letter as edge label. In this paper, we present a formalisation of these algorithms in Isabelle/HOL, providing a formally verified implementation.
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Alexander Schimpf, Jan-Georg Smaus. Büchi Automata Optimisations Formalised in Isabelle/HOL. 6th Indian Conference on Logics and its Applications (ICLA 2015), Jan 2015, Mumbai, India. pp.158-169, ⟨10.1007/978-3-662-45824-2_11⟩. ⟨hal-01782564⟩

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