Construction of Büchi Automata for LTL Model Checking Verified in Isabelle/HOL

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Abstract

We present the implementation in Isabelle/HOL of a translation of LTL formulae into Büchi automata. In automaton-based model checking, systems are modelled as transition systems, and correctness properties stated as formulae of temporal logic are translated into corresponding automata. An LTL formula is represented by a (generalised) Büchi automaton that accepts precisely those behaviours allowed by the formula. The model checking problem is then reduced to checking language inclusion between the two automata. The automaton construction is thus an essential component of an LTL model checking algorithm. We implemented a standard translation algorithm due to Gerth et al. The correctness and termination of our implementation are proven in Isabelle/HOL, and executable code is generated using the Isabelle/HOL code generator.