An Automata Theoretic Approach to Temporal Logic

A syntax directed mapping is presented from Propositional Temporal Logic (PTL) formulae to Müller type finite automata. This is a direct and much more elegant and easier to implement approach than previously described methods. Most of these methods are based on tableau methods for satisfiability checking, and after that a Büchi type of automaton is extracted. Büchi and Müller automata are equally expressive. However, Müller automata have nicer properties than Büchi automata, for instance deterministic Müller automata are expressive as non-deterministic ones, while this is not true for Büchi automata. Also deterministic Büchi automata are not closed under complement. This transformation is the first step in a decision procedure, since the resulting Müller automaton represents the models of the temporal logic formula, and on which further verification and analysis can be performed.