Efficient Büchi Automata from LTL Formulae

We present an algorithm to generate small Buchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal within a certain class of translation procedures. The simplification algorithm can be used for Buchi automata in general. It reduces the number of states and transitions, as well as the number and size of the accepting sets—possibly reducing the strength of the resulting automaton. This leads to more efficient model checking of linear-time logic formulae. We compare our method to previous work, and show that it is significantly more efficient for both random formulae, and formulae in common use and from the literature.

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