From LTL Formulae to B?chi Automata: A Direct Translation Using On-the-Fly De-Generalization

In this paper, we present a conversion algorithm to translate a linear temporal logic (LTL) formula to a Büchi automaton (BA) directly. A label, acceptance degree (AD), is presented to record acceptance conditions satisfied in each state or transition of an automaton. The AD for an automaton is a set of {U, F, R, G}-subformula of the given LTL formula. According to ADs attached to states and transitions, the on-the-fly de-generalization algorithm is presented. This on-the-fly de-generalization algorithm is used to transform a generalized Büchi automaton (GBA) into a Büchi automaton. It is different from the execution of the classic de-generalization algorithm that the on-the-fly de-generalization algorithm is performed during the expansion of the given LTL formula. A direct conversion algorithm based on the on-the-fly de-generalization algorithm is conceived and implemented. We compare the conversion algorithm presented in this paper with previous works, and show that it is more efficient for a series of formulae in usual use and random formulae generated by LBTT 1.2.1 (an LTL-to-BA translator testbench).