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Expressiveness of propositional projection temporal logic with star. (English) Zbl 1221.03018
Summary: This paper investigates the expressiveness of propositional projection temporal logic with star (PPTL\(^*\)). To this end, Büchi automata and \(\omega \)-regular expressions are first extended as stutter Büchi automata (SBA) and extended regular expressions (ERE) to include both finite and infinite strings. Further, by equivalent transformations among PPTL\(^*\) formulas, SBAs and EREs, PPTL\(^*\) is proved to represent exactly the full regular language. Moreover, some fragments of PPTL\(^*\) are characterized and, finally, PPTL\(^*\) and its fragments are classified into five different language classes.

MSC:
03B44 Temporal logic
03C05 Equational classes, universal algebra in model theory
68Q45 Formal languages and automata
68Q60 Specification and verification (program logics, model checking, etc.)
Software:
SPIN
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