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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.

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.)
Full Text: DOI
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