Past is for free: on the complexity of verifying linear temporal properties with past

Authors:
Nicolas Markey
Affiliations:
Université Libre de Bruxelles, Département d’Informatique, Belgium
Venue:
Acta Informatica
Year:
2004

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Abstract

We study the complexity of satisfiability and model checking problems for fragments of linear-time temporal logic with past (PLTL). We consider many fragments of PLTL, obtained by restricting the set of allowed temporal modalities, the use of negations or the nesting of future formulas into past formulas. Our results strengthen the widely accepted fact that “past is for free”, in the sense that allowing symmetric past-time modalities does not bring additional theoretical complexity. This result holds even for small fragments and even when nesting future formulas into past formulas.