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

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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.

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  1. Département d’Informatique, Université Libre de Bruxelles, Boulevard du Triomphe CP 212, 1050, Bruxelles, Belgium

    Nicolas Markey

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  1. Nicolas Markey
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Correspondence to Nicolas Markey.

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Received: 4 September 2002, Published online: 17 March 2004

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Markey, N. Past is for free: on the complexity of verifying linear temporal properties with past. Acta Informatica 40, 431–458 (2004). https://doi.org/10.1007/s00236-003-0136-5

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  • DOI: https://doi.org/10.1007/s00236-003-0136-5

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