License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2020.21
URN: urn:nbn:de:0030-drops-126898
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12689/
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Bozzelli, Laura ; Montanari, Angelo ; Peron, Adriano ; Sala, Pietro

On a Temporal Logic of Prefixes and Infixes

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Abstract

A classic result by Stockmeyer [Stockmeyer, 1974] gives a non-elementary lower bound to the emptiness problem for star-free generalized regular expressions. This result is intimately connected to the satisfiability problem for interval temporal logic, notably for formulas that make use of the so-called chop operator. Such an operator can indeed be interpreted as the inverse of the concatenation operation on regular languages, and this correspondence enables reductions between non-emptiness of star-free generalized regular expressions and satisfiability of formulas of the interval temporal logic of the chop operator under the homogeneity assumption [Halpern et al., 1983]. In this paper, we study the complexity of the satisfiability problem for a suitable weakening of the chop interval temporal logic, that can be equivalently viewed as a fragment of Halpern and Shoham interval logic featuring the operators B, for "begins", corresponding to the prefix relation on pairs of intervals, and D, for "during", corresponding to the infix relation. The homogeneous models of the considered logic naturally correspond to languages defined by restricted forms of regular expressions, that use union, complementation, and the inverses of the prefix and infix relations.

BibTeX - Entry

@InProceedings{bozzelli_et_al:LIPIcs:2020:12689,
  author =	{Laura Bozzelli and Angelo Montanari and Adriano Peron and Pietro Sala},
  title =	{{On a Temporal Logic of Prefixes and Infixes}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Javier Esparza and Daniel Kr{\'a}ΔΎ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12689},
  URN =		{urn:nbn:de:0030-drops-126898},
  doi =		{10.4230/LIPIcs.MFCS.2020.21},
  annote =	{Keywords: Interval Temporal Logic, Star-Free Regular Languages, Satisfiability, Complexity}
}

Keywords: Interval Temporal Logic, Star-Free Regular Languages, Satisfiability, Complexity
Collection: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue Date: 2020
Date of publication: 18.08.2020

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