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Pspace-Completeness of the Temporal Logic of Sub-Intervals and Suffixes

Authors Laura Bozzelli, Angelo Montanari, Adriano Peron, Pietro Sala

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Author Details

Laura Bozzelli
  • University of Napoli "Federico II", Italy
Angelo Montanari
  • University of Udine, Italy
Adriano Peron
  • University of Napoli "Federico II", Italy
Pietro Sala
  • University of Verona, Italy

Acknowledgements

The open access publication of this article was supported by the Alpen-Adria-Universität Klagenfurt, Austria.

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Laura Bozzelli, Angelo Montanari, Adriano Peron, and Pietro Sala. Pspace-Completeness of the Temporal Logic of Sub-Intervals and Suffixes. In 28th International Symposium on Temporal Representation and Reasoning (TIME 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 206, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.TIME.2021.9

Abstract

In this paper, we establish Pspace-completeness of the finite satisfiability and model checking problems for the fragment of Halpern and Shoham interval logic with modality ⟨E⟩, for the "suffix" relation on pairs of intervals, and modality ⟨D⟩, for the "sub-interval" relation, under the homogeneity assumption. The result significantly improves the Expspace upper bound recently established for the same fragment, and proves the rather surprising fact that the complexity of the considered problems does not change when we add either the modality for suffixes (⟨E⟩) or, symmetrically, the modality for prefixes (⟨B⟩) to the logic of sub-intervals (featuring only ⟨D⟩).

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • Interval temporal logic
  • Satisfiability
  • Model checking

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