On the Complexity of Model Checking Knowledge and Time-Reference-Cited by-同舟云学术

On the Complexity of Model Checking Knowledge and Time

Published:2024-01-16 Issue:1 Volume:25 Page:1-42
ISSN:1529-3785
Container-title:ACM Transactions on Computational Logic
language:en
Short-container-title:ACM Trans. Comput. Logic

Author:

Bozzelli Laura¹^ORCID,Maubert Bastien¹^ORCID,Murano Aniello¹^ORCID

Affiliation:

1. Università degli Studi di Napoli Federico II, Italy

Abstract

We establish the precise complexity of the model-checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for 20 years. We close it by establishing improved upper bounds for CTL * with knowledge and providing matching lower bounds that also apply for epistemic extensions of LTL and CTL . We also study the model-checking problem for these logics on systems satisfying the “no learning” property, introduced by Halpern and Vardi in their taxonomy of logics of knowledge and time, and we settle the complexity in almost all cases.

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

Link

https://dl.acm.org/doi/pdf/10.1145/3637212

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