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Computer Science > Logic in Computer Science

arXiv:2509.14089v1 (cs)
[Submitted on 17 Sep 2025]

Title:The Complexity of Deciding Characteristic Formulae Modulo Nested Simulation (extended abstract)

Authors:Luca Aceto, Antonis Achilleos, Aggeliki Chalki, Anna Ingólfsdóttir
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Abstract:This paper studies the complexity of determining whether a formula in the modal logics characterizing the nested-simulation semantics is characteristic for some process, which is equivalent to determining whether the formula is satisfiable and prime. The main results are that the problem of determining whether a formula is prime in the modal logic characterizing the 2-nested-simulation preorder is coNP-complete and is PSPACE-complete in the case of the n-nested-simulation preorder, when n>=3. This establishes that deciding characteristic formulae for the n-nested simulation semantics is PSPACE-complete, when n>=3. In the case of the 2-nested simulation semantics, that problem lies in the complexity class DP, which consists of languages that can be expressed as the intersection of one language in NP and of one in coNP.
Comments: In Proceedings GandALF 2025, arXiv:2509.13258. A full version of this paper, containing all proofs, appears at arXiv:2505.22277
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:2509.14089 [cs.LO]
  (or arXiv:2509.14089v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2509.14089
Journal reference: EPTCS 428, 2025, pp. 13-28
Related DOI: https://doi.org/10.4204/EPTCS.428.3

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Wed, 17 Sep 2025 15:32:23 UTC (60 KB)
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