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Computer Science > Computational Complexity

arXiv:2302.04522 (cs)
[Submitted on 9 Feb 2023 (v1), last revised 18 Jun 2024 (this version, v2)]

Title:Hardness of monadic second-order formulae over succinct graphs

Authors:Guilhem Gamard (MOCQUA), Pierre Guillon (I2M), Kévin Perrot (LIS), Guillaume Theyssier (I2M)
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Abstract:Our main result is a succinct counterpoint to Courcelle's meta-theorem as follows: every arborescent monadic second-order (MSO) property is either NP-hard or coNP-hard over graphs given by succinct representations. Succint representations are Boolean circuits computing the adjacency relation. Arborescent properties are those which have infinitely many models and countermodels with bounded treewidth. Moreover, we explore what happens when the arborescence condition is dropped and show that, under a reasonable complexity assumption, the previous dichotomy fails, even for questions expressible in first-order logic.
Subjects: Computational Complexity (cs.CC); Logic in Computer Science (cs.LO)
Cite as: arXiv:2302.04522 [cs.CC]
  (or arXiv:2302.04522v2 [cs.CC] for this version)
  https://doi.org/10.48550/arXiv.2302.04522

Submission history

From: Guillaume Theyssier [view email] [via CCSD proxy]
[v1] Thu, 9 Feb 2023 09:30:28 UTC (30 KB)
[v2] Tue, 18 Jun 2024 08:00:44 UTC (32 KB)
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