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Pré-Publication, Document De Travail Année : 2023

Hardness of monadic second-order formulae over succinct graphs

Résumé

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.
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Dates et versions

hal-03978957 , version 1 (08-02-2023)
hal-03978957 , version 2 (13-06-2024)

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Guilhem Gamard, Pierre Guillon, Kévin Perrot, Guillaume Theyssier. Hardness of monadic second-order formulae over succinct graphs. 2023. ⟨hal-03978957v2⟩
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