Model-Checking on Ordered Structures
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Publication date
2020Author
Abstract
We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but it does become tractable on interesting classes of structures, such as on classes whose Gaifman graphs have bounded treewidth. In this article, we continue this line of research and study model-checking for first- and monadic second-order logic in the presence of an ordering on the input structure. We do so in two settings: the general ordered case, where the input structures are equipped with a fixed order or successor relation, and the order-invariant case, where the formulas may resort to an ordering, but their truth must be independent of the particular choice of order. In the first setting we show very strong intractability results for most interesting classes of structures. In contrast, in the order-invariant case we obtain tractability results for order-invariant monadic second-order formulas on the same classes of graphs as in the unordered case. For first-order logic, we obtain tractability of successor-invariant formulas on classes whose Gaifman graphs have bounded expansion. Furthermore, we show that model-checking for order-invariant first-order formulas is tractable on coloured posets of bounded width.
Patrocinador
European Research Council (ERC)
648527
CE-ITI
European Associated Laboratory "Structures in Combinatorics" (LEA STRUCO)
P202/12/G061
National Science Centre of Poland
UMO-2015/19/P/ST6/03998
European Union (EU)
665778
CONICYT, PIA/Concurso Apoyo a Centros Cientificos y Tecnologicos de Excelencia con Financiamiento Basal
AFB170001
ERCCZ LL-1201
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Artículo de publicación ISI Artículo de publicación SCOPUS
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ACM Transactions on Computational Logic, 21 (2020): article 11
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