
Ordered graphs of bounded twinwidth
We consider hereditary classes of graphs equipped with a total order. We...
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On the Complexity of Existential Positive Queries
We systematically investigate the complexity of model checking the exist...
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Query Preserving Watermarking Schemes for Locally Treelike Databases
Watermarking is a way of embedding information in digital documents. Muc...
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FO model checking of geometric graphs
Over the past two decades the main focus of research into firstorder (F...
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Courcelle's Theorem Made Dynamic
Dynamic complexity is concerned with updating the output of a problem wh...
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The Expressiveness of Looping Terms in the Semantic Programming
We consider the complexity of reasoning in extensions of the language of...
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Initial Limit Datalog: a New Extensible Class of Decidable Constrained Horn Clauses
We present initial limit Datalog, a new extensible class of constrained ...
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ModelChecking on Ordered Structures
We study the modelchecking problem for first and monadic secondorder 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 paper we continue this line of research and study modelchecking for first and monadic secondorder 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 orderinvariant monadic secondorder formulas on the same classes of graphs as in the unordered case. For firstorder logic, we obtain tractability of successorinvariant formulas on classes whose Gaifman graphs have bounded expansion. Furthermore, we show that modelchecking for orderinvariant firstorder formulas is tractable on coloured posets of bounded width.
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