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Showing 1 to 6 of 6 for “"Finite Model Theory"”.
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Game comonads and beyond: compositional constructions for logic and algorithms
… of category theoretic methods to the fields of finite model theory and descriptive complexity. First introduced by Abramsky, Dawar and Wang in 2017, these new constructions exposed connections between Spoiler-Duplicator games used in logic, related algorithms for constraint satisfaction and …
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Average-case complexity of detecting cliques
… is known. Our results show that, in certain models of computation, solving k-CLIQUE in the average case requires Q(nk/4) resources (moreover, k/4 is tight). Here the models of computation are bounded-depth Boolean circuits and unbounded-depth monotone circuits, the complexity measure is the …
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Symmetric Circuits and Model-Theoretic Logics
… is arguably the most important open question in finite model theory. The study of extensions of fixed-point logic are of central importance to this question. It was shown by Anderson and Dawar that fixed-point logic with counting (FPC) has the same expressive power as uniform families of …
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Descriptive complexity of constraint problems
… constraint satisfaction problems (CSPs), which model strictly decision problems, and so-called valued constraint satisfaction problems (VCSPs), which also include optimisation problems. A key open problem in this field is the long-standing dichotomy conjecture by Feder and Vardi. It claims that …
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Logic, Learning, and Explanation: Theoretical and Applied Perspectives on Machine Reasoning
… methods for GNNs, and the use of Large Language Models (LLMs) in legal reasoning. The first part develops a novel Ehrenfeucht-Fraïssé game tailored to counting logic with a bounded number of variables, which characterizes formula size. This provides the first known formula size lower bound in …
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From game comonads to dynamical systems: property-preserving maps as a logical unifying principle
… are essential for achieving results such as the finite model property, completeness, and decidability. To a large extent, one must control all manners of structural relations in order to achieve all types of results. We contribute to each of these areas: We extend the use of coKleisli morphisms …