Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 9 of 9 for “"Finite Model Theory"”.
-
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 …
-
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 …
-
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 …
-
Pure and applied fixed point logics
… mappings. They are particularly well suited for modelling recursion in logical languages and consequently they have found applications in various areas of theoretical computer science such as database theory, finite model theory, and computer-aided verification. The topic of this thesis is the …
-
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 …
-
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 …
-
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 …
-
Logic and games on automatic structures
… formulas of first and second-order logic on finite structures. We extend the game-based algorithmic approach to first-order logic on infinite structures that arise in computer science. Such structures are stored and manipulated by a computer, thus elements and relations must be represented in …