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|Title:||Constraint satisfaction problems and related logic|
|Presented at:||University of Leicester|
|Abstract:||Feder and Vardi have proved that the class captured by a monadic fragment of existential second-order logic, MMSNP, is computationally equivalent (via randomised reductions) to the class of constraint satisfaction problems (CSP) while the latter is strictly included in the former. I introduce a new class of combinatorial problems, the so-called forbidden patterns problems (FP), that correspond exactly to the logic MMSNP and introduce some novel algebraic tools like the re-colouring that allow me to construct a normal form. This leads to a constructive characterisation of the borderline of CSP within FP: a given problem in FP is either given as a problem in CSP or we build counter-examples. I relate this result to a recent and independent work by Tardif and Nesetril which relies heavily on a correspondence between duality and density. I generalise this approach to FP. Finally, I investigate homomorphism problems for unary algebras.|
|Rights:||Copyright © the author. All rights reserved.|
|Appears in Collections:||Theses, Dept. of Mathematics|
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