U488065.pdf (8.07 MB)
Constraint satisfaction problems and related logic
thesis
posted on 2014-12-15, 10:40 authored by Florent MadelaineFeder 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.
History
Date of award
2003-01-01Author affiliation
MathematicsAwarding institution
University of LeicesterQualification level
- Doctoral
Qualification name
- PhD