Constraint Satisfaction with Weakly Oligomorphic Template

Maximal Infinite-Valued Constraint Languages

We systematically investigate the computational complexity of constraint satisfaction problems for constraint languages over an infinite domain. In particular, we study a generalization of the well-established notion of maximal constraint languages from finite to infinite domains. If the constraint language can be defined with an ω-categorical structure, then maximal constraint languages are in...

Weakly Oligomorphic Clones

Equations in oligomorphic clones and the Constraint Satisfaction Problem for $ω$-categorical structures

There exist two conjectures for constraint satisfaction problems (CSPs) of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain non-trivial linear identity modulo outer embeddings. The second conjecture, challenging the a...

Spatial Template Recognition Learning Complexity and Implementation

This report details three aspects of work in progress involving the automatic or interactive recogin tion of spatial templates using constraint satisfaction techniques The rst section discusses the incorporation of information about template models acquired through interactive search for tem plate instances into updated models a preliminary study the complexity of the spatial template recogniti...

Non-dichotomies in Constraint Satisfaction Complexity

We show that every computational decision problem is polynomialtime equivalent to a constraint satisfaction problem (CSP) with an infinite template. We also construct for every decision problem L an ω-categorical template Γ such that L reduces to CSP(Γ ) and CSP(Γ ) is in coNP (i.e., the class coNP with an oracle for L). CSPs with ω-categorical templates are of special interest, because the uni...