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The universal-algebraic approach has proved a powerful tool in the study of the computational complexity of constraint satisfaction problems (CSPs). This approach has previously been applied to the study of CSPs with finite or (infinite) ω-categorical templates. Our first result is an exact characterization of those CSPs that can be formulated with (a finite or) an ω-categorical template. The universal-algebraic...
We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(B). We introduce subjective hyper-endomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through...
We study two containment problems related to the quantified constraint satisfaction problem (QCSP). Firstly, we give a combinatorial condition on finite structures A and B that is necessary and sufficient to render QCSP(A) a subset of QCSP(B). The required condition is the existence of a positive integer r such that there is a surjective homomorphism from the power structure A^r to B. We note that...
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