We improve upon the best known upper and lower bounds on the sizes of minimal feedback vertex sets in butterflies. Also, we construct new feedback vertex sets in grids so that for a large number ofâ€¦ (More)

We study non-uniform constraint satisfaction problems where the underlying signature contains constant and function symbols as well as relation symbols. Amongst our results are the following. Weâ€¦ (More)

In the early nineties, Feder and Vardi attempted to find a large sub-class of NP which exhibits a dichotomy; that is, where every problem in the sub-class is either solvable in polynomial-time orâ€¦ (More)

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 andâ€¦ (More)

We show that forbidden patterns problems, when restricted to some classes of input structures, are in fact constraint satisfaction problems. This contrasts with the case of unrestricted inputâ€¦ (More)

We classify completely the complexity of evaluating positive equality-free sentences of first-order logic over a fixed, finite structure D. This problem may be seen as a natural generalisation of theâ€¦ (More)

2015 30th Annual ACM/IEEE Symposium on Logic inâ€¦

2015

Inspired by computational complexity results for the quantified constraint satisfaction problem, we study the clones of idem potent polymorphisms of certain digraph classes. Our first results are twoâ€¦ (More)

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 nonuniformâ€¦ (More)