# Logical compactness and constraint satisfaction problems

@article{Rorabaugh2016LogicalCA, title={Logical compactness and constraint satisfaction problems}, author={Danny Rorabaugh and Claude Tardif and David L. Wehlau}, journal={Log. Methods Comput. Sci.}, year={2016}, volume={13} }

We investigate a correspondence between the complexity hierarchy of constraint satisfaction problems and a hierarchy of logical compactness hypotheses for finite relational structures. It seems that the harder a constraint satisfaction problem is, the stronger the corresponding compactness hypothesis is. At the top level, the NP-complete constraint satisfaction problems correspond to compactness hypotheses that are equivalent to the ultrafilter axiom in all the cases we have investigated. At…

## 4 Citations

### The Power of the Combined Basic Linear Programming and Affine Relaxation for Promise Constraint Satisfaction Problems

- Computer ScienceSIAM J. Comput.
- 2020

In the field of constraint satisfaction problems (CSPs), promise CSPs are an exciting new direction of study and this paper presents a meta-analyses of two promising approaches to this problem.

### The Power of the Combined Basic LP and Affine Relaxation for Promise CSPs

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2020

A simple algorithm which in polynomial time solves the decision problem for all promise CSPs that admit infinitely many symmetric polymorphisms, that is the coordinates are permutation invariant, and it is shown that block symmetrical polymorphisms are not only sufficient but also necessary for this algorithm to work, thus establishing its precise power.

### Hierarchies of Minion Tests for PCSPs through Tensors

- Computer Science, MathematicsSODA
- 2023

In order to analyse the Sum-of-Squares SDP hierarchy, the solvability of the standard SDP relaxation is characterised through a new minion, and the geometry of the tensor spaces arising from the construction are exploited to prove general properties of hierarchies.

### CLAP: A New Algorithm for Promise CSPs

- Computer ScienceSODA
- 2022

It is demonstrated that there arePCSPs solved by CLAP that are not solved by any of the existing algorithms for PCSPs; in particular, not by the BLP+AIP algorithm of Brakensiek et al. and not by a reduction to tractable finite-domain CSPs.

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