Sandwiches for Promise Constraint Satisfaction
Abstract
Promise Constraint Satisfaction Problems (PCSP) were proposed recently by Brakensiek and Guruswami arXiv:1704.01937 as a framework to study approximations for Constraint Satisfaction Problems (CSP). Informally a PCSP asks to distinguish between whether a given instance of a CSP has a solution or not even a specified relaxation can be satisfied. All currently known tractable PCSPs can be reduced in a natural way to tractable CSPs. Barto arXiv:1909.04878 presented an example of a PCSP over Boolean structures for which this reduction requires solving a CSP over an infinite structure. We give a first example of a PCSP over Boolean structures which reduces to a tractable CSP over a structure of size but not smaller. Further we investigate properties of PCSPs that reduce to systems of linear equations or to CSPs over structures with semilattice or majority polymorphism.
Cite
@article{arxiv.2003.07487,
title = {Sandwiches for Promise Constraint Satisfaction},
author = {Guofeng Deng and Ezzeddine El Sai and Trevor Manders and Peter Mayr and Poramate Nakkirt and Athena Sparks},
journal= {arXiv preprint arXiv:2003.07487},
year = {2020}
}