Injective hardness condition for PCSPs
Computational Complexity
2024-05-20 v1
Abstract
We present a template for the Promise Constraint Satisfaction Problem (PCSP) which is NP-hard but does not satisfy the current state-of-the-art hardness condition [ACMTCT'21]. We introduce a new "injective" condition based on the smooth version of the layered PCP Theorem and use this new condition to confirm that the problem is indeed NP-hard. In the second part of the article, we establish a dichotomy for Boolean PCSPs defined by templates with polymorphisms in the set of linear threshold functions. The reasoning relies on the new injective condition.
Keywords
Cite
@article{arxiv.2405.10774,
title = {Injective hardness condition for PCSPs},
author = {Demian Banakh and Marcin Kozik},
journal= {arXiv preprint arXiv:2405.10774},
year = {2024}
}
Comments
To be published in LICS'24