CSPs with global modular constraints: algorithms and hardness via polynomial representations

@article{Brakensiek2019CSPsWG,
  title={CSPs with global modular constraints: algorithms and hardness via polynomial representations},
  author={Joshua Brakensiek and Sivakanth Gopi and Venkatesan Guruswami},
  journal={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing},
  year={2019}
}
We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable Boolean CSPs, this mainly reduces to the study of three cases: 2-SAT, HORN-SAT, and LIN-2 (linear equations mod 2). We classify the moduli M for which these respective problems are polynomial time solvable, and when they are not (assuming the ETH). Our study… Expand
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