On the Complexity of Convex and Reverse Convex Prequadratic Constraints

19 pages•Published: June 3, 2023

Rodrigo Raya, Jad Hamza and Viktor Kuncak

Abstract

Motivated by satisfiability of constraints with function symbols, we consider numerical inequalities on non-negative integers. The constraints we address are a conjunction of a linear system Ax = b and an arbitrary number of (reverse) convex constraints of the form xi ≥ xdj (xi ≤ xdj ). We show that the satisfiability of these constraints is NP-complete even if the solution to the linear part is given explicitly. As a consequence, we obtain NP- completeness for an extension of certain quantifier-free constraints on sets with cardinalities and function images.

Keyphrases: automated reasoning, computational complexity, non linear arithmetic, satisfiability modulo theories

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 350-368.

Links:	https://easychair.org/publications/paper/T6kG
	https://doi.org/10.29007/wdd7

BibTeX entry

@inproceedings{LPAR2023:Complexity_Convex_Reverse_Convex,
  author    = {Rodrigo Raya and Jad Hamza and Viktor Kuncak},
  title     = {On the Complexity of Convex and Reverse Convex Prequadratic Constraints},
  booktitle = {Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ruzica Piskac and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {94},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/T6kG},
  doi       = {10.29007/wdd7},
  pages     = {350-368},
  year      = {2023}}

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