Orbit-finite linear programming
Logic in Computer Science
2024-11-14 v4 Formal Languages and Automata Theory
Abstract
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of linear inequalities. As our principal contribution we provide a decision procedure for checking if such a system has a real solution, and for computing the minimal/maximal value of a linear objective function over the solution set. We also show undecidability of these problems in case when only integer solutions are considered. Therefore orbit-finite linear programming is decidable, while orbit-finite integer linear programming is not.
Cite
@article{arxiv.2302.00802,
title = {Orbit-finite linear programming},
author = {Arka Ghosh and Piotr Hofman and Sławomir Lasota},
journal= {arXiv preprint arXiv:2302.00802},
year = {2024}
}
Comments
Full version of LICS 2023 paper published in Journal of the ACM