Abelian networks II. Halting on all inputs
Formal Languages and Automata Theory
2015-08-06 v2 Statistical Mechanics
Combinatorics
Abstract
Abelian networks are systems of communicating automata satisfying a local commutativity condition. We show that a finite irreducible abelian network halts on all inputs if and only if all eigenvalues of its production matrix lie in the open unit disk.
Cite
@article{arxiv.1409.0169,
title = {Abelian networks II. Halting on all inputs},
author = {Benjamin Bond and Lionel Levine},
journal= {arXiv preprint arXiv:1409.0169},
year = {2015}
}
Comments
Supersedes sections 5 and 6 of arXiv:1309.3445v1. To appear in Selecta Mathematica