English

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

R2 v1 2026-06-22T05:44:50.349Z