Abelian networks II. Halting on all inputs

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.

arXiv commentSupersedes sections 5 and 6 of arXiv:1309.3445v1. To appear in Selecta Mathematica