Abelian networks I. Foundations and examples
Abstract
In Deepak Dhar's model of abelian distributed processors, automata occupy the vertices of a graph and communicate via the edges. We show that two simple axioms ensure that the final output does not depend on the order in which the automata process their inputs. A collection of automata obeying these axioms is called an "abelian network". We prove a least action principle for abelian networks. As an application, we show how abelian networks can solve certain linear and nonlinear integer programs asynchronously. In most previously studied abelian networks, the input alphabet of each automaton consists of a single letter; in contrast, we propose two non-unary examples of abelian networks: "oil and water" and "abelian mobile agents".
Cite
@article{arxiv.1309.3445,
title = {Abelian networks I. Foundations and examples},
author = {Benjamin Bond and Lionel Levine},
journal= {arXiv preprint arXiv:1309.3445},
year = {2016}
}
Comments
To appear in SIAM J. Discrete Math. The original v1 has been split into three parts, of which this is the first. This part covers the least action principle, halting dichotomy, local abelianness implies global abelianness, and monotone integer programming. The other parts are arXiv:1409.0169 (Abelian networks II. Halting on all inputs) and arXiv:1409.0170 (Abelian networks III. The critical group)