149 citations · 841 across the 44 of their papers we have counts for
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cs.FL2018★ 4 cited
Abelian networks IV. Dynamics of nonhalting networks
Swee Hong Chan, Lionel Levine
An abelian network is a collection of communicating automata whose state transitions and message passing each satisfy a local commutativity condition. This paper is a continuation…
cs.FL2014
Abelian networks II. Halting on all inputs
Benjamin Bond, Lionel Levine
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…
cs.FL2013
Abelian networks I. Foundations and examples
Benjamin Bond, Lionel Levine
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 fina…