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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 ...
The critical group of an abelian network is a finite abelian group that governs the behavior of the network on large inputs. It generalizes the sandpile group of a graph. We show that the critical gro...
In Dhar’s model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges. A local commutativity condition ensures that the final output does not ...