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Abelian networks II: halting on all inputs

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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.

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Acknowledgments

This research was supported by an NSF postdoctoral fellowship and NSF Grants DMS-1105960 and DMS-1243606 and by the UROP and SPUR programs at MIT.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Benjamin Bond

  2. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Lionel Levine

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  1. Benjamin Bond
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  2. Lionel Levine
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Correspondence to Lionel Levine.

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Bond, B., Levine, L. Abelian networks II: halting on all inputs. Sel. Math. New Ser. 22, 319–340 (2016). https://doi.org/10.1007/s00029-015-0192-z

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