Abelian networks II: halting on all inputs

作者：Bondi Benjamin; Levine Lionel^*

来源：Selecta Mathematica, New Series, 2016, 22(1): 319-340.

DOI：10.1007/s00029-015-0192-z

• Abelian distributed processors
• Asynchronous computation
• Automata network
• Chip firing
• Commutative monoid action
• Dickson's lemma
• Least action principle
• M-matrix
• Sandpile
• Torsor

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.

• 出版日期2016-1