Tropical Semirings

Jean-Eric Pin (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

This article has been published in the proceedings of the "Idempotency" conference, organized by Jeremy Gunawardena in Bristol in october 1994. The aim of this paper is to present the tropical semirings and to survey a few problems relevant to them. Two apparently disconnected applications of the tropical semirings are presented: the Burnside type problems in group and semigroup theory and decidability problems in formal language theory.

Mots clés: Tropical semiring; finite automata; Burnside problem; finiteness condition

Domaines: Autre [cs.OH]; Théorie des groupes [math.GR]; Mathématique discrète [cs.DM]

Jean-Eric Pin. Tropical Semirings. J. Gunawardena. Idempotency (Bristol, 1994), Cambridge Univ. Press, Cambridge, pp.50-69, 1998, Publ. Newton Inst. 11. ⟨hal-00113779⟩