Approximate comparison of distance automata

Thomas Colcombet (1) , Laure Daviaud (1)

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

Distance automata are automata weighted over the semiring the tropical semiring. Such automata compute functions from words to N such as the number of occurrences of a given letter. It is known that testing f < g is an undecidable problem for f,g computed by distance automata. The main contribution of this paper is to show that an approximation of this problem becomes decidable. We present an algorithm which, given epsilon>0 and two functions f,g computed by distance automata, answers ''yes'' if f < (1-epsilon)g, ''no'' if there is a word w such that f(w)>g(w), and may answer ''yes'' or ''no'' in all other cases. This result highly refines previously known decidability results of the same type. The core argument behind this quasi-decision procedure is an algorithm which is able to provide an approximated finite presentation to the closure under product of set of matrices over the tropical semiring.

Mots clés: distance automata; comparison

Domaines: Théorie et langage formel [cs.FL]

Thomas Colcombet, Laure Daviaud. Approximate comparison of distance automata. 2012. ⟨hal-00712771⟩