Cost Functions Definable by Min/Max Automata

Thomas Colcombet (1) , Denis Kuperberg (2, 3) , Amaldev Manuel (1) , Szymon Toruńczyk (4)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 IRIT - Institut de recherche en informatique de Toulouse
3 ONERA - The French Aerospace Lab [Toulouse]
4 Institute of Computer Science

Regular cost functions form a quantitative extension of regular languages that share the array of characterisations the latter possess. In this theory, functions are treated only up to preservation of boundedness on all subsets of the domain. In this work, we subject the well known distance automata (also called min-automata), and their dual max-automata to this framework, and obtain a number of effective characterisations in terms of logic, expressions and algebra.

Mots clés: automata; max-automata; regular cost functions; min-automata; B-automata; stabilisation monoids; decidability

Domaines: Théorie et langage formel [cs.FL]

Thomas Colcombet, Denis Kuperberg, Amaldev Manuel, Szymon Toruńczyk. Cost Functions Definable by Min/Max Automata. 33rd International Symposium on Theoretical Aspects of Computer Science (STACS 2016), 2016, Orléans, France. pp.1 - 36, ⟨10.4230/LIPIcs.STACS.2016.29⟩. ⟨hal-02070812⟩