Cost Functions Definable by Min/Max Automata
Thomas Colcombet, Denis Kuperberg, Amaldev Manuel, Szymon Toruńczyk · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2016
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.