Cost Functions Definable by Min/Max Automata

Authors Thomas Colcombet, Denis Kuperberg, Amaldev Manuel, Szymon Torunczyk

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Thomas Colcombet
Denis Kuperberg
Amaldev Manuel
Szymon Torunczyk

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Thomas Colcombet, Denis Kuperberg, Amaldev Manuel, and Szymon Torunczyk. Cost Functions Definable by Min/Max Automata. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (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.
  • distance automata
  • B-automata
  • regular cost functions
  • stabilisation monoids
  • decidability
  • min-automata
  • max-automata


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