The Bridge Between Regular Cost Functions and Omega-Regular Languages

Authors Thomas Colcombet, Nathanaël Fijalkow

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Thomas Colcombet
Nathanaël Fijalkow

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Thomas Colcombet and Nathanaël Fijalkow. The Bridge Between Regular Cost Functions and Omega-Regular Languages. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 126:1-126:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


In this paper, we exhibit a one-to-one correspondence between omega-regular languages and a subclass of regular cost functions over finite words, called omega-regular like cost functions. This bridge between the two models allows one to readily import classical results such as the last appearance record or the McNaughton-Safra constructions to the realm of regular cost functions. In combination with game theoretic techniques, this also yields a simple description of an optimal procedure of history-determinisation for cost automata, a central result in the theory of regular cost functions.
  • Theory of Regular Cost Functions
  • Automata with Counters
  • Costautomata
  • Quantitative Extensions of Automata
  • Determinisation of Automata


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