Abstract
We introduce the notion of regular cost functions: a quantitative extension to the standard theory of regular languages.
We provide equivalent characterisations of this notion by means of automata (extending the nested distance desert automata of Kirsten), of history-deterministic automata (history-determinism is a weakening of the standard notion of determinism, that replaces it in this context), and a suitable notion of recognisability by stabilisation monoids. We also provide closure and decidability results.
Supported by the Anr project Jade: ‘Jeux et Automates, Décidabilité et Extensions’.
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Colcombet, T. (2009). The Theory of Stabilisation Monoids and Regular Cost Functions. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_12
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DOI: https://doi.org/10.1007/978-3-642-02930-1_12
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