The Theory of Stabilisation Monoids and Regular Cost Functions

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.

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Thomas Colcombet
• Keywords: Distance Desert Automata, ICALP 2009, Standard Notion, Suitable Notion, Theoretical Computer Science