Automata on Linear Orderings

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce finite automata and rational expressions for these words. We prove that for countable scattered linear orderings, these two notions are equivalent. This result extends Kleene’s theorem.

• Type: Conference
• Year: 2001
• Where: MFCS
• Authors: Véronique Bruyère, Olivier Carton
• Keywords: Bi-)infinite Words, Countable Scattered Linear, Linear Orderings, MFCS 2001, Theoretical Computer Science