Representing Small Ordinals by Finite Automata
It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than omega^omega. We design a polynomial time algorithm that constructs, for each well-ordered regular language L with respect to the lexicographic ordering, given by a determi...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2010-08-01
|
| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1008.1650v1 |
| Summary: | It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than omega^omega. We design a polynomial time algorithm that constructs, for each well-ordered regular language L with respect to the lexicographic ordering, given by a deterministic finite automaton, the Cantor Normal Form of its order type. It follows that there is a polynomial time algorithm to decide whether two deterministic finite automata accepting well-ordered regular languages accept isomorphic languages. We also give estimates on the size of the smallest automaton representing an ordinal less than omega^omega, together with an algorithm that translates each such ordinal to an automaton. |
|---|---|
| ISSN: | 2075-2180 |