Representing Small Ordinals by Finite Automata

Zoltan Ésik
(University of Szeged)

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.

In Ian McQuillan and Giovanni Pighizzini: Proceedings Twelfth Annual Workshop on Descriptional Complexity of Formal Systems (DCFS 2010), Saskatoon, Canada, 8-10th August 2010, Electronic Proceedings in Theoretical Computer Science 31, pp. 78–87.
Published: 7th August 2010.

ArXived at: bibtex PDF

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