Algorithms for determining relative star height and star height
Information and Computation
Automata, Languages, and Machines
Automata, Languages, and Machines
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Star height of certain families of regular events
Journal of Computer and System Sciences
General properties of star height of regular events
Journal of Computer and System Sciences
On the Construction of Reversible Automata for Reversible Languages
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Theoretical Computer Science - Implementation and application of automata
On the efficient construction of quasi-reversible automata for reversible languages
Information Processing Letters
Theoretical Computer Science
Remarks on multiple entry deterministic finite automata
Journal of Automata, Languages and Combinatorics
Syntactic semiring and universal automaton
DLT'03 Proceedings of the 7th international conference on Developments in language theory
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
On the size of the universal automaton of a regular language
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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The star height of a regular language is an invariant that has been shown to be effectively computable in 1988 by Hashiguchi. But the algorithm that corresponds to his proof leads to impossible computations even for very small instances. Here we solve the problem (of computing star height) for a special class of regular languages,called reversible languages,tha t have attracted much attention in various areas of formal language and automata theory in the past few years. These reversible languages also strictly extend the classes of languages considered by McNaughton, Cohen, and Hashiguchi for the same purpose, and with different methods.Our method is based upon the definition (inspired by the reading of Conway's book) of an automaton that is effectively associated to every language -- which we call the universal automaton of the language -- and that contains the image of any automaton that accepts the language. We show that the universal automaton of a reversible language contains a subautomaton where the star height can be computed.