A1 Refereed original research article in a scientific journal
Composition and orbits of language operations: finiteness and upper bounds
Authors: Charlier E, Domaratzki M, Harju T, Shallit J
Publisher: TAYLOR & FRANCIS LTD
Publication year: 2013
Journal: International Journal of Computer Mathematics
Journal name in source: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Journal acronym: INT J COMPUT MATH
Number in series: 6
Volume: 90
Issue: 6
First page : 1171
Last page: 1196
Number of pages: 26
ISSN: 0020-7160
eISSN: 1029-0265
DOI: https://doi.org/10.1080/00207160.2012.681305
Web address : http://www.tandfonline.com/toc/gcom20/90/6
Abstract
We consider a set of eight natural operations on formal languages (Kleene closure, positive closure, complement, prefix, suffix, factor, subword, and reversal), and compositions of them. If x and y are compositions, we say x is equivalent to y if they have the same effect on all languages L. We prove that the number of equivalence classes of these eight operations is finite. This implies that the orbit of any language L under the elements of the monoid is finite and bounded, independent of L. This generalizes previous results about complement, Kleene closure, and positive closure. We also estimate the number of distinct languages generated by various subsets of these operations.
We consider a set of eight natural operations on formal languages (Kleene closure, positive closure, complement, prefix, suffix, factor, subword, and reversal), and compositions of them. If x and y are compositions, we say x is equivalent to y if they have the same effect on all languages L. We prove that the number of equivalence classes of these eight operations is finite. This implies that the orbit of any language L under the elements of the monoid is finite and bounded, independent of L. This generalizes previous results about complement, Kleene closure, and positive closure. We also estimate the number of distinct languages generated by various subsets of these operations.
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