Abstract
The following classes of rational equivalence relations are shown to have regular cross-sections: deterministic rational equivalence relations, rational equivalence relations over a one letter alphabet, and rational equivalence relations with bounded separability. Although the general case remains open, it is shown to be reducible to that of locally-finite rational equivalence relations over a two letter alphabet. Two particular cross-sections are shown not to be regular: the set of minimum length words and the set of lexicographically minimal words.
This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A0237
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Johnson, J.H. (1985). Do rational equivalence relations have regular cross-sections?. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015755
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DOI: https://doi.org/10.1007/BFb0015755
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