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Title: Restricted ambiguity of erasing morphisms
Authors: Reidenbach, Daniel
Schneider, Johannes C.
Keywords: Erasing morphisms
Pattern languages
Issue Date: 2011
Publisher: © Elsevier
Citation: REIDENBACH, D. and SCHNEIDER, J.C., 2011. Restricted ambiguity of erasing morphisms. Theoretical Computer Science, 412 (29), pp. 3510-3523.
Abstract: A morphism h is called ambiguous for a string s if there is another morphism that maps s to the same image as h; otherwise, it is called unambiguous. In this paper, we examine some fundamental problems on the ambiguity of erasing morphisms. We provide a detailed analysis of so-called ambiguity partitions, and our main result uses this concept to characterise those strings that have a morphism of strongly restricted ambiguity. Furthermore, we demonstrate that there are strings for which the set of unambiguous morphisms, depending on the size of the target alphabet of these morphisms, is empty, finite or infinite. Finally, we show that the problem of the existence of unambiguous erasing morphisms is equivalent to some basic decision problems for nonerasing multi-pattern languages.
Version: Accepted for publication
DOI: 10.1016/j.tcs.2011.02.041
URI: https://dspace.lboro.ac.uk/2134/8395
Publisher Link: http://dx.doi.org/10.1016/j.tcs.2011.02.041
ISSN: 0304-3975
Appears in Collections:Published Articles (Computer Science)

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