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Title: Extended regular expressions: succinctness and decidability
Authors: Freydenberger, Dominik D.
Issue Date: 2013
Publisher: © Springer Science+Business Media, LLC
Citation: FREYDENBERGER, D.D., 2013. Extended regular expressions: succinctness and decidability. Theory of Computing Systems, 53 (2), pp.159-193
Abstract: Most modern implementations of regular expression engines allow the use of variables (also called backreferences). The resulting extended regular expressions (which, in the literature, are also called practical regular expressions, rewbr, or regex) are able to express non-regular languages. The present paper demonstrates that extended regular-expressions cannot be minimized effectively (neither with respect to length, nor number of variables), and that the tradeoff in size between extended and "classical" regular expressions is not bounded by any recursive function. In addition to this, we prove the undecidability of several decision problems (universality, regularity, and cofiniteness) for extended regular expressions. Furthermore, we show that all these results hold even if the extended regular expressions contain only a single variable. © 2012 Springer Science+Business Media, LLC.
Description: A preliminary version of this paper appeared in the 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011), volume 9 of Leibniz International Proceedings in Informatics (LIPIcs), pp.507-518.
Version: Accepted for publication
DOI: 10.1007/s00224-012-9389-0
URI: https://dspace.lboro.ac.uk/2134/26544
Publisher Link: http://dx.doi.org/10.1007/s00224-012-9389-0
ISSN: 1432-4350
Appears in Collections:Published Articles (Computer Science)

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