Theory of Computing Systems

, Volume 53, Issue 2, pp 159–193 | Cite as

Extended Regular Expressions: Succinctness and Decidability

  • Dominik D. Freydenberger


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.


Extended regular expressions Regex Decidability Non-recursive tradeoffs 



The author wishes to thank Nicole Schweikardt and the anonymous referees for the conference version [15] and the present version for their helpful remarks.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute for Computer ScienceGoethe-UniversityFrankfurt am MainGermany

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