Extended regular expressions: succinctness and decidability
journal contributionposted on 19.09.2017 by Dominik Freydenberger
Any type of content formally published in an academic journal, usually following a peer-review process.
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.
- Computer Science