Extended Regular Expressions: Succinctness and Decidability

Dominik Freydenberger (1)

1 Institut für Informatik [Frankfurt am Main]

Most modern implementations of regular expression engines allow the use of variables (also called back references). 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, equivalence, inclusion, 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.

Mots clés: extended regular expressions; regex; decidability; non-recursive tradeoffs

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Dominik Freydenberger. Extended Regular Expressions: Succinctness and Decidability. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.507-518, ⟨10.4230/LIPIcs.STACS.2011.507⟩. ⟨hal-00573642⟩