On Extended Regular Expressions

In this paper we extend the work of Campeanu, Salomaa and Yu [1] on extended regular expressions featured in the Unix utility egrep and the popular scripting language Perl. We settle the open issue of closure under intersection and provide an improved pumping lemma that will show that a larger class of languages is not recognizable by extended regular expressions. We also investigate some questions regarding extended multi-pattern languages introduced by Nagy in [2].

[1]  Alfred V. Aho,et al.  Algorithms for Finding Patterns in Strings , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[2]  Gheorghe Paun,et al.  Multi-Pattern Languages , 1995, Theor. Comput. Sci..

[3]  Enrico Tronci,et al.  Synchronized regular expressions , 2002, Acta Informatica.

[4]  Martin Kutrib,et al.  Finite turns and the regular closure of linear context-free languages , 2007, Discret. Appl. Math..

[5]  Tao Jiang,et al.  Decision Problems for Patterns , 1995, J. Comput. Syst. Sci..

[6]  Mark-Jan Nederhof,et al.  Regular Closure of Deterministic Languages , 1999, SIAM J. Comput..

[7]  Jean H. Gallier,et al.  Logic for Computer Science: Foundations of Automatic Theorem Proving , 1985 .

[8]  Dana Angluin,et al.  Finding Patterns Common to a Set of Strings , 1980, J. Comput. Syst. Sci..

[9]  Andrew Hume.  A tale of two greps , 1988, Softw. Pract. Exp..

[10]  Sheng Yu,et al.  A Formal Study Of Practical Regular Expressions , 2003, Int. J. Found. Comput. Sci..

[11]  Benedek Nagy.  On the language equivalence of NE star-patterns , 2005, Inf. Process. Lett..