Formal languages
Algorithms for finding patterns in strings
Handbook of theoretical computer science (vol. A)
Mastering regular expressions
Handbook of formal languages, vol. 1
Theory of Automata
Pattern expressions and pattern automata
Information Processing Letters
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Inside the class of REGEX languages
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Spanners: a formal framework for information extraction
Proceedings of the 32nd symposium on Principles of database systems
| Hi-index | 5.23 |
In this paper we revisit the semantics of extended regular expressions (regex), defined succinctly in the 90s [A.V. Aho, Algorithms for finding patterns in strings, in: Jan van Leeuwen (Ed.), Handbook of Theoretical Computer Science, in: Algorithms and Complexity, vol. A, Elsevier and MIT Press, 1990, pp. 255-300] and rigorously in 2003 by Campeanu, Salomaa and Yu [C. Campeanu, K. Salomaa, S. Yu, A formal study of practical regular expressions, IJFCS 14 (6) (2003) 1007-1018], when the authors reported an open problem, namely whether regex languages are closed under the intersection with regular languages. We give a positive answer; and for doing so, we propose a new class of machines - regex automata systems (RAS) - which are equivalent to regex. Among others, these machines provide a consistent and convenient method of implementing regex in practice. We also prove, as a consequence of this closure property, that several languages, such as the mirror language, the language of palindromes, and the language of balanced words are not regex languages.