Regular Expressions Avoiding Absorbing Patterns and the Significance of Uniform Distribution

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Broda, S (Author) FCUP; António Machiavelo (Author) FCUP; Nelma Moreira (Author) FCUP; Rogério Reis (Author) FCUP

Journal

Title: International Journal of Foundations of Computer Science

Pages: 1-18

ISSN: 0129-0541

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-016-S5Y

DOI: 10.1142/s0129054124420036

Abstract (EN): Although regular expressions do not correspond univocally to regular languages, it is still worthwhile to study their properties and algorithms. For the average case analysis one often relies on the uniform random generation using a specific grammar for regular expressions, that can represent regular languages with more or less redundancy. Generators that are uniform on the set of expressions are not necessarily uniform on the set of regular languages. Nevertheless, it is not straightforward that asymptotic estimates obtained by considering the whole set of regular expressions are different from those obtained using a more refined set that avoids some large class of equivalent expressions. In this paper we study a set of expressions that avoid a given absorbing pattern. It is shown that, although this set is significantly smaller than the standard one, the asymptotic average estimates for the size of the Glushkov automaton for these expressions does not differ from the standard case. Furthermore, for this set the asymptotic density of epsilon-accepting expressions is also the same as for the set of all standard regular expressions.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18