On the average state complexity of partial derivative automata

• Type: Article in International Scientific Journal
• Date: 2011

Authors

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

Journal

Title: International Journal of Foundations of Computer Science

Vol. 22 No. 7

Pages: 1593-1606

ISSN: 0129-0541

Publisher: World Scientific

Scientific classification

FOS: Natural sciences > Computer and information sciences

CORDIS: Physical sciences > Computer science

Other information

Abstract (EN): The partial derivative automaton Apd is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have epsilon as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptotic behaviour. This depends on the alphabet size, k, and for growing k's its limit approaches half the number of states in Apos. The lower bound corresponds to consider the Apd automaton for the marked version of the re, i.e. where all its letters are made different. Experimental results suggest that the average number of states of this automaton, and of the APd automaton for the unmarked re, are very close to each other.

Language: English

Type (Professor's evaluation): Scientific

Notes: Accepted to publication. - ISSN: 0129-0541, Online ISSN: 1793-6373