Compact and fast algorithms for safe regular expression search

Abstract

This article describes an improvement of the brute force determinization algorithm in the case of homogeneous nondeterministic finite automata (NFAs), as well as its application to pattern matching. Brute force determinization with limited memory may provide a partially determinized automaton, but its bounded complexity makes it a safe procedure contrary to the classical subset construction. Actually, our algorithm is inspired by both recent results of Champarnaud concerning the subset automaton of a homogeneous NFA and the algorithm recently designed by Navarro and Raffinot to implement the brute force determinization of the Glushkov NFA of a regular pattern. Our algorithm significantly improves Navarro–Raffinot's one since it has an average exponentially smaller memory requirement for a given level of determinization, which, considering a bounded memory, implies a quadratically smaller parsing time. This algorithm has been implemented in CCP software (http://www.univ-rouen.fr/LIFAR/aia/ccp.html). Tests have been carried out in the field of text processing and biology. Experimental results are reported.

Keywords:

• NFA determinization
• Homogeneous NFAs
• Bitwise techniques
• Regular expression search

Notes

¹E is epsilon-free if the symbol ϵ does not appear in E.

²http://www.ncbi.nlm.nih.gov/Genbank/index.html

³http://corpus.canterbury.ac.nz/