An efficient null-free procedure for deciding regular language membership

AbstractWe present a new algorithm to determine whether a given word belongs to the language denoted by a regular expression. It is based on our ZPC representation of the Glushkov automaton of a regular expression. This procedure requires a specific representation of the Glushkov automaton of the expression. The representation is computed in linear time and space using the ZPC algorithm designed by Ziadi et al

An optimal parallel algorithm to convert a regular expression into its Glushkov automaton

AbstractThe aim of this paper is to describe a CREW-PRAM optimal algorithm which converts a regular expression of size s into its Glushkov automaton in O(log s) time using O(s2log s) processors. This algorithm makes use of the star-normal form of an expression as defined by Brüggemann-Klein (1993) and is based on the sequential algorithm due to Ziadi et al. (1997) which computes an original representation of Glushkov automaton in O(s) time

Sparse Regular Expression Matching

We present the first algorithm for regular expression matching that can take advantage of sparsity in the input instance. Our main result is a new algorithm that solves regular expression matching in $O\left(\Delta \log \log \frac{nm}{\Delta} + n + m\right)$ time, where $m$ is the number of positions in the regular expression, $n$ is the length of the string, and $\Delta$ is the \emph{density} of the instance, defined as the total number of active states in a simulation of the position automaton. This measure is a lower bound on the total number of active states in simulations of all classic polynomial sized finite automata. Our bound improves the best known bounds for regular expression matching by almost a linear factor in the density of the problem. The key component in the result is a novel linear space representation of the position automaton that supports state-set transition computation in near-linear time in the size of the input and output state sets