Run-Length Encoded Nondeterministic KMP and Suffix Automata

TL;DR

This paper introduces a space-efficient bit-parallel encoding for nondeterministic KMP and suffix automata using run-length encoding, optimized for long strings over small alphabets, enabling faster automata simulation.

Contribution

It presents a novel run-length encoded bit-parallel representation for automata, improving efficiency for specific string types and complementing existing methods for large alphabets.

Findings

Requires space proportional to (σ + m) times run-length divided by word size

Enables automata simulation in time proportional to run-length divided by word size

Effective for long strings over small alphabets

Abstract

We present a novel bit-parallel representation, based on the run-length encoding, of the nondeterministic KMP and suffix automata for a string $P$ with at least two distinct symbols. Our method is targeted to the case of long strings over small alphabets and complements the method of Cantone et al. (2012), which is effective for long strings over large alphabets. Our encoding requires $O((\sigma + m)\lceil \rho / w\rceil)$ space and allows one to simulate the automata on a string in time $O(\lceil \rho / w\rceil)$ per transition, where $\sigma$ is the alphabet size, $m$ is the length of $P$, $\rho$ is the length of the run-length encoding of $P$ and $w$ is the machine word size in bits. The input string can be given in either unencoded or run-length encoded form.