Generalized Dictionary Matching under Substring Consistent Equivalence Relations

TL;DR

This paper extends dictionary matching algorithms to handle substring consistent equivalence relations, generalizing classical methods like Aho-Corasick for broader pattern matching scenarios.

Contribution

It introduces a new automaton construction and matching algorithm for dictionary matching under SCER, expanding the applicability of pattern matching techniques.

Findings

Proposes a generalized automaton construction for SCER.

Develops an algorithm for dictionary matching under SCER.

Analyzes time and space complexity of the proposed algorithms.

Abstract

Given a set of patterns called a dictionary and a text, the dictionary matching problem is a task to find all occurrence positions of all patterns in the text. The dictionary matching problem can be solved efficiently by using the Aho-Corasick algorithm. Recently, Matsuoka et al. [TCS, 2016] proposed a generalization of pattern matching problem under substring consistent equivalence relations and presented a generalization of the Knuth-Morris-Pratt algorithm to solve this problem. An equivalence relation $\approx$ is a substring consistent equivalence relation (SCER) if for two strings $X,Y$, $X \approx Y$ implies $|X| = |Y|$ and $X[i:j] \approx Y[i:j]$ for all $1 \le i \le j \le |X|$. In this paper, we propose a generalization of the dictionary matching problem and present a generalization of the Aho-Corasick algorithm for the dictionary matching under SCER. We present an algorithm that constructs SCER automata and an algorithm that performs dictionary matching under SCER by using the automata. Moreover, we show the time and space complexity of our algorithms with respect to the size of input strings.