Modification of Valiant's algorithm for the string-matching problem

The theory of formal languages and, particularly, context-free grammars has been extensively studied and applied in different areas. For example, several approaches to the recognition and classification problems in bioinformatics are based on searching the genomic subsequences possessing some specific features which can be described by a context-free grammar. Therefore, the string-matching problem can be reduced to parsing – verification if some subsequence can be derived in this grammar. Such field of application as bioinformatics requires working with a large amount of data, so it is necessary to improve the existing parsing techniques. The most asymptotically efficient parsing algorithm that can be applied to any context-free grammar is a matrix-based algorithm proposed by Valiant. This paper aims to present Valiant's algorithm modification, which main advantage is the possibility to divide the parsing table into successively computed layers of disjoint submatrices where each submatrix of the layer can be processed independently. Moreover, our approach is easily adapted for the string-matching problem. Our evaluation shows that the proposed modification retains all benefits of Valiant's algorithm, especially its high performance achieved by using fast matrix multiplication methods. Also, the modified version decreases a large amount of excessive computations and accelerates the substrings searching.