Algorithms for Matching Strings with Fuzzy Context-Free and Automata Patterns

This paper is devoted to determining the degree of compliance of a given string with a pattern represented as a grammar, the terminal symbols of which are fuzzy properties of the characters of the base alphabet. In the case when the pattern is specified as a context-free grammar in the Chomsky normal form, the matching degree is calculated by applying a fuzzy version of the Cocke–Younger–Kasami (CYK) algorithm in cubic time depending on the length of the input string. The proposed algorithm becomes a linear time algorithm for the subclass of the automata grammars, which can be considered as finite automata with fuzzy properties of alphabetic characters on transitions. This work may find application in bioinformatics to classify deoxyribonucleic acid (DNA) sequences using fuzzy prototypes described in one way or another. Other applications are related to fuzzy analysis of natural languages, pattern recognition and determination of fuzzy regularity of a string.