Inference of fuzzy regular grammars from examples

Let us consider the following situation: An oracle provides us with a finite set of examples considered as words belonging to a regular language. This oracle is not available again. In this paper we study a new and general inference algorithm of fuzzy regular grammars based on this set of words. This algorithm is created by adapting a process discovery method. The main issues in the adaptation are the development of a fuzzy version, the assignation of membership degrees to each production in the grammar, and the treatment of consecutive repeated symbols. In addition to this inference algorithm we present a practical use for automatically generating artistic designs. Specifically, we have collected a set of paintings by Piet Mondrian (1872-1944) and obtained new Mondrian-style paintings. To achieve this, we designed a code to transform the paintings into strings and also to carry out the reverse conversion. We view these strings, which represent the paintings, as words belonging to a regular language and from this finite set of examples infer a fuzzy regular grammar. The entire process has been implemented and some new paintings from the inference algorithm have been obtained. An art expert has judged that these computer-generated paintings are fully in the spirit of those painted by Mondrian.