Revistes Catalanes amb Accés Obert (RACO)

Inference of fuzzy regular grammars from examples

Inmaculada Fortes Ruiz, Rafael Morales Bueno, José Luís Pérez de la Cruz Molina, Francisco Triguero Ruiz, M. A. Comino


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.

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