Abstract
In this paper, we present two new normal forms for fuzzy linear grammars that preserving language. In addition, we introduce two new classes of fuzzy machines, Fuzzy Linear Automata (FLA) and Fuzzy Nondeterministic 2-Tape Automata (2-FNA), we show the equivalence between them and also show that the class of fuzzy languages recognized by these machines is exactly the class of fuzzy linear languages, i.e., FLA and 2-DNA are recognized machines for class of fuzzy linear languages.
Highlights
Formal language theory focuses on the study of sets of words called “languages” and in the algebraic structures that is generated and recognized by these sets of words
Linear languages are characterized by linear grammars or by states machines presented by Bedregal and Rosemberg, respectively nondeterministic linear automata [5, 4] and nondeterministic 2-tape finite automata [17]
This work will be divided in five sections, this introduction, the Background where is presented the fundamentals required for work, in 3-th section are introduced the new normal forms
Summary
Formal language theory focuses on the study of sets of words called “languages” and in the algebraic structures that is generated and recognized by these sets of words. The original Chomsky’s hierarchy is composed by four formal languages classes (see [9]) which has been widely and deeply studied. Linear languages are characterized by linear grammars or by states machines presented by Bedregal and Rosemberg, respectively nondeterministic linear automata [5, 4] and nondeterministic 2-tape finite automata [17]. In this paper we will introduce two new normal forms for fuzzy linear grammars. We will present a fuzzy generalization for the nondeterministic linear automata [5], that we called fuzzy linear automata (FLA). This work will be divided in five sections, this introduction, the Background where is presented the fundamentals required for work, in 3-th section are introduced the new normal forms.
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