Two dimensional fuzzy context-free languages and tiling patterns

Title

Two dimensional fuzzy context-free languages and tiling patterns

Creator

John Kaspar A.; Sheena Christy D.K.; Masilamani V.; Thomas D.G.

Description

Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture language) is a collection of two dimensional words, which are a rectangular array of symbols made up of finite alphabets. Two dimensional automata can recognize two dimensional languages that could not be recognized by one dimensional automata. In this paper, we introduce two dimensional fuzzy context-free languages generated by the two dimensional fuzzy context-free grammars and accepted by the two dimensional fuzzy pushdown automata in order to deal with the vagueness that arises in two dimensional context-free languages. We can construct a two dimensional fuzzy context free grammar from the given two dimensional fuzzy pushdown automata and vice versa. In addition, we prove that two dimensional fuzzy context-free languages are closed under union, column concatenation, column star, homomorphism, inverse homomorphism, reflection about right-most vertical, reflection about base, conjugation and half-turn and also show that two dimensional fuzzy context-free languages are not closed under matrix homomorphism, quarter-turn and transpose. Further, we have given the applications and the uses of closure properties in the formation of tiling patterns. 2024 Elsevier B.V.

Source

Fuzzy Sets and Systems, Vol-485

Date

2024-01-01

Publisher

Elsevier B.V.

Subject

Fuzzy languages; Fuzzy pushdown automata; Picture languages; Two dimensional fuzzy languages

Coverage

John Kaspar A., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, 560 029, India; Sheena Christy D.K., Department of Mathematics, SRM Institute of Scinece and Technology, TamilNadu, Kattankulathur, Chennai, 603 203, India; Masilamani V., Department of Computer Science, Indian Institute of Information and Design Manufacturing, TamilNadu, Kancheepuram, Chennai, 600 127, India; Thomas D.G., Department of mathematics, Madras Christian College, Former Professor, Tambaram, TamilNadu, Chennai, 600 059, India

Rights

Restricted Access

Relation

ISSN: 1650114; CODEN: FSSYD

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1016/j.fss.2024.108961

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