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Categories of Automata and Languages Based on a Complete Residuated Lattice

Author

Listed:
  • Vinay Gautam

    (Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India)

  • S. P. Tiwari

    (Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India)

  • Priyanka Pal

    (Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India)

  • Jayanti Tripathi

    (Amity Institute of Applied Science (AIAS), Amity University, Noida 201313, Uttar Pradesh, India)

Abstract

The purpose of this paper is to introduce a new category of fuzzy automata based on complete residuated lattice. We introduce and study the categorical concepts such as product, equalizer and their duals in this category. Finally, we establish a construction of a minimal fuzzy automaton for a given fuzzy language in a categorical framework. The construction of such fuzzy automaton is based on derivative of a given fuzzy language.

Suggested Citation

  • Vinay Gautam & S. P. Tiwari & Priyanka Pal & Jayanti Tripathi, 2018. "Categories of Automata and Languages Based on a Complete Residuated Lattice," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 423-444, November.
    • Handle: RePEc:wsi:nmncxx:v:14:y:2018:i:03:n:s1793005718500254
    DOI: 10.1142/S1793005718500254
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