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Different Operators in Automata Theory Based on Residuated and Co-Residuated Lattices

Author

Listed:
  • Priyanka Pal

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

  • S. P. Tiwari

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

  • Renu Verma

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

Abstract

This paper is towards the algebraic and topological study of automata based on residuated and co-residuated lattices via different operators. The interrelationships among the operators are discussed. Interestingly, we show that the algebraic concepts of an automaton based on a residuated and co-residuated lattice can be expressed in terms of L-topology/co-topology induced by operators. Finally, a composition of such automata is introduced and its categorical significance is discussed.

Suggested Citation

  • Priyanka Pal & S. P. Tiwari & Renu Verma, 2019. "Different Operators in Automata Theory Based on Residuated and Co-Residuated Lattices," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 169-190, March.
    • Handle: RePEc:wsi:nmncxx:v:15:y:2019:i:01:n:s1793005719500108
    DOI: 10.1142/S1793005719500108
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    References listed on IDEAS

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    1. Arun K. Srivastava & Wagish Shukla, 1986. "A topology for automata II," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-4, January.
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