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

Priyanka Pal (), S. P. Tiwari and Renu Verma ()
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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

New Mathematics and Natural Computation (NMNC), 2019, vol. 15, issue 01, 169-190

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.

Keywords: L-valued automaton; L-valued source and L-valued successor; L-valued core operator; homomorphism; product of L-valued automata (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S1793005719500108

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