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Automata theory based on complete residuated lattice-valued logic

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Abstract

This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and particularly presents a characterization of residuated lattice by fuzzy automata (called ℓ valued automata). After that fuzzy subautomata (called ℓ valued subautomata), successor and source operators are proposed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally anL bifuzzy topological characterization of ℓ valued automata is presented, so a more generalized fuzzy automata theory is built.

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Authors and Affiliations

  1. State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, 100084, Beijing, China

    Qiu Daowen

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  1. Qiu Daowen
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Qiu, D. Automata theory based on complete residuated lattice-valued logic. Sci China Ser F 44, 419–429 (2001). https://doi.org/10.1007/BF02713945

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  • DOI: https://doi.org/10.1007/BF02713945

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