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<p>In automata theory, Brzozowski’s algorithm is a powerful tool to construct a minimal deterministic finite automata corresponding to an automaton accepting the same language regardless of its deterministic or nondeterministic nature. This paper is towards the enrichment of the theory of crisp deterministic typical hesitant fuzzy multiset automata and typical hesitant fuzzy multiset languages and presents Brzozowski’s algorithm to construct a minimal crisp deterministic typical hesitant fuzzy multiset automaton for a given crisp deterministic typical hesitant fuzzy multiset automaton accepting a typical hesitant fuzzy multiset language. We have also presented the pumping lemma to verify regularness of a typical hesitant fuzzy multiset language. We have introduced the category <i>THFMBM</i> of typical hesitant fuzzy multiset bimonoids (thfmb-monoid) with their respective morphisms, and demonstrate the existence of a functor between the category <i>THFMBM</i> and the category <i>THFML</i> of typical hesitant fuzzy multiset languages and their morphisms. Finally, we discuss the minimal monoid representation of typical hesitant fuzzy multiset language and its properties.</p>

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On Brzozowski’s algorithm, pumping lemma, and monoid representation for a typical hesitant fuzzy multiset language

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Sunny Verma,
  • Vijay K. Yadav,
  • Shainky Ruhela,
  • Swati Yadav,
  • Binod K. Sharma

摘要

In automata theory, Brzozowski’s algorithm is a powerful tool to construct a minimal deterministic finite automata corresponding to an automaton accepting the same language regardless of its deterministic or nondeterministic nature. This paper is towards the enrichment of the theory of crisp deterministic typical hesitant fuzzy multiset automata and typical hesitant fuzzy multiset languages and presents Brzozowski’s algorithm to construct a minimal crisp deterministic typical hesitant fuzzy multiset automaton for a given crisp deterministic typical hesitant fuzzy multiset automaton accepting a typical hesitant fuzzy multiset language. We have also presented the pumping lemma to verify regularness of a typical hesitant fuzzy multiset language. We have introduced the category THFMBM of typical hesitant fuzzy multiset bimonoids (thfmb-monoid) with their respective morphisms, and demonstrate the existence of a functor between the category THFMBM and the category THFML of typical hesitant fuzzy multiset languages and their morphisms. Finally, we discuss the minimal monoid representation of typical hesitant fuzzy multiset language and its properties.