模糊仿真与模糊自动机间的双仿真

Linh Anh Nguyen
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引用次数: 3

摘要

两个模糊自动机在完全剩余格上的模拟和双模拟被\'Ciri\'c等人(2012)定义为自动机状态集之间的模糊关系。然而,它们之间的关系就像一个清脆的自动机。特别是,如果两个模糊自动机之间存在(正向)双仿真,则它们所识别的模糊语言是完全相等的。Stanimirovi等人(2020)引入的近似模拟和双模拟旨在模糊化这一现象。然而,它们仅对完全Heyting代数上的模糊自动机定义,并且没有给出自动机状态之间的确切关系。本文介绍并研究了完全残馀格上模糊自动机间的模糊模拟和双仿真。这些概念新颖,具有良好的性质。它们是对任意完备残差格上的模糊自动机定义的。证明了由模糊自动机识别的模糊语言在模糊模拟下是模糊保存的,在模糊双模拟下是模糊不变性的。我们还证明了模糊仿真和双仿真的概念具有Hennessy-Milner性质,这是两个模糊自动机之间最大的模糊仿真或双仿真的逻辑表征。此外,我们提供的结果表明,我们的模糊仿真和双仿真概念比Ciri等人引入的仿真和双仿真概念以及Stanimirovi等人引入的近似仿真和双仿真概念更通用和精细。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fuzzy Simulations and Bisimulations between Fuzzy Automata
Simulations and bisimulations between two fuzzy automata over a complete residuated lattice were defined by \'Ciri\'c et al. (2012) as fuzzy relations between the sets of states of the automata. However, they act as a crisp relationship between the automata. In particular, if there exists a (forward) bisimulation between two fuzzy automata, then the fuzzy languages recognized by them are crisply equal. Approximate simulations and bisimulations introduced by Stanimirovi\'c et al. (2020) aim at fuzzifying this phenomenon. However, they are defined only for fuzzy automata over a complete Heyting algebra and do not give the exact relationship between states of the automata. In this article, we introduce and study fuzzy simulations and bisimulations between fuzzy automata over a complete residuated lattice. These notions are novel and have good properties. They are defined for fuzzy automata over any complete residuated lattice. We prove that the fuzzy language recognized by a fuzzy automaton is fuzzily preserved by fuzzy simulations and fuzzily invariant under fuzzy bisimulations. We also prove that the notions of fuzzy simulation and bisimulation have the Hennessy-Milner properties, which are a logical characterization of the greatest fuzzy simulation or bisimulation between two fuzzy automata. In addition, we provide results showing that our notions of fuzzy simulation and bisimulation are more general and refined than the notions of simulation and bisimulation introduced by \'Ciri\'c et al. and the notions of approximate simulation and bisimulation introduced by Stanimirovi\'c et al.
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