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Equivalence in automata theory based on complete residuated lattice-valued logic

机译：基于完全剩余格值逻辑的自动机理论的等价

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Automata theory based on complete residuated lattice-valued logic, called L-valued finite automata (abbr. L-VFAs), was introduced by the second author in 2001. In this paper we deal with the problems of equivalence between L-valued sequential machines (abbr. L-VSMs) and L-VFAs. We define L-VSMs, and particularly present a method for deciding the equivalence between L-VSMs as well. An algorithm procedure for deciding the equivalence between L-VSMs is constructed. We analyze the complexity and efficiency of the algorithm procedure and obtain the relative results to L-VFAs. Moreover, the definitions of L-valued languages (abbr. L-VLs), and L-valued regular languages (abbr. L-VRLs) recognized by L-VFAs are given, and some related properties are also discussed. We show an equivalent relation between L-VRLs and conventional regular languages. By using L-valued pumping lemma, we get a necessary and sufficient condition for an L-VL to be nonconstant.
机译：第二作者于2001年提出了基于完全剩余格值逻辑的自动机理论，称为L值有限自动机（简称L-VFA）。在本文中，我们处理了L值顺序机之间的等价问题。 （缩写为L-VSM）和L-VFA。我们定义了L-VSM，特别是提出了一种确定L-VSM之间等效性的方法。构造了确定L-VSM之间等效性的算法过程。我们分析了算法过程的复杂性和效率，并获得了与L-VFA相关的结果。此外，给出了由L-VFA识别的L值语言（缩写为L-VLs）和L值常规语言（缩写为L-VRL）的定义，并讨论了一些相关属性。我们显示了L-VRL与常规常规语言之间的等效关系。通过使用L值泵定引理，我们获得了L-VL非恒定的充要条件。

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