基于量子逻辑的自动机理论的拓扑性质

Topological Characterizations of Automata Theory Based on Quantum Logic

研究了基于量子逻辑的自动机理论(简称l-值自动机理论)的拓扑性质.给出了successor算子和source算子的另一种定义,讨论了successor算子、source算子和l-值子自动机之间的关系,得到了successor算子、source算子和l-值子自动机的某种等价性.进一步描述了由successor算子、source算子和l-值子自动机来构造拓扑.得出了successor算子、source算子和l-值子自动机的一些基本性质,证明了在&关于∨分配时,successor算子、source算子以及l-值子自动机的某些特殊性质.因而得到了由它们构造拓扑的一个较弱的条件,并且澄清了三者构造拓扑时的等价性.

In this paper, some topological characterizations of automata theory based on quantum logic （abbr. l-valued automata theory） are discussed. First, l-valued successor and source operators are redefined and the equivalences of l-valued successor operators, source operators and l-valued subautomata are demonstrated. Afterwards, some topological characterizations in terms of the l-valued successor, source operators and l-valued subautomata are described, and then some fundamental properties of l-valued successor operators, source operators and l-valued subautomata are characterized. Particularly, when the multiplication （＆） is distributive over the union in the truth-value lattices, some of the special properties of l-valued successor operators, source operators and l-valued subautomata are verified. So a weaker limitation to form a topology is obtained. Finally, it is shown that the l-valued topologies in terms of the l-valued successor, source operators and l-valued subautomata are equivalent.