Topological Characterizations of Automata Theory Based on Quantum Logic
基于量子逻辑的自动机理论的拓扑性质

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.