基于量子逻辑的自动机理论的拓扑性质郭秀红基于量子逻辑的自动.pdfVIP

ISSN 1000-9825, CODEN RUXUEW E-mail: jos@ Journal of Software, Vol.18, No.6, June 2007, pp .1282−1286 http://www.j DOI: 10. 1360/jos1 81282 Tel/Fax : +86-10 © 2007 by Journal of Software. All rights reserved. ∗ 基于量子逻辑的自动机理论的拓扑性质 郭秀红 ( 四川师范大学 数学与软件科学学院, 四川 成都 610066) Topological Characterizations of Automata Theory Based on Quantum Logic GUO Xiu-Hong (College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China) + Corresponding author: Phn: +86-28 Fax: +86-28 E-mail: hmxiuxiu@, Guo XH. Topological characterizations of automata theory based on quantum logic. Journal of Softw are, 2007,18(6):1282−1286. /1000-9825/18/1282.htm Abstract: 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 term