Automata theory based on complete residuated lattice-valued logic: A categorical approach

作者：Xing, Hongyan; Qiu, Daowen^*

来源：Fuzzy Sets and Systems, 2009, 160(16): 2416-2428.

DOI：10.1016/j.fss.2009.01.007

• Category
• Automata
• Non-classical logic

Automata theory based on complete residuated lattice-valued logic, called L-valued automata (L-VAs), has been primarily established by Qiu in 2001 and 2002. In this paper, we consider the L-VAs that have L-valued initial and final states. We study the categorical issue of L-VAs. The main technical contributions include: (1) We investigate the relationship between the category of L-VAs and the category of non-deterministic automata (NDAs); also, we study the relationship between the category of generalized L-VAs and the category of NDAs. (2) We prove the existence of isomorphisms between the category of L-VAs and the subcategory of generalized L-VAs and between the category of L-VAs and the category of sets of NDAs. (3) Finally, we further investigate some specific relationships between the output L-valued subsets of generalized L-VAs and the output L-valued subsets of NDAs.

• 出版日期2009-8-16
• 单位中山大学