基于格半群的有限状态自动机的同态

摘要

本文研究了格值有限状态自动机(LFSA)的同态和强同态及其性质.利用强同态概念,在格值有限状态自动机的状态集上建立了一种等价关系,得到了格值有限状态自动机的商自动机,证明了商自动机与强同态像自动机同构.%In this article, we consider homomorphism and strong homomorphism of lattice-valued finite states automata (LFSA), and study some properties of homomorphism and strong homomorphism of LFSAs. By using the concept of strong homomorphism, we establish a kind of equivalence relation over states of LFSA and obtain quotient automata of LFSA. Finally, we get an isomorphism relation between quotient automata and the strong homomorphism image automata.