一类线性有限自动机的线性τ-弱逆

Linear Delay τ-weak Invertibility of a Class of Linear Finite Automata

戴宗铎等人在域F上的一元多项式环F[z]与域F上的形式幂级数环F[[z]]之间,定义了一种乘法"*",使得F[[z]]作成一个F[z]-模,利用此模研究了线性有限自动机。在此讨论了一类线性有限自动机的线性τ-弱逆,给出了这类线性有限自动机一定τ-弱可逆的充分条件、构成它的τ-弱逆线性有限自动机的充要条件以及τ-弱逆线性有限自动机自由响应模的最小维数。

One kind of “ ＊ ” between the field of one dimension polynomial ring FEz] and the ring of power series F[[z]] in the field of F was defined by Mr DAI Zong-duo and others. This makes the F[[z]] become a left F [z]-module. Using F [z]-module, linear finite automata and one kind of linear finite automata＇s linear r-weak invertibility are discussed in this article. The sufficient condition of this kind of linear finite automata which must be r-weak invertible is given. The sufficient and necessary condition are presented for which can be made a r-weak invertible linear finite automata. Finally,the smallest dimension of free response module is given for the r-weak invertible linear finite automata.