弱可逆拟(r,r)阶存贮线性有限自动机的分解

Decomposition of weakly invertible quasi-(r,r)-order memory linear finite automata

通过对延迟r步弱可逆拟(r,r)阶存贮线性有限自动机输出权的研究,得出对延迟r步弱可逆拟(r,r)阶存贮线性有限自动机的任意一个状态,它的长r的输出权都是1;任何一个n元拟(r,r)阶存贮线性有限自动机M延迟r步弱可逆的充分必要条件是M都可以分解为一个延迟0步弱可逆有限自动机M0和一个延迟r步弱可逆拟(0,r)阶存贮线性有限自动机M1。

This paper studies the output weight of the weakly invertible quasi-（r,r）-order memory linear finite automata,then gives a fact that the r-output weight of any given states of the weakly invertible quasi-（r,r）-order memory linear finite automata is 1.For a n-ary quasi-（r,r）-order memory linea finite automata M,whether M is weakly invertible with delay r,a necessary and sufficient condition is obtained,that M can be decomposed into a weakly invertible finite automata M0 with delay 0 and a weakly invertible quasi-（0,r）-order memory linear finite automata Mj with delay r.