中文摘要：

研究弱可逆有限自动机的分解可以为分析有限自动机公开钥密码体制的安全性提供一种重要途径。从输出权的角度讨论了一般的延迟r步弱可逆有限自动机M的分解问题，得到了它可以分解出k0（k0≤r）阶延迟元的一个充要条件，即M可以分解成延迟r-k0步弱可逆有限自动机和k0阶延迟元当且仅当M的所有状态的长k0输出权为1。

英文摘要：

It is very important to investigate the decomposition of weakly invertible finite automata,since it could provide an approach to cryptanalyzing finite automata public-key cryptosystem （FAPKC）. This paper deals with the problem about the decomposition of weakly invertible finite automata M with delay r,and a sufficient and necessary condition is obtained,which means it can be decomposed into a weakly invertible finite automata with delay r-k0 and a so-called k0-order delay unit,if and only if the k0-output weight of s is 1 for any state s in M.