Second common factor of sequential machines

For the synthesis of two or more sequential machines with the same input and specified initial states, Kohavi and Smith [1,2] have investigated the existence of a common factor machine such that, when two machinesM ₁ andM ₂ have a common factor machineM _c ,M ₁ is realized by the cascade connection ofM _c and a snccessor machineM _α, andM ₂ is realized by the cascade connection ofM _c and a snccessor machineM _β. In this paper we study a second common factor machine such that, when two machinesM ₁ andM ₂ have a second common factorM _c,M ₁ is realized by the cascade connection of a front machineM _α andM _c, andM ₂ is realized by the cascade connection of a front machineM _β andM _c.