Linear dependencies in extended LFSMs

In this paper, the linear dependencies of extended linear finite state machines (LFSMs) used as test pattern generators (TPGs) are examined. The TPG mechanism considered is a shift register whose initial portion is configured as an LFSM. This mechanism (LFSM/SR) can be used for pseudorandom and circuit-specific pseudoexhaustive test pattern generation. A formula is presented that relates the linear dependencies that can occur among the LFSM/SR cells with the characteristic polynomial of the LFSM. Previously, such an easily computable formula had only been established for Type-1 linear feedback shift registers (LFSRs). The generalization allows the fast determination of linear dependencies for any LFSM, including in particular Type-2 LFSRs and cellular automata.