Abstract—In some applications, it is desirable to find for a circuit a minimal partial description that allows a certain task to be carried out. A partial circuit description allows the task to be carried out more efficiently since fewer decision points exist based on a partial description compared to the full circuit description. We consider this problem with respect to finite state machines and the following tasks. Starting from a functional description of a finite state machine $M$ in the form of a state table $ST$, we select a minimal subset of state-transitions $ST_{part} \subset ST$ such that every output sequence that can be produced using state-transitions out of $ST$ can also be produced using state-transitions out of $ST_{part}$. We also formulate a similar problem related to the propagation of fault effects from the inputs to the outputs of $M$ and describe a procedure for solving this problem. Applications of these tasks include test generation for circuits described as interconnections of finite-state machines. Experimental results presented show that $ST_{part}$ contains a small fraction of the state-transitions of $ST$.