Equivalent States
States S1, S2, …, Sj of a completely specified sequential circuit are said to be equivalent if and only if, for every possible input sequence, the same output sequence is produced by the circuit regardless of whether S1, S2, …, Sj is the initial state.
Let Si and Sj be states of a completely specified sequential circuit. Let Sk and Sl be the next states of Si and Sj, respectively for input Ip.
Si and Sj are equivalent if and only if for every possible Ip the following are conditions are satisfied.
- The outputs produced by Si and Sj are the same,
- The next states Sk and Sl are equivalent.