State reduction merges states that are behaviorally equivalent. Equivalent states produce compatible outputs and lead to equivalent states for every relevant future input. Merely having the same present output is not enough: their future responses must also match.
Worked example
Suppose Moore states A and B both output zero. For input 0, A returns to A and B returns to B; for input 1, both go to C. If no other distinction changes their future behavior, A and B can be merged. C remains separate if its output or future behavior differs.
What to watch for
Start with output-based partitions, then refine them using transition destinations until stable. Unreachable-state removal is related but is a different operation from merging equivalent reachable states.
Try it yourself
Can two Moore states with different output values be merged while preserving behavior?
Answer: No. Their observable outputs already distinguish them, even before considering future input sequences.
How to study this topic
Begin with named states and a complete transition table. Then choose encodings and derive the logic. Trace inputs over several cycles, checking outputs as well as next states, including reset and unexpected encodings.
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