Assigned Reading in Murdocca & Heuring:
Assigned Reading in Neveln:
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Topics Covered:
The state reduction algorithm makes passes through all pairs of states (X,Y) that we have not already found to be distinguished. For each pair (X,Y), we check if X and Y are distinguished using the definition above. If no new distinguished pairs are found during a pass, then the algorithm terminates. At the end of the algorithm, states that are not found to be distinguished are in fact equivalent. (The proof of this "fact" is usually given in an Automata Theory class like CMSC 451. Though not hard, we'll dispense with the proof here.) Equivalent states can be combined to form an equivalent finite state machine with fewer states.
The finite state machine constructed in this manner has the smallest number of states possible. (Another fact proven in CMSC 451.)
Some heuristics for the state assignment problem (from Digital Design: Principles and Practices 2/e, John F. Wakerly, Prentice-Hall, 1994).