A generalization to the classical state minimization of a Finite State Machine (FSM) is described. The FSM is minimized here in two dimensions: numbers of both input symbols and internal states are minimized in an iterative sequence of input minimization and state minimization procedures. For each machine in the sequence of FSMs created b y the algorithm an equivalent FSM is found that attempts 20 minimize the state assignment b y selecting in each cell of the transition map one successor state from the set of successors. This approach leads t o a partitioned realiration of the FSM with an input encoder. Our efficient branch-and-bound program, FMINI, produces an exact minimum result for each component minimization process and a globally quasi-minimum solution to the entire two-dimensional (2D) FSM combined process of state minimization and assignment.
CG : compatible group. CGI : compatible group of input columns. COP : compatible group of present state rows. SCGP : strong compatible group of present state rows. ICGP : implying compatible group of present state rows. MCC : minimal closed and complete covering set. MCCI : minimal comlpete covering set of inputs columns. MCCP : minimal closed and complete covering set of present state rows. OMCC: optimal closed and complete covering set. OMCCI : optimal complete covering set of input columns. OMCCP : optimal closed and complete covering set of present state rows.
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