Concurrent Two-Dimensional State Minimization and State Assignment of finite State Machines

Abstract

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 by the algorithm an equivalent FSM is found that attempts 20 minimize the state assignment by selecting in each cell of the transition map one successor state from the set of successors. This approach leads to 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.