Multiple Reduction of Variable Dependency of Sequential Machines

An important step in the design of finite state sequential machines is the assignment of binary variables to represent their internal states. In [1] J. Hartmanis studied the problem of determining economical state assignments. In [2] he and R. E. Stearns generalized many of the results of [1]. Assignments obtained by the methods of [1] and [2] reduce dependence among the state variables of any sequential machine in which reduction is possible. These methods, however, will not guarantee the production of assignments with a maximal reduction of state variable dependence. The present paper generalizes these methods to produce efficiently and systematically for machines of the aforementioned class assignments in which state variable is optimally reduced.