A Fully Implicit Algorithm for Exact State Minimization

State minimization of incompletely specified machines is an important step of FSM synthesis. An exact algorithm consists of generation of prime compatibles and solution of a binate covering problem. This paper presents an implicit algorithm for exact state minimization of FSM´s. We describe how to do implicit prime computation and implicit binate covering. We show that we can handle sets of compatibles and prime compatibles of cardinality up to 2¹⁵⁰⁰. We present the first published algorithm for fully implicit exact binate covering. We show that we can reduce and solve binate tables with up to 10 ⁶ rows and columns. The entire branch-and-bound procedure is carried on implicitly. We indicate also where such examples arise in practice.