Exact algorithms for output encoding, state assignment and four-level Boolean minimization

A minimization procedure of prime-implicant generation and covering that operates on symbolic outputs rather than binary-valued outputs is proposed for solving the output encoding problem. An exact solution to this minimization problem is also an exact solution to the encoding problem. While this covering problem is more complex than the classic unate covering problem, a single O(N factorial) logic minimization step replaces O(N factorial) minimizations. An exact algorithm is presented for state assignment by generalizing the output encoding approach to the multiple-valued input case. Preliminary experimental results are presented which indicate that medium-sized problems can be solved exactly. Computationally efficient heuristic approaches based on the exact algorithms are proposed for output encoding, state assignment, and four-level Boolean minimization