Abstract
A novel 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 logic minimization step
replaces O(N-factorial) minimizations. The input
encoding problem can be exactly solved using multiple-valued Boolean
minimization. An exact algorithm is presented for state assignment by
generalizing the proposed output encoding approach to the
multiple-valued input case. Four-level Boolean minimization entails
finding a cascaded pair of two-level logic functions that implement
another logic function, such that the sum of the product terms in the
two cascaded functions or truth tables is minimum. Four-level Boolean
minimization can be formulated as an encoding problem and solved exactly
using the proposed algorithms. Preliminary experimental results are
presented which indicate that this approach is significantly more
efficient than exhaustive search. Computationally efficient heuristic
approaches based on the exact algorithms are proposed for output
encoding, state assignment, and four-level Boolean minimization
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