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Two-Level Logic Minimization

Two-Level Logic Minimization. Exact minimization problem : very large number of prime and very large number of minterm Heuristic minimization avoid computing all primes successively modify a given initial cover of the function until a suitable stopping(local search) criterion is met.

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Two-Level Logic Minimization

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  1. Two-Level Logic Minimization • Exact minimization • problem : very large number of prime and very large number of minterm • Heuristic minimization • avoid computing all primes • successively modify a given initial cover of the function until a suitable stopping(local search) criterion is met

  2. Local Search A Pictorial Representation of Local Search

  3. f(x) x g(x) local minimum absolute minimum x Local Search A Convex Optimization Problem A Non-Convex Optimization Problem

  4. z y x Expand Input, Reduce Output (Single Output) (a) (b) xyz f 0-0 1 -11 1 xyz f 000 1 01- 1 -11 1

  5. z y x z y x f1 f2 Expand Output, Reduce Input (Multiple Output) xyz f1f2 0-1 10 1-0 10 00- 01 -00 01 -11 01 f1 f2 xyz f1f2 0-1 11 1-0 10 -00 01 -11 01

  6. z y x Reduce Input, Expand Output (Multiple Output) f1 f2 xyz f1f2 1-- 10 --1 10 0-1 01 -10 01 xyz f1f2 1-- 10 0-1 11 -10 01

  7. Simple Minization Loop F = EXPAND(F,D); F = IRREDUNDANT(F,D); do { cost = F ; F = REDUCE(F,D); F = EXPAND(F,D); F = IRREDUNDANT(F,D); } while ( F < cost ); F = MAKE_SPARSE(F,D);

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