On the parallel evaluation of classes of circuits
We treat the problem of parallel evaluation of two important classes of circuits: polynomial degree circuits, and leveled monotone planar circuits. We show that if the operators form a non-commutative semi-ring, then there exists a circuit of degree 0(n) and size 0(n) for which the minimum depth after any restructuring is n. We also establish that any leveled monotone planar boolean circuit of size n can be evaluated by poly(n) processors in 0(log3n) parallel time.
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