It is shown that the time to compute a monotone boolean function depending upon $n$ variables on a CREW-PRAM satisfies the lower bound $T = \Omega$(log $l$ + (log $n$)/$l$), where $l$ is the size of the largest prime implicant. It is also shown that the bound is existentially tight by constructing a family of monotone functions that can be computed in $T = O$(log $l$ + (log $n$)/$l$), even by an EREW-PRAM. The same results hold if $l$ is replaced by $L$, the size of the largest prime clause. An intermediate result of independent interest is that $S (n,l)$, the size of the largest minimal vertex cover minimized over all (reduced) hypergraphs of $n$ vertices and maximum hyperedge size $l$, satisfies the bounds $\Omega(n^{1/l}) \leq S (n,l) \leq O (ln^{1/l}).$
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机译：结果表明，根据CREW-PRAM上$ n $变量计算单调布尔函数的时间满足下限$ T = \ Omega $（log $ l $ +（log $ n $）/ $ l $） ，其中$ l $是最大素数蕴涵的大小。通过构造一个单调函数族，即使通过EREW-，也可以以$ T = O $（log $ l $ +（log $ n $）/ $ l $）计算出单调函数的界，从而证明该边界在本质上是紧密的。 PRAM。如果将$ l $替换为最大素数子句的大小$ L $，则结果相同。独立利益的中间结果是，$ S（n，l）$（在$ n $个顶点的所有（缩小的）超图上的最大最小顶点覆盖的大小和最大超边尺寸$ l $的最小化）满足边界$ \ Ω（n ^ {1 / l}）\ leq S（n，l）\ leq O（ln ^ {1 / l}）。$
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