是最小化的布尔EX pressions NP完全？ [英] Is minimization of boolean expressions NP-Complete?

问题描述

我知道，布尔可满足性是NP完全的，但是是一个布尔值前pression最小化/简化，我指的是采取​​一个给定的前pression以符号形式和产生一个等价的，但简单的前pression以符号形式，NP完全？我不知道这有一个从可满足到最小化的减少，但我觉得可能有。有谁知道肯定？

I know that boolean satisfiability is NP-Complete, but is the minimization/simplification of a boolean expression, by which I mean taking a given expression in symbolic form and producing an equivalent but simplified expression in symbolic form, NP-Complete? I'm not sure that there's a reduction from satisfiability to minimization, but I feel like there probably is. Does anyone know for sure?

推荐答案

好了，这样看的：用一个最小化的算法，可以压缩任何非可满足EX pression字面假，对不对？这有效地解决了周六所以至少一个完整的最小化算法，势必会<删除> NP完全 NP难。

Well, look at it this way: using a minimizing algorithm, you can compact any non-satisfiable expression to the literal false, right? This effectively solves SAT. So at least a complete minimizing algorithm is bound to be NP-complete NP hard.

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