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首页> 外文期刊>Journal of logic and computation >Approximating Succinct MaxSat
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Approximating Succinct MaxSat

机译：近似简洁的MaxSat

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摘要

We study the approximability of the version of MAXS AT where exponentially large instances are succinctly represented using circuits. First, we prove that the NP-hardness for approximating MAXSAT can be lifted to a corresponding NEXP-hardness for approximating circuit-succinct MAXSAT for some constant performance ratio. Second, we consider the approximability of circuit-succinct MAXSAT with respect to lower complexity classes: in particular, we prove that computing (2 - ε)-approximate solutions for circuit-succinct MAXSAT is at least as hard as inverting one-way permutations. On the other hand, a simple randomized approximation algorithm computes a (2 + ε)-approximate solution with high probability. Recall that the standard (not succinctly represented) version of the MAXSAT problem is approximable to within a 0.78 factor and that the MAX3SAT problem is approximable to within a 7/8 factor.
机译：我们研究了MAXS AT版本的近似性，其中使用电路简洁地表示了指数级大实例。首先，我们证明了在一定的性能比下，可以将近似于MAXSAT的NP硬度提升至相应的NEXP硬度，以近似于电路简洁的MAXSAT。其次，我们考虑了电路简洁MAXSAT在较低复杂度类别方面的逼近性：特别是，我们证明了计算电路简洁MAXSAT的（2-ε）近似解至少与反转单向排列一样困难。另一方面，一种简单的随机近似算法很可能计算出（2 +ε）近似解。回想一下，MAXSAT问题的标准版本（未简洁表示）近似在0.78因子之内，而MAX3SAT问题近似在7/8因子之内。

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