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arXiv 1104.0843cs.AI
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知识编译过程中的阶段转换:一项实验研究

Phase Transitions in Knowledge Compilation: an Experimental Study

Beihang University(北京航空航天大学)

Jian Gao, Minghao Yin, Ke Xu

摘要:

在过去的十年中,许多复杂组合问题中的相变问题得到了广泛的研究。本文以DFA、OBDD和d-DNNF为目标语言,对知识编译过程中的阶段转换进行了实证研究。通过大量的实验分析编译结果的大小,得出以下结论:编译过程中存在一种简单-困难-简单的模式,当k固定时,该模式中大小的峰值点只与子句数与变量数的比值有关,而与目标语言无关;大多数编译结果的大小随变量数的增加而呈指数增长,但也存在一个将多项式增量区域与指数增量区域分开的相变;此外,通过对DFAs微结构的分析,我们解释了编译过程中相变的原因,并得出结论:一种具有两个以上变量的解的可解性在易-难-易模式的峰值点附近有一个急剧的转变,从而对DFAs的尺寸有很大的影响.

英文摘要:

Phase transitions in many complex combinational problems have been widely studied in the past decade. In this paper, we investigate phase transitions in the knowledge compilation empirically, where DFA, OBDD and d-DNNF are chosen as the target languages to compile random k-SAT instances. We perform intensive experiments to analyze the sizes of compilation results and draw the following conclusions: there exists an easy-hard-easy pattern in compilations; the peak point of sizes in the pattern is only related to the ratio of the number of clauses to that of variables when k is fixed, regardless of target languages; most sizes of compilation results increase exponentially with the number of variables growing, but there also exists a phase transition that separates a polynomial-increment region from the exponential-increment region; Moreover, we explain why the phase transition in compilations occurs by analyzing microstructures of DFAs, and conclude that a kind of solution interchangeability with more than 2 variables has a sharp transition near the peak point of the easy-hard-easy pattern, and thus it has a great impact on sizes of DFAs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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