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Automatic Generation of Optimal Reductions of Distributions

机译:自动生成最优的分布简化

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摘要

A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable with respect to the source distribution if and only if it is decomposable with respect to each smaller sized distribution (in the reduction). The notion of reduction of distributions has previously been proposed to improve the complexity of decomposability verification. In this paper, we address the problem of generating (optimal) reductions of distributions automatically. A (partial) solution to this problem is provided, which consists of an incremental algorithm for the production of candidate reductions and a reduction validation procedure. In the incremental production stage, backtracking is applied whenever a candidate reduction that cannot be validated is produced. A strengthened substitution-based proof technique is used for reduction validation, while a fixed template of candidate counter examples is used for reduction refutation; put together, they constitute our (partial) solution to the reduction verification problem. In addition, we show that a recursive approach for the generation of (small) reductions is easily supported.
机译:源分布的减少是较小规模分布的集合,这些分布在可分解性方面总体上等同于源分布。即,当且仅当相对于每个较小尺寸的分布是可分解的(针对简化而言),相对于源分布而言,任意语言都是可分解的。先前已经提出减少分布的概念以提高可分解性验证的复杂性。在本文中,我们解决了自动生成分布(最优)约简的问题。提供了对此问题的(部分)解决方案,该解决方案包括用于产生候选约简的增量算法和约简验证过程。在增量生产阶段,每当产生无法确认的候选减少量时,就会应用回溯。增强的基于替换的证明技术用于还原验证,而候选反例的固定模板用于还原反驳。放在一起,它们构成了我们针对还原验证问题的(部分)解决方案。此外,我们证明了轻松支持生成(少量)约简的递归方法。

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