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A novel basis for logic rewriting

机译:逻辑重写的新基础

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摘要

Given a set of logic primitives and a Boolean function, exact synthesis finds the optimum representation (e.g., depth or size) of the function in terms of the primitives. Due to its high computational complexity, the use of exact synthesis is limited to small networks. Some logic rewriting algorithms use exact synthesis to replace small subnetworks by their optimum representations. However, conventional approaches have two major drawbacks. First, their scalability is limited, as Boolean functions are enumerated to precompute their optimum representations. Second, the strategies used to replace subnetworks are not satisfactory. We show how the use of exact synthesis for logic rewriting can be improved. To this end, we propose a novel method that includes various improvements over conventional approaches: (i) we improve the subnetwork selection strategy, (ii) we show how enumeration can be avoided, allowing our method to scale to larger subnetworks, and (iii) we introduce XOR Majority Graphs (XMGs) as compact logic representations that make exact synthesis more efficient. We show a 45.8% geometric mean reduction (taken over size, depth, and switching activity), a 6.5% size reduction, and depth · size reductions of 8.6%, compared to the academic state-of-the-art. Finally, we outperform 3 over 9 of the best known size results for the EPFL benchmark suite, reducing size by up to 11.5% and depth up to 46.7%.
机译:给定一组逻辑原语和布尔函数,精确合成找到根据原语的函数的最佳表示(例如,深度或大小)。由于其较高的计算复杂度,因此精确合成的使用仅限于小型网络。一些逻辑重写算法使用精确的合成来以其最佳表示形式替换小型子网。然而,常规方法具有两个主要缺点。首先,它们的可扩展性受到限制,因为枚举了布尔函数以预先计算其最佳表示形式。其次,用于替换子网的策略并不令人满意。我们展示了如何改进精确综合在逻辑重写中的使用。为此,我们提出了一种新颖的方法,该方法包括对常规方法的各种改进:(i)我们改进了子网选择策略;(ii)我们展示了如何避免枚举,从而使我们的方法可以扩展到更大的子网;以及(iii) ),我们引入XOR多数图(XMG)作为紧凑的逻辑表示形式,使精确的合成更加有效。与最新技术相比,我们的几何平均减小了45.8%(包括尺寸,深度和切换活动),尺寸减小了6.5%,深度·尺寸减小了8.6%。最后,对于EPFL基准测试套件,我们在9个最著名的尺寸结果中胜过3个,将尺寸减小了11.5%,深度减小了46.7%。

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