文献学习-Conflicting rate based branching heuristic for CDCL SAT solvers

 

	As we know, the increment of EVSIDS is fixed whether the activity of variable is reached the critical value, i.e., the increment is not concerned with conflict; it is concerned with the period of conflict.译文：我们知道，无论变量的活动是否达到临界值，EVSIDS的增量都是固定的，即增量与冲突无关;它与冲突时期有关. Different variables share the same increment in some cases. Intuitively, on the basis of the rule of traversing binary tree, half of the rest of the searching space will be cut while any unassigned variable is assigned. 译文：在某些情况下，不同的变量共享相同的增量。直观地看，根据遍历二叉树的规则，当分配任何未分配的变量时，搜索空间的一半将被切割。 Hence, we are forecasted boldly that the sequence of assignments may have different influences on solving. 译文：因此，我们大胆地预测，分配的顺序可能会对求解产生不同的影响。   This is the motivation that we improve the branching algorithm and propose CRB. The CRB maintains a counter for each variable as EVSIDS, initialized to 0 at the beginning of the search. Whenever a variable is used in conflict analysis, the counter is incremented by using the following equation where f is the damping factor given by EVSIDS.译文：CRB为每个变量维护一个计数器作为EVSIDS，在搜索开始时初始化为0。每当在冲突分析中使用一个变量时，计数器就会使用以下公式递增，其中f是EVSIDS给出的阻尼因子。
	W(v) is dynamic regulatory function that embodied the sequence of assignments. This includes two aspects: decision levels and conflicts. Let nLevels be an integer variable that keeps the current decision levels, vLevel be an integer variable that keeps the nLevels while the variable is assigned, nConflicts be an integer variable that records the number of total conflict, vConflict be an integer variable that keeps the nConflicts while the variable is assigned, α be an deceleration factor with 0≤α≤1. The dynamic regulatory function used by CRB is defined as the following equation. nLevels当前决策级别的整型变量，vLevel分配变量时层级整型变量， nConflicts是一个整型变量，记录总的冲突数，vConflict是一个整型变量，在分配变量时保留nConflicts \begin{equation*} W(v)=\alpha\cdot\frac{vLevel}{nLevels}+(1-\alpha)\cdot\frac{vConflict}{nConflicts}\ (0\leq\alpha\leq 1) \tag{2} \end{equation*}
	Intuitively, W(v) approaches 1 while conflict derived by all of the unassigned variables at the current decision level. The closer to the root level v assigned, the smaller the W(v). Obviously, W(v)∈(0,1]. There have two differences between CRB and EVSIDS. First, different variables (both decision variable and propagated variable) have different damping factors even led to same conflict.译文：首先，不同的变量(包括决策变量和传播变量)具有不同的阻尼因子，甚至会导致相同的冲突。 Second, the damping factor is smaller than EVSIDS of 1. Hence, the CRB slowed the growth rate in the overall.译文：其次，阻尼因子小于EVSIDS的1。因此，CRB减缓了整体的增长率。 Large and sudden increases are the ones that tend to shorten the cycle time of entire damping and create frequent periodic damping.译文：大而突然的增加往往会缩短整个阻尼的周期时间，并产生频繁的周期性阻尼。 The CRB does not change the growth trends of score, i.e., variables which frequently led to conflict may have larger activity. 译文：CRB并没有改变得分的增长趋势，即经常导致冲突的变量可能具有更大的活动性。
	--决策层----- 决策变量------决策之前对应的冲突数     35              x4                   1001     36              x3                   1120     37              x7                   13695     38              x16                 17367
	By that analogy, W(x3)≈0.65+0.30⋅α,W(x7)≈0.79+0.19⋅α, W(x16)=α. Assume that α=0.6, the CR of those variables are 0.79, 0.83, 0.90, and 1.00, respectively. Obviously the CR of decision variables from level 35 to 38 are nonlinear increased. Fig. 2 illustrates the impact of different CR by different deceleration factors.
	Fig. 3 is a probability distribution image which illustrates how CRB is impact the searching process. The example instance is named itox _ vc1130.cnf which from SAT-Race 2015. Here, α is 0.5. The total number of bumping is about 183403 and 152999 for EVSIDS and CRB respectively. As shown in Fig. 3 the CRB covers more domain of definition than EVSIDS, i.e., more variables can be updated to a smaller activity. The CRB maintains equal levels of quantity of variables which have stronger associations with conflict. This makes the branches more accurate and effective.   译文：图3是一个概率分布图像，说明了CRB是如何影响搜索过程. 译文：如图3所示，CRB比EVSIDS覆盖了更多的定义域，也就是说，可以将更多的变量更新为更小的活跃度。 译文：CRB保持了与冲突有更强关联的变量的相同数量水平。 译文：这使得分支更加准确和有效。

SECTION V.

Experimental Results

	In this section, we empirically compare the performance between the SAT solvers with different branching heuristics, EVSIDS and CRB, respectively.译文：在本节中，我们根据经验分别比较了具有不同分支启发式的SAT求解器EVSIDS和CRB之间的性能。   Minisat [9] is a classical SAT solver with EVSIDS. Many state of the art SAT solvers are based on it. Since there are no more advanced heuristics in Minisat, it will enable us to better compare the efficiency of different branching heuristics. For the original version of Minisat, we call it Minisat+EVSIDS. For fully evaluate the performance of CRB and further analyze the impact with decision level and conflict. We have implemented 10 versions of CRB with different deceleration factors of α. The modified solver only changed the branching heuristic by replacing EVSIDS with CRB. All of the default parameter settings and other features are left.译文：我们实现了10个版本不同减速因子的CRB。改进的求解器只改变了分支启发式，用CRB代替EVSIDS。所有默认参数设置和其他特性都将保留。   This comparison is made on the set of 300 instances from SAT Race 2015, each instance is limited to 3600s. The operating system is Hat Enterprise Red 6, with farm of Core(TM) i3-3240 3.4Ghz and 16G bytes physical memory.
	Both Minisat+EVSIDS and Minisat+CRBs can run successfully without any preprocessors and all conclusions are correct. 译文：Minisat+EVSIDS和Minisat+CRBs都可以在不需要任何预处理的情况下成功运行，结论是正确的。 Table 1 shows the Number of solved instances by original Minisat versus modified versions with CRB on SAT Race 2015 main track benchmarks. Minisat with EVSIDS solved 191 instances over the entire benchmarks, all of the modified versions with different deceleration factors solved more instances than Minisat.译文：不同减速因子的改进版本求解的实例数都比Minisat多。   Table I. Number of solved instances on sat race 2015 main track with 3600s liimt.     This illustrates CRB is more powerful than EVSIDS. In particular, the number of solved instances are growing linearly on the whole while 0.1≤α≤1.0. It also shows the decision level has stronger influence than conflict number.译文：这说明CRB比EVSIDS更强大。具体而言，在0.1≤1.0的情况下，解决实例的数量总体呈线性增长。决策水平的影响比冲突数量的影响更大。
	Fig. 4 shows the cactus plot of the running times, where each dot corresponds to a SAT instance. Lines further down and to the right on the plot are better. All the CRBs solved the instances with average time between 566.78s and 923.12s, less than Minisat of 945.28s. This illustrates the CRB is more effective than EVSIDS.

 

SECTION VI.

Conclusions

The conventional branching heuristics are more concerned with the number of conflicts in the score.译文：传统的分支启发式方法更关注分数中的冲突数量。 This paper has proposed a new branching scheme, called conflicting rate branching (CRB). CRB is inspired by EVSIDS and CHB which maintains a counter of activity for each variable as the algorithms in the past, but more relevant to the decision levels and conflicts.译文：CRB是受EVSIDS和CHB的启发，后者为每个变量保持了一个计数器的活动，作为过去的算法，但更相关的决策水平和冲突。   The CRB updates the score which integrated with the decision level and conflicts whenever a variable is used in conflict analysis.译文：当冲突分析中使用一个变量时，CRB会更新与决策水平和冲突相结合的得分。 We integrated CRB with Minisat solvers and evaluated CRB on instances from the SAT Race 2015. Experimental results show that the proposed strategy can solve more instances than EVSIDS and improve performance for both SAT and UNSAT instances.

 

 个人理解：

文献“Evaluating CDCL Variable Scoring Schemes”原文如下： Typical values for g are in the range of 1.01 to 1.2. Small values have been shown to be useful for hard satisfiable instances (like cryptographic instances). Large values are useful with very frequent restarts, particularly in combination with the reuse-trail technique [28]. In Glucose 2.3, even without reusing the trail, it was thus suggested to slowly decrease g over time from a large value to a small one.1 In the (new) version of Lingeling used in our experiments, g is kept at 1.2.   if(conflicts % 5000 == 0 && var_decay < max_var_decay) var_decay += 0.01;

  小贴士：

	The conference follows the Workshops on Satisfiability held in Siena (1996), Paderborn (1998), and Renesse (2000), the Workshop on Theory and Applications of Satisfiability Testing held in Boston (2001) and in Cincinnati (2002). As in the last edition, the conference will host a SAT solver competition, and, starting from this year, also a QBF solvers comparative evaluation. Great strides have been made in recent years in the theory and practice of propositional satisfiability (SAT) testing. 译文：近年来，命题满足性(SAT)测试的理论和实践取得了很大进展。 Even more recently, we have seen a growing interest in the theory and practice of quantified Boolean formulas (QBFs 译文：量化布尔公式) satisfiability testing,witnessed by analogous advancements both on the theoretical and on the practical side. As a result there is growing interest in using SAT and QBF solvers as the basis for practical tools for solving real-world problems, as well as using the insights gained from SAT and QBF research to create problem-specific solutions. 译文：因此，使用SAT和QBF解决器作为解决现实问题的实用工具的基础， 以及使用从SAT和QBF研究中获得的见解来创建具体问题的解决方案的兴趣越来越大。
	The purpose of this conference is to bring together researchers from different communities -- including theoretical computer science, artificial intelligence, verification, mathematical theorem-proving, electrical engineering, and operations research -- in order to share ideas and increase synergy(译文：增加协同效应) between theoretical and empirical work.