Solving #SAT using vertex covers

We propose an exact algorithm for counting the models of propositional formulas in conjunctive normal form. Our algorithm is based on the detection of strong backdoor sets of bounded size; each instantiation of the variables of a strong backdoor set puts the given formula into a class of formulas for which models can be counted in polynomial time. For the backdoor set detection we utilize an efficient vertex cover algorithm applied to a certain “obstruction graph” that we associate with the given formula. This approach gives rise to a new hardness index for formulas, the clustering-width. Our algorithm runs in uniform polynomial time on formulas with bounded clustering-width. It is known that the number of models of formulas with bounded clique-width, bounded treewidth, or bounded branchwidth can be computed in polynomial time; these graph parameters are applied to formulas via certain (hyper)graphs associated with formulas. We show that clustering-width and the other parameters mentioned are incomparable: there are formulas with bounded clustering-width and arbitrarily large clique-width, treewidth, and branchwidth. Conversely, there are formulas with arbitrarily large clustering-width and bounded clique-width, treewidth, and branchwidth.     

Recognition of Simple Enlarged Horn Formulas and Simple Extended Horn Formulas

The enlarged Horn formulas generalize the extended Horn formulas introduced by Chandru and Hooker (1991). Their satisfying truth assignments can be generated with polynomial delay. Unfortunately no polynomial algorithm is known for recognizing enlarged Horn formulas or extended Horn formulas. In this paper we define the class of simple enlarged Horn formulas, a subclass of the enlarged Horn formulas, that contains the simple extended Horn formulas introduced by Swaminathan and Wagner (1995). We present recognition algorithms for the simple enlarged Horn formulas and the simple extended Horn formulas whose complexity is bounded by the complexity of the arborescence-realization problem.     

On the Learnability of Disjunctive Normal Form Formulas

We present two related results about the learnability of disjunctive normal form (DNF) formulas. First we show that a common approach for learning arbitrary DNF formulas requires exponential time. We then contrast this with a polynomial time algorithm for learning most (rather than all) DNF formulas. A natural approach for learning boolean functions involves greedily collecting the prime implicants of the hidden function. In a seminal paper of learning theory, Valiant demonstrated the efficacy of this approach for learning monotone DNF, and suggested this approach for learning DNF. Here we show that no algorithm using such an approach can learn DNF in polynomial time. We show this by constructing a counterexample DNF formula which would force such an algorithm to take exponential time. This counterexample seems to capture much of what makes DNF hard to learn, and thus is useful to consider when evaluating the run-time of a proposed DNF learning algorithm. This hardness result, as well as other hardness results for learning DNF, relies on the construction of particular hard-to-learn formulas, formulas that appear to be relatively rare. This raises the question of whether most DNF formulas are learnable. For certain natural definitions of most DNF formulas, we answer this question affirmatively.     

Delay Control and Parallel Admission Algorithms for Real-Time Anycast Flow

An anycast flow is a flow that can be connected to any one of the members in a group of designated (replicated) servers (called anycast group). In this paper, we derive a set of formulas for calculating the end-to-end delay bound for the anycast flows and present novel admission control algorithms for anycast flows with real-time constraints. Given such an anycast group, our algorithms can effectively select the paths for anycast flows' admission and connection based on the least end-to-end delay bounds evaluated. We also present a parallel admission control algorithm that can effectively calculate the available paths with a short delay bound for different destinations in the anycast group so that a best path with the shortest delay bound can be chosen.     

基于双种群的小生境差分进化算法

将非线性方程组的求解问题转化为函数优化问题,当方程组有多个解时,它的适应值函数就是具有多个最优解的多峰函数.为此,提出了基于双种群的小生境差分进化算法.在该算法中,进化在两个不同的子群间并行进行,通过使用不同的变异策略,实现种群在解空间具有尽可能分散的探索能力的同时在局部具有尽可能细致的搜索能力.通过子群重组实现子群间的信息交换,然后引入小生境淘汰机制.对典型测试函数的优化结果表明,该算法能找到全部解,而且精度好.     

Toric forms of elliptic curves and their arithmetic

We scan a large class of one-parameter families of elliptic curves for efficient arithmetic. The construction of the class is inspired by toric geometry, which provides a natural framework for the study of various forms of elliptic curves. The class both encompasses many prominent known forms and includes thousands of new forms. A powerful algorithm is described that automatically computes the most compact group operation formulas for any parameterized family of elliptic curves. The generality of this algorithm is further illustrated by computing uniform addition formulas and formulas for generalized Montgomery arithmetic.     

On learning multivalued dependencies with queries

Data dependencies play an important role in the design of relational databases. There is a strong connection between dependencies and some fragments of the propositional logic. In particular, functional dependencies are closely related to Horn formulas. Also, multivalued dependencies are characterized in terms of multivalued formulas. It is known that both Horn formulas and sets of functional dependencies are learnable in the exact model of learning with queries. Here we present an algorithm that learns a non-trivial subclass of multivalued formulas using membership and equivalence queries. Furthermore, a slight modification of the algorithm allows us to learn the corresponding subclass of multivalued dependencies.     

A general framework for computing maximal contractions

This paper investigates the problem of computing all maximal contractions of a given formula set Γ with respect to a consistent set Δ of atomic formulas and negations of atomic formulas. We first give a constructive definition of minimal inconsistent subsets and propose an algorithmic framework for computing all minimal inconsistent subsets of any given formula set. Then we present an algorithm to compute all maximal contractions fromminimal inconsistent subsets. Based on the algorithmic framework and the algorithm, we propose a general framework for computing all maximal contractions. The computability of the minimal inconsistent subset and maximal contraction problems are discussed. Finally, we demonstrate the ability of this framework by applying it to the first-order language without variables and design an algorithmfor the computation of all maximal contractions.     

Prime number generation using memetic programming

For centuries, the study of prime numbers has been regarded as a subject of pure mathematics in number theory. Recently, this vision has changed and the importance of prime numbers has increased rapidly, especially in information technology, e.g., public key cryptography algorithms, hash tables, and pseudo-random number generators. One of the most popular topics to attract attention is to find a formula that maps the set of natural numbers into the set of prime numbers. However, to date there is no known formula that produces all primes. In this article, we use a hybrid evolutionary algorithm, called the memetic programming (MP) algorithm, to generate mathematical formulas that produce distinct primes. Using the MP algorithm, we succeeded in discovering an interesting set of formulas that produce sets of distinct primes.     

Satisfiability checking using Boolean Expression Diagrams

In this paper we present an algorithm for determining satisfiability of general Boolean formulas which are not necessarily in conjunctive normal form. The algorithm extends the well-known Davis–Putnam algorithm to work on Boolean formulas represented using Boolean Expression Diagrams (BEDs). The BED data structure allows the algorithm to take advantage of the built-in reduction rules and the sharing of sub-formulas. Furthermore, it is possible to combine the algorithm with traditional BDD construction (using Bryants Apply-procedure). By adjusting a single parameter to the BedSat algorithm, it is possible to control to what extent the algorithm behaves like the Apply-algorithm or like a SAT-solver. Thus, the algorithm can be seen as bridging the gap between standard SAT-solvers and BDDs. We present promising experimental results for 566 non-clausal formulas obtained from the multi-level combinational circuits in the ISCAS85 benchmark suite and from performing model checking of a shift-and-add multiplier.     

精英改进粒子群算法在入库堆垛问题中的应用

针对钢铁企业生产与物流一体化协同管理中入库堆垛问题,基于出库次序A型约束、垛位选择分散性约束等,建立了以均衡库存垛位负载和最大化板坯综合匹配度为目标的联合优化模型。结合问题的特点,基于PSO算法,利用收敛指数判断种群进化状态,并对处于"收敛"状态的种群执行精英学习策略,提高粒子的活性,帮助种群跃出局部最优。最后通过实例仿真说明了模型与算法的有效性和可行性。     

Special types of the nonlinear dispersive Zakharov–Kuznetsov equation with compactons,solitons, and periodic solutions

In this article, we study nonlinear dispersive special types of the Zakharov–Kuznetsov equation with positive and negative exponents. The approach depends mainly on the sine–cosine algorithm. Compactons, solitary patterns, solitons, and periodic solutions are formally derived.     

Numerical simulations of the Boussinesq equation by He's variational iteration method

In this paper, we present a reliable algorithm to study the well-known model of nonlinear dispersive waves proposed by Boussinesq. We solve the Cauchy problem of Boussinesq equation using variational iteration method (VIM). The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that VIM is a powerful mathematical tool for solving nonlinear problems.     

一种求解命题公式骨干集的警示传播算法

警示传播WP算法是一类重要的信息传播算法,在命题公式的可满足性判定中非常有效。通过对WP算法的数学原理分析发现,当算法收敛时以高概率固定部分变元的赋值,可以对公式进行化简。基于这样的特征修改WP算法的迭代方程和变元赋值条件,设计了一种求解命题公式骨干集的信息传播算法。当变元数目超过400时,与经典骨干集求解算法对比,效率提高了40%,与目前常用算法对比也有10%的提高。结果表明,所提算法求解命题公式骨干集时非常有效。     

Improved subband-forward algorithm for acoustic noise reduction and speech quality enhancement

This paper addresses the problem of speech enhancement and acoustic noise reduction by adaptive filtering algorithms. Recently, we have proposed a new Forward blind source separation algorithm that enhances very noisy speech signals with a subband approach. In this paper, we propose a new variable subband step-sizes algorithm that allows improving the previous algorithm behaviour when the number of subband is selected high. This new proposed algorithm is based on recursive formulas to compute the new variable step-sizes of the cross-coupling filters by using the decorrelation criterion between the estimated sub-signals at each subband output. This new algorithm has shown an important improvement in the steady state and the mean square error values. Along this paper, we present the obtained simulation results by the proposed algorithm that confirm its superiority in comparison with its original version that employs fixed step-sizes of the cross-coupling adaptive filters and with another fullband algorithm.     

Self-correcting polynomial programs

In this paper, we introduce a new self-correction algorithm that requires less queries than the simple majority vote. We also introduce new random self-reducibility formulas.     

基于改进Hu矩算法的AGV字符识别研究

视觉导引AGV以识别标识符为基础实现工位转换。Hu矩算法可以提取字符的特征参数,结合机器学习分类算法,对特征值进行提取并分类,其运算速度快,但是识别准确率低。分析其原理公式,发现由于阶数高导致数值范围大,数据相近度差。基于此,对Hu矩公式进行改进,构造了新的算法。通过对UCI字符数据库进行检测,并在视觉导引AGV平台上进行在线测试,验证了改进后的Hu矩算法可以更快地提取特征值,并大大提高机器学习算法字符分类准确率,说明改进后的Hu矩算法在视觉导引AGV的字符识别上具有较好的实用性。     

UnitWalk: A new SAT solver that uses local search guided by unit clause elimination

In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification. Our algorithm is inspired by two randomized algorithms having the best current worst-case upper bounds ([27,28] and [30,31]). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT [34] and WalkSAT [33]) and unit clause elimination (which is rarely used in local search algorithms). In this paper we do not prove any theoretical bounds. However, we present encouraging results of computational experiments comparing several implementations of our algorithm with other SAT solvers. We also prove that our algorithm is probabilistically approximately complete (PAC).