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).     

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).     

Evaluating Optimized Decision Procedures for Propositional Modal K (m) Satisfiability

Heavily optimized decision procedures for propositional modal satisfiability are now becoming available. Two systems incorporating such procedures for modal K, DLP and KSATC, are tested on randomly generated CNF formulae with several sets of parameters, varying the maximum modal depth and ratio of propositional variable to modal subformulae. The results show some easy-hard-easy behavior, but there is as yet no sharp peak as in propositional satisfiability.     

基于图分解的(3,4)-CNF公式的可满足性

对于规则的(3,4)-CNF公式F,公式F对应的因子图GF恰好是一个(3,4)-双向正则二部图.利用正则二部图的有关性质,证明了对于任意的(3,4)-CNF公式F,若其对应的因子图GF能够被划分为两个(3,2)-双向正则二部图,则F是可满足的.     

Ordered Boolean List (OBL): reducing the footprint for evaluating Boolean expressions

An Expanded Boolean Expression (EBE) does not contain any XOR or EQUAL operators. The occurrence of each variable is a different literal. We provide a linear time algorithm that converts an EBE of n literals into a logically equivalent Ordered Boolean List (OBL) and show how to use the OBL to evaluate the EBE in n steps and O(log log n) space, if the values of the literals are each read once in the order prescribed by the OBL. (An evaluation workspace of 5 bits suffices for all EBEs of up to six billion literals.) The primary application is the SIMD architecture, where the same EBE is evaluated in parallel for different input vectors when rendering solid models on the GPU directly from their Constructive Solid Geometry (CSG) representation. We compare OBL to the Reduced Ordered Binary Decision Diagram (ROBDD) and suggest possible applications of OBL to logic verification and to circuit design.     

O(m~2)时间求解SAT问题的随机算法

传统的求解 SAT问题的随机算法主要是对满足解进行搜索 ,在找不到满足解的情况下 ,则无法正确判断问题的可满足性 .该文提出了两个时间复杂度为 O( m2 )求解 SAT问题的随机算法 Sat Test1和 Sat Test2 ,这里 m为CNF公式中的子句数 .这两个随机算法是通过对不满足解数的估计来判断 SAT问题的可满足性 ,不同于传统的随机算法 .其中第二个算法 Sat Test2在搜索满足解的同时又可以对不满足解数进行估计 ,是对传统随机算法的重要改进 .试验结果表明 ,文中提出的算法对相变区域的难 SAT实例有较好的求解能力 .     

On affine (non)equivalence of Boolean functions

In this paper we construct a multiset S(f) of a Boolean function f consisting of the weights of the second derivatives of the function f with respect to all distinct two-dimensional subspaces of the domain. We refer to S(f) as the second derivative spectrum of f. The frequency distribution of the weights of these second derivatives is referred to as the weight distribution of the second derivative spectrum. It is demonstrated in this paper that this weight distribution can be used to distinguish affine nonequivalent Boolean functions. Given a Boolean function f on n variables we present an efficient algorithm having O(n2²ⁿ ) time complexity to compute S(f). Using this weight distribution we show that all the 6-variable affine nonequivalent bents can be distinguished. We study the subclass of partial-spreads type bent functions known as PS _ap type bents. Six different weight distributions are obtained from the set of PS _ap bents on 8-variables. Using the second derivative spectrum we show that there exist 6 and 8 variable bent functions which are not affine equivalent to rotation symmetric bent functions. Lastly we prove that no non-quadratic Kasami bent function is affine equivalent to Maiorana–MacFarland type bent functions.     

Design and Results of the First Satisfiability Modulo Theories Competition (SMT-COMP 2005)

The Satisfiability Modulo Theories Competition (SMT-COMP) is intended to spark further advances in the decision procedures field, especially for applications in hardware and software verification. Public competitions are a well-known means of stimulating advancement in automated reasoning. Evaluation of SMT solvers entered in SMT-COMP took place while CAV 2005 was meeting. Twelve solvers were entered; 1,352 benchmarks were collected in seven different divisions.     

O（m^2）时间求解SAT问题的随机算法

传统的求解SAT问题的随机算法主要是对满足解进行搜索,在找不到满足解的情况下,则无法正确判断问题的可满足性。该文提出了两个时间复杂度为O（m^2）求解SAT问题的随机算法SatTestl和SatTest2,这里m为CNF公式中的子句数。这两个随机算法是通过对不满足解数的估计来判断SAT问题的可满足性,不同于传统的随机算法。其中第二个算法SatTest2在搜索满足解的同时又可以对不满足解数进行估计,是对传统随机算法的重要改进。试验结果表明,文中提出的算法对相变区域的难SAT实例有较好的求解能力。     

(2,1)-Method for solving stiff nonautonomous problems

An L-stable (2,1)-method with second-order accuracy is developed for solving stiff nonautonomous problems. At each step, the right-hand side of the system, as well as Jacobian matrix decomposition are evaluated only once. Efficiency of the integration method is illustrated using ring modulator calculation as an example.     

FDSR:一种面向SD-MANET的快速转发规则下发方法

针对软件定义网络在移动自组织网络里部署传输路径时,需要控制器为路径上所有的节点下发相关流表项,从而造成传输开始需等待较长时间的问题,文中基于分段路由提出了一种快速下发数据转发规则的方法FDSR.控制器会以分段路由的方式,通过在数据包上添加转发路径对应标签的方式下发数据转发规则,并在处理最大堆栈深度问题时,利用标签粘连技...     

Security Attack Testing (SAT)—testing the security of information systems at design time

For the last few years a considerable number of efforts have been devoted into integrating security issues into information systems development practices. This has led to a number of languages, methods, methodologies and techniques for considering security issues during the developmental stages of an information system. However, these approaches mainly focus on security requirements elicitation, analysis and design issues and neglect testing. This paper presents the Security Attack Testing (SAT) approach, a novel scenario-based approach that tests the security of an information system at the design time. The approach is illustrated with the aid of a real-life case study involving the development of a health and social care information system.     

Automated resolution of connector architectures using constraint solving (ARCAS method)

In current software systems, connectors play an important role by encapsulating the communication and coordination logic. Since they share common patterns (elements) depending on characteristics of the connections, the elements can be predefined and reused. A method of connector implementation based on a composition of predefined elements naturally comprises two steps: resolution of the connector architecture, and creation of the actual connector code based on the architecture. However, manual resolution of a connector architecture is very difficult due to the number of factors to be considered. Thus, the challenge is to come up with an automated method, able to address all the important factors. In this paper, we present a method for automated resolution of connector architectures based on constraint solving techniques. We exploit a propositional logic with relational calculus for defining a connector theory, a constraint specification reflecting both the predefined parts and the important resolution factors, and employ a constraint solver to find a suitable connector architecture as a model of the theory. As a proof of the concept, we show how the theory can be captured in the Alloy language and resolved via the Alloy Analyzer.     

Fuzzy relation equations (I): the general and specialized solving algorithms

 In this article, we develop a new method and an algorithm to solve a system of fuzzy relation equations. We first introduce a solution-base-matrix and then give a tractable mathematical logic representation of all minimal solutions. Next, we design a new universal algorithm to get them. Two simplification rules are found to simplify the solution-base-matrix. We show that a polynomial time algorithm to find all minimal solutions for a general system of fuzzy relation equations simply does not exist with expectation of P=N P. Hence, the problem of solving fuzzy relation equations is an N P-hard problem in terms of computational complexity. Our universal algorithm is still useful when one does not solve a large number of equations. In many real applications the problem of solving fuzzy relation equations can be simplified in polynomial time problems. In this article, we will discuss several cases of practical applications which have such polynomial algorithms.     

Z-type and G-type models for time-varying inverse square root (TVISR) solving

A class of neural dynamics, called Zhang dynamics (ZD), has been proposed to solve online various time-varying problems. In this paper, different Z-type (Zhang type) models based on different Zhang functions (ZFs) are proposed, investigated and simulated for solving the time-varying inverse square root (or in short, TVISR) problem. Then, for the same problem-solving task, different G-type (gradient type) models based on different energy functions (EFs) are developed and investigated as well. Moreover, the convergence analyses of Z-type and G-type models are studied in-depth for the completeness of this paper. Besides, for possible circuit and/or computer realization, Matlab Simulink modeling of Z-type and G-type models is illustrated. Through illustrative examples, the efficacy and superiority of the proposed Z-type and G-type models for TVISR problem solving are verified and substantiated.     

Approximation of experimental data by solving linear difference equations with constant coefficients (in particular,by exponentials and exponential cosines)

This paper proposes a method for approximating experimental data points by the curves representing the solutions of linear difference equations with constant coefficients, in particular, by the curves of the expcos class. An algorithm for finding the coefficients and initial conditions of this approximation is described. The proposed approach minimizes the root mean square (RMS) deviation. The method is tested on some model examples, including the refinement of the beginning of QRS complexes on a three-dimensional ECG loop (in the form of Frank leads).