The complexity of the satisfiability problem for Krom formulas

We study the computational complexity of the satisfiability problem for Krom (CNF-2) formulas. Upper and lower bounds are obtained for several decidable classes of formulas determined by quantifier prefix and degree of predicate letters. For example, we show that determining satisfiability of Krom formulas with quantifier prefix of the form ……… is complete for deterministic exponential time, but that if the number of universal quantifiers is bounded then polynomial time suffices.     

A bidirectional shortest-path algorithm with good average-case behavior

The two-terminal shortest-path problem asks for the shortest directed path from a specified nodes to a specified noded in a complete directed graphG onn nodes, where each edge has a nonnegative length. We show that if the length of each edge is chosen independently from the exponential distribution, and adjacency lists at each node are sorted by length, then a priority-queue implementation of Dijkstra's unidirectional search algorithm has the expected running time (n logn). We present a bidirectional search algorithm that has expected running time (n logn). These results are generalized to apply to a wide class of edge-length distributions, and to sparse graphs. If adjacency lists are not sorted, bidirectional search has the expected running time (an) on graphs of average degreea, as compared with (an) for unidirectional search.     

A bidirectional shortest-path algorithm with good average-case behavior

The two-terminal shortest-path problem asks for the shortest directed path from a specified nodes to a specified noded in a complete directed graphG onn nodes, where each edge has a nonnegative length. We show that if the length of each edge is chosen independently from the exponential distribution, and adjacency lists at each node are sorted by length, then a priority-queue implementation of Dijkstra's unidirectional search algorithm has the expected running time Θ(n logn). We present a bidirectional search algorithm that has expected running time Θ(√n logn). These results are generalized to apply to a wide class of edge-length distributions, and to sparse graphs. If adjacency lists are not sorted, bidirectional search has the expected running time Θ(a√n) on graphs of average degreea, as compared with Θ(an) for unidirectional search.     

Minimizing worst-case and average-case makespan over scenarios

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all scenarios in an explicitly given set. Each scenario is a subset of jobs that must be executed in that scenario. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. We also consider some (easier) special cases. Combinatorial optimization problems under scenarios in general, and scheduling problems under scenarios in particular, have seen only limited research attention so far. With this paper, we make a step in this interesting research direction.     

Separable resolution method for checking the satisfiability of formulas in the languageL

Conclusion This paper offers an effective resolution method for checking the satisfiability of a collection of disjuncts in the languageL. The method permits one to substantially reduce the number of generated resolvents in comparison with the method ofR-resolution. One more factor ensuring the efficiency of the method is a significant reduction in the number of disjunct pairs checked for the possibility of resolving them. As for the number of generated disjuncts, its greatest reduction is obtained in the case of the use of the disjunct-set partition corresponding to the limiting system of predicate-symbol subsets given by symbol ordering. It is possible to interpret the result obtained for this case as proof of the completeness of the strategy combining an ordering of predicate symbols andR-resolution. It is necessary to note that to different orderings of predicate symbols correspond different partitions of the disjunct set giving, in turn, different numbers of generated disjuncts in the process ofSp-completion. Nevertheless, the methods described in Sec. 2, which use partition of the disjunct set into two classes, are of independent importance. As has already been said, completion of a disjunct set is used for solution of a number of problems during the design of a procedural automaton specification. For example, in the case of checking the consistency of two interacting automata [5] based on completion of a disjunct set, there exists a natural partition of the predicate symbols into input and output symbols, to which corresponds the partition of the disjunct set into subsets specifying the interacting automata. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 13–20, November–December, 1998.     

A simplifier for propositional formulas with many binary clauses

Deciding whether a propositional formula in conjunctive normal form is satisfiable (SAT) is an NP-complete problem. The problem becomes linear when the formula contains binary clauses only. Interestingly, the reduction to SAT of a number of well-known and important problems--such as classical AI planning and automatic test pattern generation for circuits--yields formulas containing many binary clauses. In this paper we introduce and experiment with 2-SIMPLIFY, a formula simplifier targeted at such problems. 2-SIMPLIFY constructs the transitive closure of the implication graph corresponding to the binary clauses in the formula and uses this graph to deduce new unit literals. The deduced literals are used to simplify the formula and update the graph, and so on, until stabilization. Finally, we use the graph to construct an equivalent, simpler set of binary clauses. Experimental evaluation of this simplifier on a number of bench-mark formulas produced by encoding AI planning problems prove 2-SIMPLIFY to be a useful tool in many circumstances.     

An effective heuristic algorithm for the maximum satisfiability problem

Stochastic local search algorithms (SLS) have been increasingly applied to approximate solutions of the weighted maximum satisfiability problem (MAXSAT), a model for solutions of major problems in AI and combinatorial optimization. While MAXSAT instances have generally a strong intrinsic dependency between their variables, most of SLS algorithms start the search process with a random initial solution where the value of each variable is generated independently with the same uniform distribution. In this paper, we propose a new SLS algorithm for MAXSAT based on an unconventional distribution known as the Bose-Einstein distribution in quantum physics. It provides a stochastic initialization scheme to an efficient and very simple heuristic inspired by the co-evolution process of natural species and called Extremal Optimization (EO). This heuristic was introduced for finding high quality solutions to hard optimization problems such as colouring and partitioning. We examine the effectiveness of the resulting algorithm by computational experiments on a large set of test instances and compare it with some of the most powerful existing algorithms. Our results are remarkable and show that this approach is appropriate for this class of problems.     

Performance analysis of diamond search algorithm over full search algorithm

Microsystem Technologies - Motion estimation is a progression used to estimate motion vectors between two or more images with a high degree of temporal redundancy. It is commonly used in video...     

二元域多项式基的按字求模算法

介绍了二元域多项式基及其按位(bit)求模算法,给出了一种新的通用的不要预计算的二元域多项式基按字(word)求模算法,由于可以选择不同的字长如8位字长或16位字长等,因而该算法既适合软件也适合硬件。在32位字长PC机环境下,给出了针对特定二元域和模约多项式的简化算法。在大量实验的基础上,对按字求模算法和按位求模算法的运算结果和运算速度的比较结果表明,两者运算结果相同,但前者平均运算速度比后者快30多倍。     

A modified full multigrid algorithm for the Navier-Stokes equations

A modified full multigrid (FMG) method for the solution of the Navier-Stokes equations is presented. The method proposed is based on a V-cycle omitting the restriction procedure for dependent variables but retaining it for the residuals. This modification avoids possible mismatches between the mass fluxes and the restricted velocities as well as the turbulent viscosity and the turbulence quantities on the coarse grid. In addition, the pressure on the coarse grid can be constructed in the same way as the velocities. These features simplify the multigrid strategy and corresponding programming efforts. This algorithm is applied to accelerate the convergence of the solution of the Navier-Stokes equations for both laminar and high-Reynolds number turbulent flows. Numerical simulations of academic and practical engineering problems show that the modified algorithm is much more efficient than the FMG-FAS (Full Approximation Storage) method.     

GASAT: a genetic local search algorithm for the satisfiability problem

This paper presents GASAT, a hybrid algorithm for the satisfiability problem (SAT). The main feature of GASAT is that it includes a recombination stage based on a specific crossover and a tabu search stage. We have conducted experiments to evaluate the different components of GASAT and to compare its overall performance with state-of-the-art SAT algorithms. These experiments show that GASAT provides very competitive results.     

A constructive algorithm for binary neural networks: the oil-spot algorithm.

This paper presents a constructive training algorithm for supervised neural networks. The algorithm relies on a topological approach, based on the representation of the mapping of interest onto the binary hypercube of the input space. It dynamically constructs a two-layer neural network by involving successively binary examples. A convenient treatment of real-valued data is possible by means of a suitable real-to-binary codification. In the case of target functions that have efficient halfspace union representations, simulations show the constructed networks result optimized in terms of number of neurons.     

密码芯片中二元扩域Eta双线性对安全算法

为了在密码芯片中安全快速地实现二元扩域Eta双线性对,提出了基于平方方法的抗功耗攻击实现算法。分别研究了基于平方方法的密钥盲化和明文盲化方案,给出了具体的基于平方方法的抗功耗攻击算法的实现细节。在典型有限域下,基于平方方法的抗功耗攻击算法的实现效率比基于平方根方法提升10%以上,并且不需要存储任何预计算变量。另外,讨论了将目前用于三元扩域的Loop Unrolling方法的思想应用到所提算法后,进一步将运算效率提升了约3%。效率的提升和存储量的优化使得算法更适用于安全密码芯片。     

Uniform satisfiability problem for local temporal logics over Mazurkiewicz traces

We continue our study of the complexity of MSO-definable local temporal logics over concurrent systems that can be described by Mazurkiewicz traces. In previous papers, we showed that the satisfiability problem for any such logic is in PSPACE (provided the dependence alphabet is fixed, Gastin and Kuske (2003) [10]) and remains in PSPACE for all classical local temporal logics even if the dependence alphabet is part of the input, Gastin and Kuske (2007) [8]. In this paper, we consider the uniform satisfiability problem for arbitrary MSO-definable local temporal logics. For this problem, we prove multi-exponential lower and upper bounds that depend on the number of alternations of set quantifiers present in the chosen MSO-modalities.     

二元联系数A+Bi的理论基础与基本算法及在人工智能中的应用

二元联系数4＋Bi的特点是把确定性测度与不确定测度联系在一起,基本思想是把一个确定集与一个不确定集联系在一起去研究同一个客观对象,其理论基础是集对论,概率、模糊隶属度、区间数可以转换成二元联系数,基本算法简明实用,因而可用于不同不确定性问题的处理．     

A new decode algorithm for binary bar codes

Distortion is the major obstacle to more aggressive decoding in current bar code decoders. The new decoder introduced in this paper is one of the solutions to this problem for binary bar codes (e.g. CODE 39). The new decoder is basically a minimum distance decoder that also utilizes distortion information from the start/stop characters. Security and execution time issues are also addressed in the paper.