基于MCN和MO启发式策略的扩展规则知识编译方法

在基于扩展规则的知识编译算法的基础上提出了2种启发式策略:MCN策略和MO策略.MCN策略和MO策略利用子句集的信息分别选择相应子句和变量,减少扩展规则的使用次数,进而降低知识编译后目标子句集的规模.在此基础上,设计并实现了MCN_KCER,MO_KCER和MCN_MO_KCER算法.实验结果表明:2种启发式策略都可以大幅度减小编译后的子句集规模,同时使用它们的效果更为明显,经过编译后得到的子句集规模是原算法的1/3～1/39,从而大幅度提高之后的在线推理阶段的效率.     

C2E:一个高性能的EPCCL编译器

提出一个新的基于DPLL的编译算法KCDP,从而成功地将EPCCL理论和SAT求解联系起来,使得目前很多应用在基于DPLL的SAT求解器中先进的技术都能被引入到EPCCL理论的编译中以提高编译效率;提出规约规则,并基于该规则,提出能在多项式时间内终止的REDUCE算法对EPCCL理论进行规约;结合KCDP和REDUCE算法,实现了编译器C2E,并在随机问题和国际通用的测试用例上测试了C2E的编译效率和编译质量,实验结果表明,无论从编译效率还是编译质量来说,C2E都是一个高性能的EPCCL编译器.     

基于半扩展规则的定理证明方法

自动定理证明一直是人工智能领域中最重要的问题之一,基于归结的方法是通过推出空子句的方法来判定子句集的可满足性.基于扩展规则的定理证明方法在一定意义上是和归结原理对偶的方法,是通过子句集能否推导出所有极大项组成的子句集来判定可满足性.通过对扩展规则的研究给出了半扩展规则的概念,并提出了基于半扩展规则的定理证明算法SER.然后分析及证明了该算法的正确性、完备性和复杂性.实验结果表明,算法SER的执行效率较基于归结的有向归结算法DR和基于扩展规则算法IER,NER有明显的提高.     

一类可分离SAT问题的O(1.890n)精确算法

布尔可满足性问题（SAT）是指对于给定的布尔公式,是否存在一个可满足的真值指派.这是第1个被证明的NP完全问题,一般认为不存在多项式时间算法,除非P=NP.学者们大都研究了子句长度不超过k的SAT问题（k-SAT）,从全局搜索到局部搜索,给出了大量的相对有效算法,包括随机算法和确定算法.目前,最好算法的时间复杂度不超过O（（2-2/k）ⁿ）,当k=3时,最好算法时间复杂度为O（1.308ⁿ）.而对于更一般的与子句长度k无关的SAT问题,很少有文献涉及.引入了一类可分离SAT问题,即3-正则可分离可满足性问题（3-RSSAT）,证明了3-RSSAT是NP完全问题,给出了一般SAT问题3-正则可分离性的O（1.890ⁿ）判定算法.然后,利用矩阵相乘算法的研究成果,给出了3-RSSAT问题的O（1.890ⁿ）精确算法,该算法与子句长度无关.     

半扩展规则下分解的定理证明方法

基于扩展规则的定理证明方法在一定意义上是与归结原理对偶的方法,通过子句集能否推导出所有极大项来判定可满足性.IER(improved extension rule)算法是不完备的算法,在判定子句集子空间不可满足时,并不能判定子句集的满足性,算法还需重新调用ER(extension rule)算法,降低了算法的求解效率.通过对子句集的极大项空间的研究,给出了子句集的极大项空间分解后子空间的求解方法.通过对扩展规则的研究,给出了极大项部分空间可满足性判定方法PSER(partial semi-extension rule).在IER算法判定子空间不可满足时,可以调用PSER算法判定子空间对应的补空间的可满足性,从而得到子句集的可满足性,避免了不能判定极大项子空间可满足性时需重新调用ER算法的缺点,使得IER算法更完备.在此基础上,还提出DPSER(degree partial semi-extension rule)定理证明方法.实验结果表明:所提出的DPSER和IPSER的执行效率较基于归结的有向归结算法DR、IER及NER算法有明显的提高.     

一类非规则并行应用问题的通信集生成算法

非规则计算是大规模并行应用中普遍存在和影响效率的关键问题.在基于分布式内存的数据并行范例中,如何针对非规则数组引用,有效地生成本地内存访问序列和通信集,是并行编译生成SPMD结点程序所必须解决的重要问题.文中针对两重嵌套循环中,下一层循环边界是上一层循环变量的线性或非线性函数,数组下标是两层循环变量的非线性函数这样一类包含非规则数组引用的并行应用问题,提出了一种在编译时生成通信集的代数算法.并且针对cyclic(k)数据分布和线性对齐模板,借助整数格概念,给出了编译时全局地址和本地地址之间的转换方法.文中还给出了相应的经过通信优化的SPMD结点程序.最后通过实例验证了算法的正确性.该算法的意义在于避免了传统Inspector/Executor非规则计算模型中的Inspector阶段,从而节省了运行时Inspector阶段通过穷举下标生成通信集的巨大开销.     

命题模态逻辑S5系统中并行推理方法

S5系统是一类知识表示能力和处理能力都较强的模态公理系统,它是认知逻辑、信念逻辑等非经典逻辑理论的基础。根据Kripke语义模型以及S5系统中部分公理,对命题模态逻辑S5公理系统的性质进行了较为深入的研究,并对S5系统中一类具有代表性的标准模态子句集的特性进行了分析,提出了一种基于扩展规则方法的命题模态逻辑推理算法(propositional modal clausal reasoning based on novel extension rule,PMCRNER)。针对朴素算法时间复杂度较高的问题,利用任务间潜在的关联性对算法同时进行了粗粒度与细粒度并行化,提出了并行算法PPMCRNER(parallel PMCRNER)理论框架,并且与基本算法进行了对比。实验结果表明,PPMCRNER算法在不可满足的子句集上的推理具有良好的加速比,为高时间复杂性的模态推理方法的进一步研究提供了一种可行方案。     

基于软集的无标记信息代数模型与算法

在给定的一个初始论域U和参数集E上的全体软集中引入扩展运算与转移运算,研究了它们的性质.在此基础上引入商软集的概念,并在全体商软集中引入联合运算与聚焦运算,得到其构成一个无标记的信息代数,并且若参数集E有限,这个信息代数还是一个无标记的紧信息代数.最后,给出运用无标记信息代数的模型解决软集中不确定问题的决策算法与实例,并与Cagman等人提出的uni-int决策算法做了比较说明.     

基于类型理论的领域数据建模和验证及案例

数据作为软件系统的主要处理对象,其规范性有助于软件系统的设计开发和软件系统之间的数据交换。本文面向行业数据规范及其验证,提出了一种基于类型理论的领域数据建模语言（DDML）和领域建模方法（DDMM）。DDML语言通过定义类型和项的语法和语义,描述领域数据类型和对象的结构,通过定义类型规则及其类型检查算法判定任意项t：T?。DDMM给出了领域数据建模的方法,即构建K₁（原子类型）、K₂（数据元）、K₃（数据元目录）三层框架,生成表示K3层数据元目录之间关系的类型规则。在此基础上,给出了数据元目录序列的定义及其正确性判定算法。基于上述方法,实现了一种领域数据建模工具原型系统,并通过领域数据建模与自动验证的一个实际案例,完成了一个较大规模行业数据规范的制定与验证。     

完全析取范式群判定SHOIN(D)-可满足性

针对非循环概念提出了一种对SHOIN(D)-概念可满足性进行判断的方法——CDNF(complete disjunctive normal form)算法.该算法通过把非循环定义的概念描述本身构建成分层次的析取范式群,并通过子句重用技术阻止无谓的子概念扩展,这样的析取范式群具有可满足性自明性,从而可以实现对SHOIN(D)-概念可满足性的直接判断.该算法基本上消除了判断过程中描述重复的现象,从而在空间、时间性能上都比Tableau算法有更好的表现.     

Knowledge Compilation Using the Extension Rule

In this paper, we define a new class of tractable theories: EPCCL theories. Using EPCCL theories as a target language, we propose a new method for knowledge compilation. It is different from existing approaches in that both the compilation and the querying are based on the extension rule, a newly introduced inference rule. With our compilation method, arbitrary queries about the compiled knowledge base can be answered in linear time in the size of the compiled knowledge base. For some theories, the compilation can be done very efficiently, and the size of the compiled theory is small. Furthermore, our method suggests a new family of knowledge compilation methods.     

结合扩展规则重构的#SAT问题增量求解方法

#SAT问题是人工智能中的重要问题,在人工智能领域被广泛应用.在对基于扩展规则的模型计数求解方法CER深入研究的基础上,重构CER中使用的计算公式,并对其正确性进行了证明;提出极大项相交集和扩展极大项相交集的概念,并给出根据两者关系重用极大项相交集计算结果的增量求解方法,且对广义互补子句集对应的所有扩展极大项相交集进行剪枝,有效避免了计算所有极大项相交集对应极大项个数时的冗余求解;提出构建记录子句间互补关系的互补表方法,给出重用极大项相交集基础子句集互补结果的增量互补判定方法,较好地避免了判断子句间和各极大项相交集的基础子句集互补关系时的重复计算.实验结果表明:RCER方法易于实现,扩展性强,比CER方法效率更高,尤其是在互补因子较低时,效率提升更为显著.     

基于IMOM和IBOHM启发式策略的扩展规则算法

基于扩展规则的方法是一种定理证明方法.在IER(improved extension rule)扩展规则算法的基础上,提出了IMOM(improved maximum occurrences on clauses of maximum size)和IBOHM(improved BOHM)启发式策略,并将两种启发式策略用于IER算法中,有指导性地选择限定搜索空间的子句,设计并实现了算法IMOMH_IER和IBOHMH_IER.实验结果表明,由于这两种启发式策略能够选择较为合适的搜索空间,可以尽快地判定出原问     

可能性扩展规则的推理和知识编译

在扩展规则的基础上提出了可能性扩展规则。给出了基于可能性扩展规则的可能性逻辑推理方法,利用互补因子的概念来估价推理问题的复杂度。扩展了经典逻辑的蕴含可控制类和可满足可控制类的定义,提出了可能性蕴含可控制类、不一致性程度计算可控制类的概念。在可能性扩展规则的基础上提出了EPPCCCL(each pair of possibilistic clauses contains complementary literals)理论,并证明了该理论是在最优化形式蕴含可控制类和不一致性程度计算可控制类中的,可以作为可能性     

基于局部搜索的并行扩展规则推理方法

扩展规则推理方法在经典的可满足性问题求解中已得到广泛应用,若干个基于扩展规则的推理方法已被提出,皆得到国内外的认可,例如完备的NER,IMOMH_IER,PPSER算法以及基于局部搜索的不完备算法ERACC等,都具有良好的求解效果.其中,ERACC算法是当前扩展规则求解器中求解效率最高、能力最强的算法.但是,串行的ERACC算法在启发式和预处理上仍然具有可提升的空间.基于此,设计了相应的并行框架,提出了PERACC算法.该算法基于格局检测的局部搜索方法,从变量赋初始值、化简解空间和启发式这3个阶段出发,将原极大项空间分解成为若干极大项子空间,并对原子句集进行化简后,并行处理各个子空间.通过实验显示：该算法与原算法相比,不仅在求解效率方面有较大提高,而且可以求解规模更大的测试用例,使扩展规则方法再次突破公式规模的限制.     

Semantic properties of Lucid's compute clause and its compilation

Compilation algorithms for a subset of the programming language Lucid are extended so that programs with nested compute clauses can be compiled.The extension is derived from the semantic properties of the compute clause construct, and is applicable to a broad class of compilation algorithms for a subset of Lucid. A correctness proof of the extension is also given.This work has been supported in part by an NSF grant MCS 78-01812     

Redundancy checking algorithms based on parallel novel extension rule

Abstract

Redundancy checking (RC) is a key knowledge reduction technology. Extension rule (ER) is a new reasoning method, first presented in 2003 and well received by experts at home and abroad. Novel extension rule (NER) is an improved ER-based reasoning method, presented in 2009. In this paper, we first analyse the characteristics of the extension rule, and then present a simple algorithm for redundancy checking based on extension rule (RCER). In addition, we introduce MIMF, a type of heuristic strategy. Using the aforementioned rule and strategy, we design and implement RCHER algorithm, which relies on MIMF. Next we design and implement an RCNER (redundancy checking based on NER) algorithm based on NER. Parallel computing greatly accelerates the NER algorithm, which has weak dependence among tasks when executed. Considering this, we present PNER (parallel NER) and apply it to redundancy checking and necessity checking. Furthermore, we design and implement the RCPNER (redundancy checking based on PNER) and NCPPNER (necessary clause partition based on PNER) algorithms as well. The experimental results show that MIMF significantly influences the acceleration of algorithm RCER in formulae on a large scale and high redundancy. Comparing PNER with NER and RCPNER with RCNER, the average speedup can reach up to the number of task decompositions when executed. Comparing NCPNER with the RCNER-based algorithm on separating redundant formulae, speedup increases steadily as the scale of the formulae is incrementing. Finally, we describe the challenges that the extension rule will be faced with and suggest possible solutions.     

Comparative investigation of GPU-accelerated triangle-triangle intersection algorithms for collision detection

Efficient collision detection is critical in 3D geometric modeling. In this paper, we first implement three parallel triangle-triangle intersection algorithms on a GPU and then compare the computational efficiency of these three GPU-accelerated parallel triangle-triangle intersection algorithms in an application that detects collisions between triangulated models. The presented GPU-based parallel collision detection method for triangulated models has two stages: first, we propose a straightforward and efficient parallel approach to reduce the number of potentially intersecting triangle pairs based on AABBs, and second, we conduct intersection tests with the remaining triangle pairs in parallel based on three triangle-triangle intersection algorithms, i.e., the Möller’s algorithm, Devillers’ and Guigue’s algorithm, and Shen’s algorithm. To evaluate the performance of the presented GPU-based parallel collision detection method for triangulated models, we conduct four groups of benchmarks. The experimental results show the following: (1) the time required to detect collisions for the triangulated model consisting of approximately 1.5 billion triangle pairs is less than 0.5 s; (2) the GPU-based parallel collision detection method speedup over the corresponding serial version is 50x - 60x, and (3) Devillers’ and Guigue’s algorithm is comparatively and comprehensively the best of the three GPU-based parallel triangle-triangle intersection algorithms. The presented GPU-accelerated method is capable of efficiently detecting the potential collisions of triangulated models. Overall, the GPU-accelerated parallel Devillers’ and Guigue’s triangle-triangle intersection algorithm is recommended when performing practical collision detections between large triangulated models.

     

The same origin ray set query for realistic illumination: Algorithm and analysis

The same origin ray set (SORS) is a computational primitive which can be used by ray tracing, radiosity and multiple pass illumination simulation algorithms for realistic image synthesis. A SORS consists of a set of rays emanating from the same point in space. The SORS query computes the first object intersected by each ray and the intersection point. In this paper we present an efficient projection algorithm for computing a SORS query for polygonal scenes. The algorithm achieves its efficiency by separating ray-polygon intersection detection from the computation of the intersection point between the ray and the polygon's plane. The algorithm can be integrated with all current illumination acceleration schemes. We analyse the projection algorithm and compare it to the alternative of computing the SORS query one ray at a time. The analysis' results are expressed in terms of a few intuitive parameters, measuring the success of the acceleration scheme in culling irrelevant objects and the concentration of the ray set. The projection algorithm can be up to five times more efficient, depending on these parameters and the quality of the image. The relative advantage of the projection increases with image quality.