16142848
DPLL with a Trace: From SAT to Knowledge Compilation
We show that the trace of an exhaustive DPLL search can be viewed as a compilation of the propositional theory. With different constraints imposed or lifted on the DPLL algorithm, this compilation will belong to the language of d-DNNF, FBDD, and OBDD, respectively. These languages are decreasingly succinct, yet increasingly tractable, supporting such polynomial-time queries as model counting and equivalence testing. Our contribution is thus twofold. First, we provide a uniform framework, supported by empirical evaluations, for compiling knowledge into various languages of interest. Second, we show that given a particular variant of DPLL, by identifying the language membership of its traces, one gains a fundamental understanding of the intrinsic complexity and computational power of the search algorithm itself. As interesting examples, we unveil the "hidden power" of several recent model counters, point to one of their potential limitations, and identify a key limitation of DPLL-based procedures in general.
5118559
The Effect of Restarts on the Efficiency of Clause Learning
Given the common use of restarts in today's clause learning SAT solvers, the task of choosing a good restart policy appears to have attracted remarkably little interest. On the other hand, results have been reported on the use of different restart policies for combinatorial search algorithms. Such results are not directly applicable to clause learning SAT solvers, as the latter are now understood as performing a form of resolution, something fundamentally different from search (in the sense of backtracking search for satisfying assignments). In this paper we provide strong evidence that a clause learning SAT solver could benefit substantially from a carefully designed restart policy (which may not yet be available). We begin by pointing out that the restart policy works together with other aspects of a SAT solver in determining the sequence of resolution steps performed by the solver, and hence its efficiency. In this spirit we implement a prototype clause learning SAT solver that facilitates restarts at arbitrary points, and conduct experiments on an extensive set of industrial benchmarks using various restart policies, including those used by well-known SAT solvers as well as a universal policy proposed in 1993 by Luby et al. The results indicate a substantial impact of the restart policy on the efficiency of the solver, and provide motivation for the design of better restart policies, particularly dynamic ones.
7486661
The Language of Search
This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace of a search can be interpreted as a combinational circuit, and a search algorithm then defines a propositional language consisting of circuits that are generated across all possible executions of the algorithm. In particular, we show that several versions of exhaustive DPLL search correspond to such well-known languages as FBDD, OBDD, and a precisely-defined subset of d-DNNF. By thus mapping search algorithms to propositional languages, we provide a uniform and practical framework in which successful search techniques can be harnessed for compilation of knowledge into various languages of interest, and a new methodology whereby the power and limitations of search algorithms can be understood by looking up the tractability and succinctness of the corresponding propositional languages.
8956273
Hierarchical Diagnosis of Multiple Faults
Due to large search spaces, diagnosis of combinational circuits is often practical for finding only single and double faults. In principle, system models can be compiled into a tractable representation (such as DNNF) on which faults of arbitrary cardinality can be found efficiently. For large circuits, however, compilation can become a bottleneck due to the large number of variables necessary to model the health of individual gates. We propose a novel method that greatly reduces this number, allowing the compilation, as well as the diagnosis, to scale to larger circuits. The basic idea is to identify regions of a circuit, called cones, that are dominated by single gates, and model the health of each cone with a single health variable. When a cone is found to be possibly faulty, we diagnose it by again identifying the cones inside it, and so on, until we reach a base case. We show that results combined from these hierarchical sessions are sound and complete with respect to minimum-cardinality diagnoses. We implement this method on top of the diagnoser developed by Huang and Darwiche in 2005, and present evidence that it significantly improves the efficiency and scalability of diagnosis on the ISCAS-85 circuits.
400858
Toward good elimination orders for symbolic SAT solving
Fundamentally different from DPLL, a new approach to SAT has recently emerged that abandons search and enlists BDDs to symbolically represent clauses of the CNF. These BDDs are conjoined according to a schedule where some variables may be eliminated by quantification at each step to reduce the size of the intermediate BDDs. SAT solving then reduces to checking whether the final BDD is the zero constant. For this approach to be practical, finding a good quantification schedule is critical. We study the use of a variable elimination algorithm for this purpose, as well as two specific methods for the generation of good elimination orders based on CNF structure. While neither method appears to dominate, we show how one can heuristically select the better using the notion of width. We implement a symbolic SAT solver based on these techniques and evaluate its efficiency and robustness on a set of benchmarks against five other solvers, each having unique characteristics, including winners of the most recent SAT competition.
17763521
High-Quality Splatting on Rectilinear Grids with Efficient Culling of Occluded Voxels
Splatting is a popular volume rendering algorithm that pairs good image quality with an efficient volume projection scheme. The current axis-aligned sheet-buffer approach, however, bears certain inaccuracies. The effect of these is less noticeable in still images, but clearly revealed in animated viewing, where disturbing popping of object brightness occurs at certain view angle transitions. In previous work, we presented a new variant of sheet-buffered splatting in which the compositing sheets are oriented parallel to the image plane. This scheme not only eliminates the condition for popping, but also produces images of higher quality. In this paper, we summarize this new paradigm and extend it in a number of ways. We devise a new solution to render rectilinear grids of equivalent cost to the traditional approach that treats the anisotropic volume as being warped into a cubic grid. This enables us to use the usual radially symmetric kernels, which can be projected without inaccuracies. Next, current splatting approaches necessitate the projection of all voxels in the iso-interval(s), although only a subset of these voxels may eventually be visible in the final image. To eliminate these wasteful computations we propose a novel front-to-back approach that employs an occlusion map to determine if a splat contributes to the image before it is projected, thus skipping occluded splats. Additional measures are presented for further speedups. In addition, we present an efficient list-based volume traversal scheme that facilitates the quick modification of transfer functions and iso-values.
1414584
Broadcast program generation for unordered queries with data replication
We study in this paper the problem of broadcasting dependent data for unordered queries. However, most prior studies on dependent data broadcasting are limited to the premise of no data replication. Different from other prior studies, we investigate the effect of data replication in this paper. Specifically, we first derive several theoretical properties for the average access time by analyzing the model of dependent data broadcasting. On the basis of the theoretical results, we develop a genetic algorithm to generate broadcast programs with replication. In order to compare the performance of the proposed algorithm and the prior studies, several experiments are conducted. Our experimental results show that with the analytical results derived, the theoretical results derived are able to guide the search of the genetic algorithm very effectively, and lead to solution broadcast programs of higher quality than those of the prior studies.
9984897
Structure Alignment Using Bilingual Chunking
A new statistical method called "bilingual chunking" for structure alignment is proposed. Different with the existing approaches which align hierarchical structures like sub-trees, our method conducts alignment on chunks. The alignment is finished through a simultaneous bilingual chunking algorithm. Using the constrains of chunk correspondence between source language (SL) and target language (TL), our algorithm can dramatically reduce search space, support time synchronous DP algorithm, and lead to highly consistent chunking. Furthermore, by unifying the POS tagging and chunking in the search process, our algorithm alleviates effectively the influence of POS tagging deficiency to the chunking result.The experimental results with English-Chinese structure alignment show that our model can produce 90% in precision for chunking, and 87% in precision for chunk alignment.
207081005
Certifying LexBFS Recognition Algorithms for Proper Interval Graphs and Proper Interval Bigraphs
Recently, D. Corneil found a simple 3-sweep lexicographic breadth first search (LexBFS) algorithm for the recognition of proper interval graphs. We point out how to modify Corneil's algorithm to make it a certifying algorithm, and then describe a similar certifying 3-sweep LexBFS algorithm for the recognition of proper interval bigraphs. It follows from an earlier paper that the class of proper interval bigraphs is equal to the better known class of bipartite permutation graphs, and so we have a certifying algorithm for that class as well. All our algorithms run in time O(m+n), including the certification phase. The certificates of representability (the intervals) can be authenticated in time O(m+n). The certificates of nonrepresentability (the forbidden subgraphs) can be authenticated in time O(n).
6321071
The Myth of the Boundaryless Organization
Technology does not make cultural and business boundaries disappear simply because it exists.