6127426
A Complete Axiomatization for Blocks World
Blocks World (BW) has been one of the most popular model domains in AI history. However, there has not been serious work on axiomatizing the state constraints of BW and giving justification for its soundness and completeness. In this paper, we model a state of BW by a finite collection of finite chains, and call the theory of all these structures BW theory. We present seven simple axioms and prove that their consequences are precisely BW theory, using Ehrenfeucht-Fräıssé games. We give a simple decision procedure for the theory which can be implemented in exponential space, and prove that every decision procedure (even if nondeterministic) for the theory must take at least exponential time. We also give a characterization of all nonstandard models for the theory. Finally, we present an expansion of BW theory and show that it admits elimination of quantifiers. As a result, we are able to characterize all definable predicates in BW theory, and give simple examples of undefinable predicates.
16346812
A hoare-style proof system for robot programs
Golog is a situation calculus-based logic programming language for high-level robotic control, This paper explores Hoare's axiomatic approach to program verification in the Golog context. We present a novel Hoare-style proof system for partial correctness of Golog programs. We prove total soundness of the proof system, and relative completeness of a subsystem of it for procedureless Golog programs. Examples are given to illustrate the use of the proof system.
117877852
A Tractability Result for Reasoning with Incomplete First-Order Knowledge Bases
In previous work, Levesque proposed an extension to classical databases that would allow for a certain form of incomplete first-order knowledge. Since this extension was sufficient to make full logical deduction undecidable, he also proposed an alternative reasoning scheme with desirable logical properties. He also claimed (without proof) that this reasoning could be implemented efficiently using database techniques such as projections and joins. In this paper, we substantiate this claim and show how to adapt a bottom-up database query evaluation algorithm for this purpose, thus obtaining a tractability result comparable to those that exist for databases.
8135119
Tractable Reasoning with Incomplete First-Order Knowledge in Dynamic Systems with Context-Dependent Actions
A basic reasoning problem in dynamic systems is the projection problem: determine if a formula holds after a sequence of actions has been performed. In this paper, we propose a tractable solution to the projection problem in the presence of incomplete first-order knowledge and contextdependent actions. Our solution is based on a type of progression, that is, we progress the initial knowledge base (KB) wrt the action sequence and answer the query against the resulting KB. The form of reasoning we propose is always logically sound and is also logically complete when the query is in a certain normal form and the agent has complete knowledge about the context of any context-dependent actions.
7009361
Tractable Reasoning in First-Order Knowledge Bases with Disjunctive Information
This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive first-order knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduced to the model checking problem for a small number of characteristic models; and second, the model checking problem itself is tractable for formulas with a bounded number of variables. We show this methodology in action for the reasoning service previously proposed by Liu, Lakemeyer and Levesque for dealing with disjunctive information. They show that their reasoning is tractable in the propositional case and decidable in the first-order case. Here we apply the methodology and prove that the reasoning is also tractable in the first-order case if the knowledge base and the query both use a bounded number of variables.
5262963
Texture replacement in real images
Texture replacement in real images has many applications, such as interior design, digital movie making and computer graphics. The goal is to replace some specified texture patterns in an image while preserving lighting effects, shadows and occlusions. To achieve convincing replacement results we have to detect texture patterns and estimate the lighting map from a given image. Near regular planar texture patterns are considered in this paper. Given a sample texture patch, a standard tile is computed. Candidate texture regions are determined by mutual information between the standard tile and each image patch. Regions with high mutual information scores are used to estimate the admissible lighting distributions, which is represented by cached statistics. Spatial lighting change constraints are represented by a Markov random field model. Maximum a posteriori estimation of the texture segmentation and lighting map is solved in a stochastic annealing fashion, namely, the Markov chain Monte Carlo method. Visually satisfactory result is achieved using this statistical sampling model.
44495329
Enumeration on Nonseparable Planar Maps
Abstract This paper provides some functional equations satisfied by the generating functions for nonseparable rooted planar maps with the valency of root-vertex, the number of edges and the valency of root-faces of the maps as three parameters. But the solutions of these equations can only be obtained indirectly by considering some relations between nonseparable and general rooted planar maps. One of them is an answer to the open problem 6.1 in Liu (1983, Comb. Optim. CORR83-26, University of Waterloo).
12544972
Fluid models and solutions for large-scale IP networks
In this paper we present a scalable model of a network of Active Queue Management (AQM) routers serving a large population of TCP flows. We present efficient solution techniques that allow one to obtain the transient behavior of the average queue lengths, packet loss probabilities, and average end-to-end latencies. We model different versions of TCP as well as different versions of RED, the most popular AQM scheme currently in use. Comparisons between our models and <tt>ns</tt> simulation show our models to be quite accurate while at the same time requiring substantially less time to solve, especially when workloads and bandwidths are high.
2394019
A computational model for periodic pattern perception based on frieze and wallpaper groups
We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each N-dimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there are seven frieze groups describing monochrome patterns that repeat along one direction and 17 wallpaper groups for patterns that repeat along two linearly independent directions to tile the plane. We develop a set of computer algorithms that "understand" a given periodic pattern by automatically finding its underlying lattice, identifying its symmetry group, and extracting its representative motifs. We also extend this computational model for near-periodic patterns using geometric AIC. Applications of such a computational model include pattern indexing, texture synthesis, image compression, and gait analysis.
18654744
Evaluating collinearity constraint for automatic range image registration
While most of the existing range image registration algorithms either have to extract and match structural (geometric or optical) features or have to estimate the motion parameters of interest from outliers corrupted point correspondence data for the elimination of false matches in the process of image registration, the registration error and the collinearity error derived directly from the traditional closest point criterion are also capable of doing the same job. However, the latter has an advantage of easy implementation. The purpose of this paper is to investigate which definition of collinearity is more accurate and stable in eliminating false matches inevitably introduced by the closest point criterion. The experiments based on real images show the advantages and disadvantages of different definitions of collinearity.