5055655
The Complexity of Global Constraints
We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when decomposing constraints will lose pruning, and when combining constraints is tractable. We also show how the same tools can be used to study symmetry breaking, meta-constraints like the cardinality constraint, and learning nogoods.
2156641
Multiset Ordering Constraints
We identify a new and important global (or nonbinary) constraint which ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement a linear time algorithm for enforcing generalised arc-consistency on such a multiset ordering constraint. Experimental results show considerable promise.
5289412
Theories of Abstraction
universitt a di genova facoltt a di ingegneria dipartimento informatica sistemistica telematica Abstract This article surveys the eld of Artiicial Intelligence for theories of abstraction. We identify several unifying themes and argue that, even though these theories make diierent representational choices, they are all trying to capture the same intuitive ideas. Progress has also been made in understanding the reduction in search brought by abstraction. In this paper, we demonstrate how these theories of abstraction have helped comprehend the advantages abstraction provides. Finally, several diierent systems with abstraction have been implemented, tested and used. We focus on how the theories of abstraction have been innuenced by and have themselves innuenced the development of such systems.
18410341
A Theory of Abstraction
Abstract Informally , abstraction can be described as the process of mapping a representation of a problem onto a new representation. The aim of this paper is to propose the beginnings of a theory of reasoning with abstraction which captures and generalizes most previous work in the area. The theory allows us to study the properties of abstraction mappings and provides the foundations for the mechanization of abstraction inside an abstract proof checker.
7417163
Easy Problems are Sometimes Hard
We present a detailed experimental investigation of the easy-hard-easy phase transition for randomly generated instances of satisfiability problems. Problems in the hard part of the phase transition have been extensively used for benchmarking satisfiability algorithms. This study demonstrates that problem classes and regions of the phase transition previously thought to be easy can sometimes be orders of magnitude more difficult than the worst problems in problem classes and regions of the phase transition considered hard. These difficult problems are either hard unsatisfiable problems or are satisfiable problems which give a hard unsatisfiable subproblem following a wrong split. Whilst these hard unsatisfiable problems may have short proofs, these appear to be difficult to find, and other proofs are long and hard.
12061015
Automatic Invention of Integer Sequences
We report on the application of the HR program (Colton, Bundy, & Walsh 1999) to the problem of automatically inventing integer sequences. Seventeen sequences invented by HR are interesting enough to have been accepted into the Encyclopedia of Integer Sequences (Sloane 2000) and all were supplied with interesting conjectures about their nature, also discovered by HR. By extending HR, we have enabled it to perform a two stage process of invention and investigation. This involves generating both the definition and terms of a new sequence, relating it to sequences already in the Encyclopedia and pruning the output to help identify the most surprising and interesting results.
44916266
Inversion of Cycle Index Sum Relations for 2- and 3-Connected Graphs
Abstract Algebraic inversion of cycle index sum relations is employed to derive new algorithms for counting unlabeled 2-connected graphs, homeomorphically irreducible 2-connected graphs, and 3-connected graphs. The new algorithms are significantly more efficient than earlier ones, both asymptotically and for modest values of the order. Tables of computed results are included.
17164164
Towards Measuring Similarity in Description Logics
We review several kinds of previously studied concept similarity measures, and then rephrase them in terms of a simple DL. We discuss the difficulties encountered in trying to generalize these formulations to more complex DLs, and settle on one based on probability/information theory as being the most principled. 1 Motivation and Goals The idea of measuring concept similarity has received considerable attention in several domains, including psychology, cognitive science, and computational linguistics and information retrieval. This work has been applied and extended recently in the field of Information Integration, which often relies on ontologies and hence concepts described in DLs. Most past work has concentrated on the similarity of “atomic” concepts (word senses), rather than composite, defined concepts, which are the stock-in-trade of DLs. This has sometimes been characterized as the difference between considering nouns appearing in a dictionary, e.g. WordNet, and general arbitrary noun phrases. The modest goal of this paper is to consider the problem of generalizing previous efforts to define similarity for primitive concepts to composite ones. To this end, we review three classes of approaches found in the current literature, rephrase them in terms of a very simple description logic, and then try to generalize this to a complex DL. These extensions invite a host of new questions that we leave open for further research. To begin with, we make several observations about possible real-valued function(s) sim(C,D) that would measure concept similarity in general. First, any effort to assess simlarity via absolute numeric values seems ill-advised — in small experiments even human judgments have been shown to correlate only in the .91 to .94 range. A less exacting target is to use sim to provide relative orderings over concepts. Some researchers have studied a complementary measure, distance dist(C,D), which can similarly be used for ordering alternatives. To the extent that two functions provide similar orderings (e.g., consistently differing by a constant factor) they are essentially indistinguishable for our purposes. Nonetheless, there are two important general properties that are widely agreed to be desirable for sim(C,D): 1. sim(C,D) is positively correlated with the amount of commonality between C and D. 2. sim(C,D) is negatively correlated with the amount of difference between C and D. The key question then becomes how to measure “commonality”; in turn, this is related to how information about the concept is captured. 2 Three approaches to concept similarity Clearly, in order to compare concepts we need to consider what information we have available about them. We follow Rodriguez [14] in categorizing a variety of approaches, and for each we give a few of the best known functions, which we shall follow. Feature-based Models In this approach, a concept C is characterized by a a set of features ftrs(C). In his pioneering work on similarity, the psychologist Amos Tversky [16] introduced two families of measures: the “contrast model”, where the similarity of C and D is a linear function: contrasttv(C,D) = θf(ftrs(C) ∩ ftrs(D)) − αf(ftrs(C) \ ftrs(D))− βf(ftrs(D) \ ftrs(C)), where \ is set difference, θ, α, and β are non-negative constants, and where f(.) is often taken as the count of features in the set (written |.|). Tversky also proposed a normalized “ratio model”, where similarity is a fraction involving these sets:
1960492
Challenges in securing voice over IP
Although VoIP offers lower cost and greater flexibility, it can also introduce significant risks and vulnerabilities. This article explains the challenges of VoIP security and outlines steps for helping to secure an organization's VoIP network.
43061363
Counting labelled three-connected and homeomorphically irreducible two-connected graphs
Abstract Recursive procedures are obtained for counting isomorphism classes of three-connected graphs and of two-connected graphs without vertices of degree 2. We apply an enumeration tool developed by R. W. Robinson to count non-isomorphic 2-connected graphs: he expressed the sums of cycle indices of automorphism groups of connected graphs in terms of those of their 2-connected components, and we do the same for 2-connected graphs and their 3-connected components.
18489826
Counting unrooted loopless planar maps
We present a formula for the number of n-edge unrooted loopless planar maps considered up to orientation-preserving isomorphism. The only sum contained in this formula is over the divisors of n.