SAT Encoding and CSP Reduction for Interconnected Alldiff Constraints

Constraint satisfaction problems (CSP) or Boolean satisfiability problem (SAT) are two well known paradigm to model and solve combinatorial problems. Modeling and resolution of CSP is often strengthened by global constraints (e.g., Alldiff constraint). This paper highlights two different ways of handling specific structural information: a uniform propagation framework to handle (interleaved) Alldiff constraints with some CSP reduction rules; and a SAT encoding of these rules that preserves the reduction properties of CSP

Set Constraint Model and Automated Encoding into SAT: Application to the Social Golfer Problem

On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively model set constraint problems and to encode them automatically into SAT instances. We apply our technique to the Social Golfer Problem and we also use it to break symmetries of the problem. Our technique is simpler, more declarative, and less error-prone than direct and improved hand modeling. The SAT instances that we automatically generate contain less clauses than improved hand-written instances such as in [20], and with unit propagation they also contain less variables. Moreover, they are well-suited for SAT solvers and they are solved faster as shown when solving difficult instances of the Social Golfer Problem.Comment: Submitted to Annals of Operations researc

Solving hard subgraph problems in parallel

This thesis improves the state of the art in exact, practical algorithms for finding subgraphs. We study maximum clique, subgraph isomorphism, and maximum common subgraph problems. These are widely applicable: within computing science, subgraph problems arise in document clustering, computer vision, the design of communication protocols, model checking, compiler code generation, malware detection, cryptography, and robotics; beyond, applications occur in biochemistry, electrical engineering, mathematics, law enforcement, fraud detection, fault diagnosis, manufacturing, and sociology. We therefore consider both the ``pure'' forms of these problems, and variants with labels and other domain-specific constraints. Although subgraph-finding should theoretically be hard, the constraint-based search algorithms we discuss can easily solve real-world instances involving graphs with thousands of vertices, and millions of edges. We therefore ask: is it possible to generate ``really hard'' instances for these problems, and if so, what can we learn? By extending research into combinatorial phase transition phenomena, we develop a better understanding of branching heuristics, as well as highlighting a serious flaw in the design of graph database systems. This thesis also demonstrates how to exploit two of the kinds of parallelism offered by current computer hardware. Bit parallelism allows us to carry out operations on whole sets of vertices in a single instruction---this is largely routine. Thread parallelism, to make use of the multiple cores offered by all modern processors, is more complex. We suggest three desirable performance characteristics that we would like when introducing thread parallelism: lack of risk (parallel cannot be exponentially slower than sequential), scalability (adding more processing cores cannot make runtimes worse), and reproducibility (the same instance on the same hardware will take roughly the same time every time it is run). We then detail the difficulties in guaranteeing these characteristics when using modern algorithmic techniques. Besides ensuring that parallelism cannot make things worse, we also increase the likelihood of it making things better. We compare randomised work stealing to new tailored strategies, and perform experiments to identify the factors contributing to good speedups. We show that whilst load balancing is difficult, the primary factor influencing the results is the interaction between branching heuristics and parallelism. By using parallelism to explicitly offset the commitment made to weak early branching choices, we obtain parallel subgraph solvers which are substantially and consistently better than the best sequential algorithms

A global workspace framework for combined reasoning

Artificial Intelligence research has produced many effective techniques for solving a wide range of problems. Practitioners tend to concentrate their efforts in one particular problem solving paradigm and, in the main, AI research describes new methods for solving particular types of problems or improvements in existing approaches. By contrast, much less research has considered how to fruitfully combine different problem solving techniques. Numerous studies have demonstrated how a combination of reasoning approaches can improve the effectiveness of one of those methods. Others have demonstrated how, by using several different reasoning techniques, a system or method can be developed to accomplish a novel task, that none of the individual techniques could perform. Combined reasoning systems, i.e., systems which apply disparate reasoning techniques in concert, can be more than the sum of their parts. In addition, they gain leverage from advances in the individual methods they encompass. However, the benefits of combined reasoning systems are not easily accessible, and systems have been hand-crafted to very specific tasks in certain domains. This approach means those systems often suffer from a lack of clarity of design and are inflexible to extension. In order for the field of combined reasoning to advance, we need to determine best practice and identify effective general approaches. By developing useful frameworks, we can empower researchers to explore the potential of combined reasoning, and AI in general. We present here a framework for developing combined reasoning systems, based upon Baars’ Global Workspace Theory. The architecture describes a collection of processes, embodying individual reasoning techniques, which communicate via a global workspace. We present, also, a software toolkit which allows users to implement systems according to the framework. We describe how, despite the restrictions of the framework, we have used it to create systems to perform a number of combined reasoning tasks. As well as being as effective as previous implementations, the simplicity of the underlying framework means they are structured in a straightforward and comprehensible manner. It also makes the systems easy to extend to new capabilities, which we demonstrate in a number of case studies. Furthermore, the framework and toolkit we describe allow developers to harness the parallel nature of the underlying theory by enabling them to readily convert their implementations into distributed systems. We have experimented with the framework in a number of application domains and, through these applications, we have contributed to constraint satisfaction problem solving and automated theory formation

Propagation Networks: A Flexible and Expressive Substrate for Computation

PhD thesisI propose a shift in the foundations of computation. Practically all ideas of general-purpose computation today are founded either on execution of sequences of atomic instructions, i.e., assembly languages, or on evaluation of tree-structured expressions, i.e., most higher level programming languages. Both have served us well in the past, but it is increasingly clear that we need something more. I suggest that we can build general-purpose computation on propagation of information through networks of stateful cells interconnected with stateless autonomous asynchronous computing elements. Various forms of this general idea have been used with great success for various special purposes; perhaps the most immediate example is constraint propagation in constraint satisfaction systems. These special-purpose systems, however, are all complex and all different, and neither compose well, nor interoperate well, nor generalize well. A foundational layer is missing. The key insight in this work is that a cell should not be seen as storing a value, but as accumulating information about a value. The cells should never forget information -- such monotonicity prevents race conditions in the behavior of the network. Monotonicity of information need not be a severe restriction: for example, carrying reasons for believing each thing makes it possible to explore but thenpossibly reject tentative hypotheses, thus appearing to undo something, while maintaining monotonicity. Accumulating information is a broad enough design principle to encompass arbitrary computation. The object of this dissertation is therefore to architect a general-purpose computing system based on propagation networks; to subsume expression evaluation under propagation just as instruction execution is subsumed under expression evaluation; to demonstrate that a general-purpose propagation system can recover all the benefits that have been derived from special-purpose propagation systems, allow them to compose andinteroperate, and offer further expressive power beyond what we have known in the past; and finally to contemplate the lessons that such a fundamental shift can teach us about the deep nature of computation.My graduate career in general, and this work in particular, have been sponsored in part by a National Science Foundation Graduate Research Fellowship, by the Disruptive Technology Office as part of the AQUAINT Phase 3 research program, by the Massachusetts Institute of Technology, by Google, Inc., and by the National Science Foundation Cybertrust (05-518) program.Doctor of Philosoph

Flexible and expressive substrate for computation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 167-174).In this dissertation I propose a shift in the foundations of computation. Modem programming systems are not expressive enough. The traditional image of a single computer that has global effects on a large memory is too restrictive. The propagation paradigm replaces this with computing by networks of local, independent, stateless machines interconnected with stateful storage cells. In so doing, it offers great flexibility and expressive power, and has therefore been much studied, but has not yet been tamed for general-purpose computation. The novel insight that should finally permit computing with general-purpose propagation is that a cell should not be seen as storing a value, but as accumulating information about a value. Various forms of the general idea of propagation have been used with great success for various special purposes; perhaps the most immediate example is constraint propagation in constraint satisfaction systems. This success is evidence both that traditional linear computation is not expressive enough, and that propagation is more expressive. These special-purpose systems, however, are all complex and all different, and neither compose well, nor interoperate well, nor generalize well. A foundational layer is missing. I present in this dissertation the design and implementation of a prototype general-purpose propagation system. I argue that the structure of the prototype follows from the overarching principle of computing by propagation and of storage by accumulating information-there are no important arbitrary decisions. I illustrate on several worked examples how the resulting organization supports arbitrary computation; recovers the expressivity benefits that have been derived from special-purpose propagation systems in a single general-purpose framework, allowing them to compose and interoperate; and offers further expressive power beyond what we have known in the past. I reflect on the new light the propagation perspective sheds on the deep nature of computation.by Alexey Andreyevich Radul.Ph.D