In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified additional conditions. Using the guarded decomposition framework we are also able to define a new form of decomposition, which we call a spread cut. We show that discovery of width k spread-cut decompositions is tractable for each k, and that the spread cut decomposition strongly generalize all existing decompositions except hypertrees. Finally we exhibit a family of hypergraphs Hn, for n = 1, 2, 3..., where the width of the best hypertree decomposition of each Hn is at least 3n, but the width of the best spreadcut decomposition is at most 2n. 1

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that may be used to assign weights to the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems correspond to the special case of 0,1-valued functions. We show that the partition function, i.e. the sum of the weights of all configurations, can be computed in polynomial time if either (1) every function in F is of “product type”, or (2) every function in F is “pure affine”. For every other fixed set F, computing the partition function is FP #P-complete. 1

We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in constraints. If every relation in the constraint language is affine then the number of satisfying assignments can be exactly counted in polynomial time. Otherwise, if every relation in the constraint language is in the co-clone IM2 from Post’s lattice, then the problem of counting satisfying assignments is complete with respect to approximation-preserving reductions in the complexity class #RHΠ1. This means that the problem of approximately counting satisfying assignments of such a CSP instance is equivalent in complexity to several other known counting problems, including the problem of approximately counting the number of independent sets in a bipartite graph. For every other fixed constraint language, the problem is complete for #P with respect to approximation-preserving reductions, meaning that there is no fully polynomial randomised approximation scheme for counting satisfying assignments unless NP=RP. 1

Abstract. We analyze the datatype system of OWL and OWL 2, and discuss certain nontrivial consequences of its definition, such as the extensibility of the set of supported datatypes and complexity of reasoning. We also argue that certain datatypes from the list of normative datatypes in the current OWL 2 Working Draft are inappropriate and should be replaced with different ones. Finally, we present an algorithm for datatype reasoning. Our algorithm is modular in the sense that it can handle any datatype that supports certain basic operations. We show how to implement these operations for number and string datatypes. 1

Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as text or music generation that imitate a given style. However, Markov sequences are traditionally generated using greedy, left-to-right algorithms. While this approach is computationally cheap, it is fundamentally unsuited for interactive control. This paper addresses the issue of generating steerable Markovian sequences. We target interactive applications such as games, in which users want to control, through simple input devices, the way the system generates a Markovian sequence, such as a text, a musical sequence or a drawing. To this aim, we propose to revisit Markov sequence generation as a branch and bound constraint satisfaction problem (CSP). We propose a CSP formulation of the basic Markovian hypothesis as elementary Markov Constraints (EMC). We propose algorithms that achieve domain-consistency for the propagators of EMCs, in an event-based implementation of CSP. We show how EMCs can be combined to estimate the global Markovian probability of a whole sequence, and accommodate for different species of Markov generation such as fixed order, variable-order, or smoothing. Such a formulation, although more costly than traditional greedy generation algorithms, yields the immense advantage of being naturally steerable, since control specifications can be represented by arbitrary additional constraints, without any modification of the generation algorithm. We illustrate our approach on simple yet combinatorial chord sequence and melody generation problems and give some performance results.

Abstract. The semiring-based formalism to model soft constraint has been introduced in 1995 by Ugo Montanari and the authors of this paper. The idea was to make constraint programming more flexible and widely applicable. We also wanted to define the extension via a general formalism, so that all its instances could inherit its properties and be easily compared. Since then, much work has been done to study, extend, and apply this formalism. This papers gives a brief summary of some of these research activities. 1 Before soft constraints: a brief introduction to constraint programming

We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set Γ of rational functions, each of which assigns a weight to each variable assignment. Our dichotomy extends previous work in which the weight functions were restricted to being non-negative. We represent a weight function as a product of the form (−1) s g, where the polynomial s determines the sign of the weight and the non-negative function g determines its magnitude. We show that the problem of computing the partition function (the sum of the weights of all possible variable assignments) is computable in polynomial time if either every function in Γ can be defined by a “pure affine ” magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of “product type” with a linear sign polynomial. In all other cases, computing the partition function is FP #P-complete.

Arc consistency algorithms are widely used to prune the search space of Constraint Satisfaction Problems (CSPs). Since many researchers associate arc consistency with binary normalized CSPs, there is a confusion between the notion of arc consistency and 2-consistency. 2-consistency guarantees that any instantiation of a value to a variable can be consistently extended to any second variable. Thus, 2-consistency can be stronger than arc-consistency in binary CSPs. In this paper, we present a new algorithm, called 2-C3, which achieves 2-consistency in binary and non-normalized CSPs. This algorithm is a reformulation of the well-known AC3 algorithm. The evaluation section shows that 2-C3 is able to prune more search space than AC3 and AC4.

soft constraints to bipolar preferences:

c ○ Zijie Li 2009I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public.