Distributed splitting of constraint satisfaction problems

Constraint propagation aims to reduce a constraint satisfaction problem into an equivalent but simpler one. However, constraint propagation must be interleaved with a splitting mechanism in order to compose a complete solver. In~cite{monfroy:sac2000 a framework for constraint propagation based on a control-driven coordination model was presented. In this paper we extend this framework in order to integrate a distributed splitting mechanism. This technique has three main advantages: 1),in a single distributed and generic framework, propagation and splitting can be interleaved in order to realize complete distributed solvers, 2), by changing only one agent, we can perform different kinds of search, and 3), splitting of variables can be dynamically triggered before the fixed point of a propagation is reached

Constraint Programming viewed as Rule-based Programming

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling.We consider here two types of rules. The first type, that we call equality rules, leads to a new notion of local consistency, called {\em rule consistency} that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in \cite{MS98b}). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming we show how both types of rules can be automatically generated, as {\tt CHR} rules of \cite{fruhwirth-constraint-95}. This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.Comment: 39 pages. To appear in Theory and Practice of Logic Programming Journa

Generalized Support and Formal Development of Constraint Propagators

Abstract The concept of support is pervasive in constraint programming. Traditionally, when a domain value ceases to have support, it may be removed because it takes part in no solutions. Arc-consistency algorithms such as AC2001 [8] make use of support in the form of a single domain value. GAC algorithms such as GAC-Schema We design a methodology for developing correct propagators using generalized support. A constraint is expressed as a family of support properties, which may be proven correct against the formal semantics of the constraint. Using CurryHoward isomorphism to interpret constructive proofs as programs, we show how to derive correct propagators from the constructive proofs of the support properties. The framework is carefully designed to allow efficient algorithms to be produced. Derived algorithms may make use of dynamic literal triggers or watched literal

Box constraint collections for adhoc constraints.

Cheng Chi Kan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 101-105).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Background --- p.4Chapter 2.1 --- Propagation Based Constraint Solving --- p.4Chapter 2.1.1 --- "Valuations, Domains and Constraints" --- p.4Chapter 2.1.2 --- Solving a CSP --- p.6Chapter 2.1.3 --- Propagators --- p.7Chapter 2.1.4 --- Domain Consistency --- p.8Chapter 2.1.5 --- Bounds Consistency --- p.9Chapter 2.1.6 --- Propagation-based Backtracking Search --- p.10Chapter 2.2 --- Disjunction --- p.12Chapter 2.2.1 --- Speculative --- p.12Chapter 2.2.2 --- Cardinality --- p.12Chapter 2.2.3 --- Constructive Disjunction --- p.13Chapter 3 --- Box Constraint Collections --- p.15Chapter 3.1 --- Box Constraint Collections --- p.15Chapter 3.2 --- Separable Constraints --- p.17Chapter 4 --- Building Box Constraint Collections --- p.22Chapter 4.1 --- The bccFinder Algorithm --- p.22Chapter 4.2 --- Heuristics for the bccFinder Algorithm --- p.30Chapter 4.2.1 --- The Order of Box Expansion --- p.30Chapter 4.2.2 --- The Conditions of Box Expansion --- p.35Chapter 5 --- Compiling BCCs into Indexicals --- p.37Chapter 5.1 --- Indexicals --- p.37Chapter 5.2 --- Basic Compilation --- p.45Chapter 5.3 --- Optimizing Compilation --- p.49Chapter 5.3.1 --- Subsumption Indexicals --- p.49Chapter 5.3.2 --- Union Indexicals --- p.50Chapter 5.4 --- Hybrid Approach --- p.71Chapter 6 --- Experiments --- p.76Chapter 7 --- Related Work --- p.93Chapter 8 --- Concluding Remarks --- p.98Chapter 8.1 --- Contributions --- p.98Chapter 8.2 --- Future Work --- p.9

Automatic Generation of Constraint Propagation Algorithms for Small Finite Domains

We study here constraint satisfaction problems that are based on predefined, explicitly given finite constraints. To solve them we propose a notion of rule consistency that can be expressed in terms of rules derived from the explicit representation of the initial constraints. This notion of local consistency is weaker than arc consistency for constraints of arbitrary arity but coincides with it when all domains are unary or binary. For Boolean constraints rule consistency coincides with the closure under the wellknown propagation rules for Boolean constraints. By generalizing the format of the rules we obtain a characterization of arc consistency in terms of so-called inclusion rules. The advantage of rule consistency and this rule based characterization of the arc consistency is that the algorithms that enforce both notions can be automatically generated, as CHR rules. So these algorithms could be integrated into constraint logic programming systems such as ECLiPSe ..

Constraint solving over multi-valued logics - application to digital circuits

Due to usage conditions, hazardous environments or intentional causes, physical and virtual systems are subject to faults in their components, which may affect their overall behaviour. In a ‘black-box’ agent modelled by a set of propositional logic rules, in which just a subset of components is externally visible, such faults may only be recognised by examining some output function of the agent. A (fault-free) model of the agent’s system provides the expected output given some input. If the real output differs from that predicted output, then the system is faulty. However, some faults may only become apparent in the system output when appropriate inputs are given. A number of problems regarding both testing and diagnosis thus arise, such as testing a fault, testing the whole system, finding possible faults and differentiating them to locate the correct one. The corresponding optimisation problems of finding solutions that require minimum resources are also very relevant in industry, as is minimal diagnosis. In this dissertation we use a well established set of benchmark circuits to address such diagnostic related problems and propose and develop models with different logics that we formalise and generalise as much as possible. We also prove that all techniques generalise to agents and to multiple faults. The developed multi-valued logics extend the usual Boolean logic (suitable for faultfree models) by encoding values with some dependency (usually on faults). Such logics thus allow modelling an arbitrary number of diagnostic theories. Each problem is subsequently solved with CLP solvers that we implement and discuss, together with a new efficient search technique that we present. We compare our results with other approaches such as SAT (that require substantial duplication of circuits), showing the effectiveness of constraints over multi-valued logics, and also the adequacy of a general set constraint solver (with special inferences over set functions such as cardinality) on other problems. In addition, for an optimisation problem, we integrate local search with a constructive approach (branch-and-bound) using a variety of logics to improve an existing efficient tool based on SAT and ILP