New Algebraic Tools for Constraint Satisfaction

The Galois correspondence involving polymorphisms and co-clones has received a lot of attention in regard to constraint satisfaction problems. However, it fails if we are interested in a reduction giving equivalence instead of only satisfiability-equivalence. We show how a similar Galois connection involving weaker closure operators can be applied for these problems. As an example of the usefulness of our construction, we show how to obtain very short proofs of complexity classifications in this context

Constraint Satisfaction Techniques for Combinatorial Problems

The last two decades have seen extraordinary advances in tools and techniques for constraint satisfaction. These advances have in turn created great interest in their industrial applications. As a result, tools and techniques are often tailored to meet the needs of industrial applications out of the box. We claim that in the case of abstract combinatorial problems in discrete mathematics, the standard tools and techniques require special considerations in order to be applied effectively. The main objective of this thesis is to help researchers in discrete mathematics weave through the landscape of constraint satisfaction techniques in order to pick the right tool for the job. We consider constraint satisfaction paradigms like satisfiability of Boolean formulas and answer set programming, and techniques like symmetry breaking. Our contributions range from theoretical results to practical issues regarding tool applications to combinatorial problems. We prove search-versus-decision complexity results for problems about backbones and backdoors of Boolean formulas. We consider applications of constraint satisfaction techniques to problems in graph arrowing (specifically in Ramsey and Folkman theory) and computational social choice. Our contributions show how applying constraint satisfaction techniques to abstract combinatorial problems poses additional challenges. We show how these challenges can be addressed. Additionally, we consider the issue of trusting the results of applying constraint satisfaction techniques to combinatorial problems by relying on verified computations

A constraint manager to support virtual maintainability

Virtual prototyping tools have already captivated the industry's interest as viable design tool. One of the key challenges for the research community is to extend the capabilities of Virtual Reality technology beyond its current scope of ergonomics and design reviews. The research presented in this paper is part of a larger research programme that aims to perform maintainability assessment on virtual prototypes. This paper discusses the design and implementation of a geometric constraint manager that has been designed to support physical realism and interactive assembly and disassembly tasks within virtual environments. The key techniques employed by the constraint manager are direct interaction, automatic constraint recognition, constraint satisfaction and constrained motion. Various optimization techniques have been implemented to achieve real-time interaction with large industrial models

Schaefer's theorem for graphs

Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in polynomial time, or is NP-complete. We present an analog of this dichotomy result for the propositional logic of graphs instead of Boolean logic. In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi\ of statements ("constraints") about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi\ of allowed quantifier-free first-order formulas; the question is whether \Phi\ is satisfiable in a graph. We prove that either \Psi\ is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete. This is achieved by a universal-algebraic approach, which in turn allows us to use structural Ramsey theory. To apply the universal-algebraic approach, we formulate the computational problems under consideration as constraint satisfaction problems (CSPs) whose templates are first-order definable in the countably infinite random graph. Our method to classify the computational complexity of those CSPs is based on a Ramsey-theoretic analysis of functions acting on the random graph, and we develop general tools suitable for such an analysis which are of independent mathematical interest.Comment: 54 page

CoAKTinG: Collaborative Advanced Knowledge Technologies in the Grid

Grid infrastructures coupled with semantic web linkage and reasoning open up intriguing new possibilities for scientific collaboration. In this short paper, we outline the research agenda and collaboration technologies under development within the CoAKTinG project: Collaborative Advanced Knowledge Technologies in the Grid. CoAKTinG will provide tools to assist scientific collaboration by integrating intelligent meeting spaces, ontologically annotated media streams from online meetings, decision rationale and group memory capture, meeting facilitation, issue handling, planning and coordination support, constraint satisfaction, and instant messaging/presence. Their integration is illustrated through an extended use scenario

Experimenting with Constraint Programming Techniques in Artificial Intelligence: Automated System Design and Verification of Neural Networks

This thesis focuses on the application of Constraint Satisfaction and Optimization techniques in two Artificial Intelligence (AI) domains: automated design of elevator systems and verification of Neural Networks (NNs). The three main areas of interest for my work are (i) the languages for defining the constraints for the systems, (ii) the algorithms and encodings that enable solving the problems considered and (iii) the tools that implement such algorithms. Given the expressivity of the domain description languages and the availability of effective tools, several problems in diverse application fields have been solved successfully using constraint satisfaction techniques. The two case studies herewith presented are no exception, even if they entail different challenges in the adoption of such techniques. Automated design of elevator systems not only requires encoding of feasibility (hard) constraints, but should also take into account design preferences, which can be expressed in terms of cost functions whose optimal or near-optimal value characterizes “good” design choices versus “poor” ones. Verification of NNs (and other machine-learned implements) requires solving large-scale constraint problems which may become the main bottlenecks in the overall verification procedure. This thesis proposes some ideas for tackling such challenges, including encoding techniques for automated design problems and new algorithms for handling the optimization problems arising from verification of NNs. The proposed algorithms and techniques are evaluated experimentally by developing tools that are made available to the research community for further evaluation and improvement

Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. Many real life problems come from uncertain and dynamic environments, where the initial constraints and domains may change during its execution. Thus, the solution found for the problem may become invalid. The search forrobustsolutions for constraint satisfaction problems (CSPs) has become an important issue in the ¿eld of constraint programming. In some cases, there exists knowledge about the uncertain and dynamic environment. In other cases, this information is unknown or hard to obtain. In this paper, we consider CSPs with discrete and ordered domains where changes only involve restrictions or expansions of domains or constraints. To this end, we model CSPs as weighted CSPs (WCSPs) by assigning weights to each valid tuple of the problem constraints and domains. The weight of each valid tuple is based on its distance from the borders of the space of valid tuples in the corresponding constraint/domain. This distance is estimated by a new concept introduced in this paper: coverings. Thus, the best solution for the modeled WCSP can be considered as a most robust solution for the original CSP according to these assumptionsThis work has been partially supported by the research projects TIN2010-20976-C02-01 (Min. de Ciencia e Innovacion, Spain) and P19/08 (Min. de Fomento, Spain-FEDER), and the fellowship program FPU.Climent Aunés, LI.; Wallace, RJ.; Salido Gregorio, MA.; Barber Sanchís, F. (2013). Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings. Artificial Intelligence Review. 1-26. https://doi.org/10.1007/s10462-013-9420-0S126Climent L, Salido M, Barber F (2011) Reformulating dynamic linear constraint satisfaction problems as weighted csps for searching robust solutions. 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Using Java Csp Solvers in the Automated Analyses of Feature Models

Feature Models are used in different stages of software development and are recognized to be an important asset in model transformation techniques and software product line development. The automated analysis of feature models is being recognized as one of the key challenges for automated software development in the context of Software Product Lines. in our previous work we explained how a feature model can be transformed into a constraint satisfaction problem. However cardinalities were not considered. in this paper we present how a cardinality-based feature model can be also translated into a constraint satisfaction problem. in that connection, it is possible to use off-the-shelf tools to automatically accomplish several tasks such as calculating the number of possible feature configurations and detecting possible conflicts. in addition, we present a performance test between two off-the-shelf Java constraint solvers. To the best of our knowledge, this is the first time a performance test is presented using solvers for feature modelling proposesMinisterio de Educación y Ciencia TIC2003-02737-C02-0