This paper studies how to verify the conformity of a program with its specification and proposes a novel constraint-programming framework for bounded program verification (CPBPV). The CPBPV framework uses constraint stores to represent the specification and the program and explores execution paths nondeterministically. The input program is partially correct if each constraint store so produced implies the post-condition. CPBPV does not explore spurious execution paths as it incrementally prunes execution paths early by detecting that the constraint store is not consistent. CPBPV uses the rich language of constraint programming to express the constraint store. Finally, CPBPV is parametrized with a list of solvers which are tried in sequence, starting with the least expensive and less general. Experimental results often produce orders of magnitude improvements over earlier approaches, running times being often independent of the variable domains. Moreover, CPBPV was able to detect subtle errors in some programs while other frameworks based on model checking have failed.

Literature on Constraint Satisfaction exhibits the definition of several ``structural'' properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically detect such properties efficiently by means of incomplete yet effective algorithms, and use them to reduce the search space and boost search. In this paper, we provide a unifying framework encompassing most of the properties known so far, both in CSP and other fields' literature, and shed light on the semantical relationships among them. This gives a unified and comprehensive view of the topic, allows new, unknown, properties to emerge, and clarifies the computational complexity of the various detection problems. In particular, among the others, two new concepts, fixability and removability emerge, that come out to be the ideal characterisations of values that may be safely assigned or removed from a variable's domain, while preserving problem satisfiability. These two notions subsume a large number of known properties, including inconsistency, substitutability and others. Because of the computational intractability of all the property-detection problems, by following the CSP approach we then determine a number of relaxations which provide sufficient conditions for their tractability. In particular, we exploit forms of language restrictions and local reasoning.

We describe decomposition during search (DDS), an integration of And/Or tree search into propagation-based constraint solvers. The presented search algorithm dynamically decomposes sub-problems of a constraint satisfaction problem into independent partial problems, avoiding redundant work. The paper discusses how DDS interacts with key features that make propagation-based solvers successful: constraint propagation, especially for global constraints, and dynamic search heuristics. We have implemented DDS for the Gecode constraint programming library.

When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear equations both with and without coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not prohibitive) effort and decreases maintainability, but will deliver better performance. This paper shows how to use variable views, previously introduced for an implementation architecture, to derive perfect propagator variants. A model for views and derived propagators is introduced. Derived propagators are proved to be indeed perfect in that they inherit essential properties such as correctness and domain and bounds consistency. Techniques for systematically deriving propagators such as transformation, generalization, specialization, and channeling are developed for several variable domains. We evaluate the massive impact of derived propagators. Without derived propagators, Gecode would require 140 000 rather than 40 000 lines of code for propagators.

Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly distinguished. That is what is done, for example, in Cumulative Prospect Theory. However, contraryto the latter framework that presupposes genuine numerical assessments, human agents often decide on the basis of an ordinal ranking of the pros and the cons, and by focusing on the most salient arguments. In other terms, the decision process is qualitative as well as bipolar. In this article, based on a bipolar extension of possibility theory, we define and axiomatically characterize several decision rules tailored for the joint handling of positive and negative arguments in an ordinal setting. The simplest rules can be viewed as extensions of the maximin and maximax criteria to the bipolar case, and consequently suffer from poor decisive power. More decisive rules that refine the former are also proposed. These refinements agree both with principles of efficiency and with the spirit of order-of-magnitude reasoning, that prevails in qualitative decision theory. The most refined decision rule uses leximin rankings of the pros and the cons, and the ideas of counting arguments of equal strength and cancelling pros by cons. It is shown to come down to a special case of Cumulative Prospect Theory, and to subsume the ``Take the Best'' heuristic studied by cognitive psychologists.

In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is minimized while the expected back room staffing is sufficient to perform all work. Three novel constraint programming models and several shaving procedures for these models are presented. Experimental results show that a model based on closed-form expressions together with a combination of shaving procedures is the most efficient. This model is able to find and prove optimal solutions for many problem instances within a reasonable run-time. Previously, the only available approach was a heuristic algorithm. Furthermore, a hybrid method combining the heuristic and the best constraint programming method is shown to perform as well as the heuristic in terms of solution quality over time, while achieving the same performance in terms of proving optimality as the pure constraint programming model. This is the first work of which we are aware that solves such queueing-based problems with constraint programming.

Determining the evolutionary history of a given biological data is an important task in biological sciences. Given a set of quartet topologies over a set of taxa, the Maximum Quartet Consistency (MQC) problem consists of computing a global phylogeny that satisfies the maximum number of quartets. A number of solutions have been proposed for the MQC problem, including Dynamic Programming, Constraint Programming, and more recently Answer Set Programming (ASP). ASP is currently the most efficient approach for optimally solving the MQC problem. This paper proposes encoding the MQC problem with pseudo-Boolean (PB) constraints. The use of PB allows solving the MQC problem with efficient PB solvers, and also allows considering different modeling approaches for the MQC problem. Initial results are promising, and suggest that PB can be an effective alternative for solving the MQC problem.

The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of three formalisms used for different purposes in reasoning about multi-agent systems: strategic games, CP-nets, and soft constraints. To relate the notions of optimality in these formalisms we introduce a natural qualitative modification of the notion of a strategic game. We show then that the optimal outcomes of a CP-net are exactly the Nash equilibria of such games. This allows us to use the techniques of game theory to search for optimal outcomes of CP-nets and vice-versa, to use techniques developed for CP-nets to search for Nash equilibria of the considered games. Then, we relate the notion of optimality used in the area of soft constraints to that used in a generalization of strategic games, called graphical games. In particular we prove that for a natural class of soft constraints that includes weighted constraints every optimal solution is both a Nash equilibrium and Pareto efficient joint strategy. For a natural mapping in the other direction we show that Pareto efficient joint strategies coincide with the optimal solutions of soft constraints.

We present a formal model to represent and solve the unicast/multicast routing problem in networks with Quality of Service (QoS) requirements. To attain this, first we translate the network adapting it to a weighted graph (unicast) or and-or graph (multicast), where the weight on a connector corresponds to the multidimensional cost of sending a packet on the related network link: each component of the weights vector represents a different QoS metric value (e.g. bandwidth, cost, delay, packet loss). The second step consists in writing this graph as a program in Soft Constraint Logic Programming (SCLP): the engine of this framework is then able to find the best paths/trees by optimizing their costs and solving the constraints imposed on them (e.g. delay < 40msec), thus finding a solution to QoS routing problems. Moreover, c-semiring structures are a convenient tool to model QoS metrics. At last, we provide an implementation of the framework over scale-free networks and we suggest how the performance can be improved.

Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique for solving hard problems. The identification of SBPs in SAT has been the subject of significant improvements in recent years, resulting in more compact SBPs and more effective algorithms. The identification of SBPs has also been applied to pseudo-Boolean (PB) constraints, showing that symmetry breaking can also be an effective technique for PB constraints. This paper extends further the application of SBPs, and shows that SBPs can be identified and used in Maximum Satisfiability (MaxSAT), as well as in its most well-known variants, including partial MaxSAT, weighted MaxSAT and weighted partial MaxSAT. As with SAT and PB, symmetry breaking predicates for MaxSAT and variants are shown to be effective for a representative number of problem domains, allowing solving problem instances that current state of the art MaxSAT solvers could not otherwise solve.