Background: In Constraint Programming, constraint acquisition is the subfield that addresses the issue of modelling problems as sets of constraints, so that they can be solved by a constraint solver. This is a way to dramatically extend the use of Constraint Programming technology. Most active constraint acquisition systems suffer from two weaknesses. They require the explicit generation of the set of potential constraints (the bias), whose size can be prohibitive for practical use of these systems, and the answers to queries contain little information. Objectives: We introduce AcqNogoods, an active learning schema that does not require the construction of a bias. We then propose LlmAcq, an active learning system that incorporates a Large Language Model (LLM) component in the AcqNogoods schema. LlmAcq interprets the user’s answers given in natural language, leading to more informative communication. Methods: LlmAcq was instantiated with (i) a fine-tuned LLM encoder and (ii) a prompt-engineered LLM decoder. We evaluated both variants on classical logic-puzzle benchmarks (Purdey, Zebra, Sudoku, Kakuro). For greater realism, we also collected written feedback from 12 human subjects and used these data to design a pseudo-real experiment. Results: Across all benchmarks, LlmAcq dramatically decreases the number of queries, while learning constraints of arbitrary arity without the need of an explicit bias. The version of LlmAcq using a decoder LLM shows better accuracy and an interesting abstraction capability that allows it to learn several constraints from a single user’s answer. Conclusions: Our results suggest that combining natural-language feedback with bias-free learning is a promising step toward more user-friendly Constraint Programming modeling.

Passive constraint acquisition aims to learn constraint networks from examples of solutions and non-solutions. There typically exist many constraint networks that are consistent with a given set of examples, so the performance of an acquisition system is critically dependent on its ability to determine which network will generalize the best to unseen data. We introduce a framework for representing constraint networks in compressed form and present a novel method for constraint acquisition. Our method learns a constraint network that achieves a high compression ratio, with the idea that such networks are highly structured and therefore less prone to overfitting. Experiments demonstrate that this approach significantly reduces the number of examples needed for training and achieves a high accuracy on unseen data.

Constraint acquisition is the task of learning a constraint network from examples of solutions and non-solutions. Existing constraint acquisition systems typically require advance knowledge of the target network's constraint language, which significantly narrows their scope of applicability. In this paper we propose a constraint acquisition method that computes a suitable constraint language as part of the learning process, eliminating the need for any advance knowledge. We report preliminary experiments on various acquisition benchmarks.

The goal of constraint acquisition is to learn exactly a constraint network given access to an oracle that answers truthfully certain types of queries. In this paper we focus on partial membership queries and initiate a systematic investigation of the learning complexity of constraint languages. First, we use the notion of chain length to show that a wide class of languages can be learned with as few as O(n log(n)) queries. Then, we combine this result with generic lower bounds to derive a dichotomy in the learning complexity of binary languages. Finally, we identify a class of ternary languages that eludes our framework and hints at new research directions.

Frequent itemset mining is one of the most studied tasks in knowledge discovery. It is often reduced to mining the positive border of frequent itemsets, i.e. maximal frequent itemsets. Infrequent itemset mining, on the other hand, can be reduced to mining the negative border, i.e. minimal infrequent itemsets. We propose a generic framework based on constraint programming to mine both borders of frequent itemsets.One can easily decide which border to mine by setting a simple parameter. For this, we introduce two new global constraints, FREQUENTSUBS and INFREQUENTSUPERS, with complete polynomial propagators. We then consider the problem of mining borders with additional constraints. We prove that this problem is coNP-hard, ruling out the hope for the existence of a single CSP solving this problem (unless coNP ⊆ NP).

Discovering association rules among items in a dataset is one of the fundamental problems in data mining. It has recently been shown that constraint programming is a flexible way to tackle data mining tasks. In this paper we propose a declarative model based on constraint programming to capture association rules. Our model also allows us to specify any additional property and/or user's constraints on the kind of rules the user is looking for. To implement our model, we introduce a new global constraint, Confident, for ensuring the confidence of rules. We prove that completely propagating Confident is NP-hard. We thus provide a decomposition of Confident. In addition to user's constraints on the items composing body and head of the rules, we show that we can capture the popular minimal non-redundant property of association rules. An experimental analysis shows the practical effectiveness of our approach compared to existing approaches.

Answer Set Programming (ASP) is a powerful modeling formalism for combinatorial problems. However, writing ASP models can be hard. We propose a novel method, called Sketched Answer Set Programming (SkASP), aimed at facilitating this. In SkASP, the user writes partial ASP programs, in which uncertain parts are left open and marked with question marks. In addition, the user provides a number of positive and negative examples of the desired program behaviour. SkASP then synthesises a complete ASP program. This is realized by rewriting the SkASP program into another ASP program, which can then be solved by traditional ASP solvers. We evaluate our approach on 21 well known puzzles and combinatorial problems inspired by Karp's 21 NP-complete problems and on publicly available ASP encodings.

We describe an online, interactive system with a graphical interface to illustrate the power and operation of consistency algorithms in a friendly and popular context, namely, solving Sudoku puzzles. Our tool implements algorithms for enforcing five (domain-based) consistency properties on binary and non-binary constraint models. Our tool is useful for research, education, and outreach. From a scientific standpoint, we propose a new consistency property that can solve the hardest known 9×9 Sudoku instances without search, but leave open the question of the lowest level of consistency needed to solve every 9×9 Sudoku puzzle. We have used the current tool and its predecessor in the classroom to introduce students to modeling problems with constraints, explain consistency properties, and illustrate the operations of constraint propagation and lookahead. Finally, we have also used this tool during outreach activities to demystify AI to children and the general public and show them how computers think.

Constraint propagation during backtrack search significantly improves the performance of solving a Constraint Satisfaction Problem. While Generalized Arc Consistency (GAC) is the most popular level of propagation, higher-level consistencies (HLC) are needed to solve difficult instances. Deciding to enforce an HLC instead of GAC remains the topic of active research. We propose a simple and effective strategy that reactively triggers an HLC by monitoring search performance: When search starts thrashing, we trigger an HLC, then conservatively revert to GAC. We detect thrashing by counting the number of backtracks at each level of the search tree and geometrically adjust the frequency of triggering an HLC based on its filtering effectiveness. We validate our approach on benchmark problems using Partition-One Arc-Consistency as an HLC. However, our strategy is generic and can be used with other higher-level consistency algorithms.

We propose to exploit cycles in the constraint network of a Constraint Satisfaction Problem (CSP) to vehicle constraint propagation and improve the effectiveness of local consistency algorithms. We focus our attention on the consistency property Partition-One Arc-Consistency (POAC), which is a stronger variant of Singleton Arc-Consistency (SAC). We modify the algorithm for enforcing POAC to operate on a minimum cycle basis (MCB) of the incidence graph of the CSP. We empirically show that our approach improves the performance of problem solving and constitutes a novel and effective localization of consistency algorithms. Although this paper focuses on POAC, we believe that exploiting cycles, such as MCBs, is applicable to other consistency algorithms and that our study opens a new direction in the design of consistency algorithms. This research is documented in a technical report (Woordward, Choueiry, and Bessiere 2016). http://consystlab.unl.edu/our_work/StudentReports/TR-UNL-CSE-2016-0004.pdf

Preference reasoning is a central problem in decision support. There exist various ways to interpret a set of qualitative preferences. Conditional preference logics allow to deal with semantics such as optimistic, pessimistic, strong or not. In this paper, we study the complexity of the main problems in optimistic/pessimistic preference logic: undominated, consistency and dominance. We show that they are all NP-hard in general, with some becoming polynomial under specific semantics. Our second contribution is to show that the dominance problem, which has an online component in its definition, is compilable to polynomial time.

We propose two local consistencies that extend bounds consistency (BC) by simultaneously considering combinations of constraints as opposed to single constraints. We prove that these two local consistencies are both stronger than BC, but are NP-hard to enforce even when constraints are linear. Hence, we propose two polynomial-time techniques to enforce approximations of these two consistencies on linear constraints. One is a reformulation of the constraints on which we enforce BC whereas the other is a polynomial time algorithm. Both achieve stronger pruning than BC. Our experiments show large differences in favor of our approaches.

During the last decade several constraint acquisition systems have been proposed for assisting non-expert users in building constraint programming models. GENACQ is an algorithm based on generalization queries that can be plugged into many constraint acquisition systems. However, generalization queries require the aggregation of variables into types which is not always a simple task for non-expert users. In this paper, we propose a new algorithm that is able to learn types during the constraint acquisition process. The idea is to infer potential types by analyzing the structure of the current constraint network and to use the extracted types to ask generalization queries. Our approach gives good results although no knowledge on the types is provided.

Singleton-based consistencies have been shown to dramatically improve the performance of constraint solvers on some difficult instances. However, they are in general too expensive to be applied exhaustively during the whole search. In this paper, we focus on partition-one-AC, a singleton-based consistency which, as opposed to singleton arc consistency, is able to prune values on all variables when it performs singleton tests on one of them. We propose adaptive variants of partition-one-AC that do not necessarily run until having proved the fixpoint. The pruning can be weaker than the full version but the computational effort can be significantly reduced. Our experiments show that adaptive Partition-one-AC can obtain significant speed-ups over arc consistency and over the full version of partition-one-AC.

Constraint acquisition assists a non-expert user in modeling her problem as a constraint network. In existing constraint acquisition systems the user is only asked to answer very basic questions. The drawback is that when no background knowledge is provided, the user may need to answer a great number of such questions to learn all the constraints. In this paper, we introduce the concept of generalization query based on an aggregation of variables into types. We present a constraint generalization algorithm that can be plugged into any constraint acquisition system. We propose several strategies to make our approach more efficient in terms of number of queries. Finally we experimentally compare the recent QUACQ system to an extended version boosted by the use of our generalization functionality. The results show that the extended version dramatically improves the basic QUACQ.

We study how to find a solution to a constraint problem without modeling it. Constraint acquisition systems such as Conacq or ModelSeeker are not able to solve a single instance of a problem because they require positive examples to learn. The recent QuAcq algorithm for constraint acquisition does not require positive examples to learn a constraint network. It is thus able to solve a constraint problem without modeling it: we simply exit from QuAcq as soon as a complete example is classified as positive by the user. In this paper, we propose ASK&SOLVE, an elicitation-based solver that tries to find the best trade off between learning and solving to converge as soon as possible on a solution. We propose several strategies to speed-up ASK&SOLVE. Finally we give an experimental evaluation that shows that our approach improves the state of the art.

Virtual Arc Consistency (VAC) is a recent local consistency for processing cost function networks (aka weighted constraint networks) that exploits a simple but powerful connection with standard constraint networks. It has allowed to close hard frequency assignment benchmarks and is capable of directly solving networks of sub modular functions. The algorithm enforcing VAC is an iterative algorithm that solves a sequence of standard constraint networks. This algorithm has been improved by exploiting the idea of dynamic arc consistency between each iteration, leading to the dynamic VAC algorithm. When VAC is maintained during search, the difference between two adjacent nodes in the search tree is also limited. In this paper, we show that the incrementality of Dynamic VAC can also be useful when maintaining VAC during search and we present results showing that maintaining dynamic VAC during search can effectively accelerate search.

Global constraints are an essential component in the efficiency of centralized constraint programming. We propose to include global constraints in distributed constraint satisfaction problem (DisCSP) and distributed constraint optimization problem (DCOP). We detail how this inclusion can be done, considering different representations for global constraints (direct, nested, binary). We explore the relation of global constraints with local consistency (both in the hard and soft cases), in particular, for generalized arc consistency (GAC). We provide experimental evidence of the benefits of global constraints on several benchmarks, both for distributed constraint satisfaction and for distributed constraint optimization.

As (Lee et al., 2012) have shown, weighted constraint satisfaction problems can benefit from the introduction of global cost functions, leading to a new Cost Function Programming paradigm. In this paper, we explore the possibility of decomposing global cost functions in such a way that enforcing soft local consistencies on the decomposition offers guarantees on the level of consistency enforced on the original global cost function. We show that directional arc consistency and virtual arc consistency offer such guarantees. We conclude by experiments on decomposable cost functions showing that decompositions may be very useful to easily integrate efficient global cost functions in solvers.

We recently proposed No good-Based Asynchronous Forward Checking (AFC-ng), an efficient and robust algorithm for solving Distributed Constraint Satisfaction Problems (DisCSPs). AFC-ng performs an asynchronous forward checking phase during synchronous search. In this paper, we propose two new algorithms based on the same mechanism as AFC-ng. However, instead of using forward checking as a filtering property, we propose to maintain arc consistency asynchronously (MACA). The first algorithm we propose, MACA-del, enforces arc consistency thanks to an additional type of messages, deletion messages. The second algorithm, MACA-not, achieves arc consistency without any new type of message. We provide a theoretical analysis and an experimental evaluation of the proposed approach. Our experiments show the good performance of MACA algorithms, particularly those of MACA-not.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational Neighborhood Inverse Consistency (RNIC) as a local consistency property that operates on the dual graph of a non-binary CSP. We describe and characterize a practical algorithm for enforcing it. We argue that defining RNIC on the dual graph unveils unsuspected opportunities to reduce the computational cost of our algorithm and increase its filtering effectiveness. We show how to achieve those effects by modifying the topology of the dual graph, yielding new variations the RNIC property. We also introduce an adaptive strategy to automatically select the appropriate property to enforce given the connectivity of the dual graph. We integrate the resulting techniques as full lookahead strategies in a backtrack search procedure for solving CSPs, and demonstrate the effectiveness of our approach for solving known difficult benchmark problems.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) for binary CSPs. In this paper, we introduce RNIC, the extension of NIC to non-binary CSPs, and describe a practical algorithm for enforcing it. We propose an adaptive strategy to weaken or strengthen this property based on the connectivity of the network. We demonstrate the effectiveness of RNIC as a full lookahead strategy during search for solving difficult benchmark problems.

Asynchronous Backtracking is the standard search procedure for distributed constraint reasoning. It requires a total ordering on the agents. All polynomial space algorithms proposed so far to improve Asynchronous Backtracking by reordering agents during search only allow a limited amount of reordering. In this paper, we propose Agile-ABT, a search procedure that is able to change the ordering of agents more than previous approaches. This is done via the original notion of termination value, a vector of stamps labelling the new orders exchanged by agents during search. In Agile-ABT, agents can reorder themselves as much as they want as long as the termination value decreases as the search progresses. Our experiments show the good performance of Agile-ABT when compared to other dynamic reordering techniques.

We study propagation algorithms for the conjunction of two AllDifferent constraints. Solutions of an AllDifferent constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of finding simultaneous bipartite matchings. We present an extension of the famous Hall theorem which characterizes when simultaneous bipartite matchings exists. Unfortunately, finding such matchings is NP-hard in general. However, we prove a surprising result that finding a simultaneous matching on a convex bipartite graph takes just polynomial time. Based on this theoretical result, we provide the first polynomial time bound consistency algorithm for the conjunction of two AllDifferent constraints. We identify a pathological problem on which this propagator is exponentially faster compared to existing propagators. Our experiments show that this new propagator can offer significant benefits over existing methods.

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(*,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(*,m)C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tightening the existing relations and without introducing new ones. We empirically show that wR(*,m)C solves in a backtrack-free manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.

We study the CARDPATH constraint. This ensures a given constraint holds a number of times down a sequence of variables. We show that SLIDE, a special case of CARDPATH where the slid constraint must hold always, can be used to encode a wide range of sliding sequence constraints including CARDPATH itself. We consider how to propagate SLIDE and provide a complete propagator for CARDPATH. Since propagation is NP-hard in general, we identify special cases where propagation takes polynomial time. Our experiments demonstrate that using SLIDE to encode global constraints can be as efficient and effective as specialised propagators.

We propose a new algorithm for solving Distributed Constraint Optimization Problems (DCOPs). Our algorithm, called DyBop, is based on branch and bound search with dynamic ordering of agents. A distinctive feature of this algorithm is that it uses the concept of valued nogood. Combining lower bounds on inferred valued nogoods computed cooperatively helps pruning dynamically unfeasible sub-problems and speeds up the search. DyBop requires a polynomial space at each agent. Experiments show that DyBop has significantly better performance than other DCOP algorithms.

Control architectures, such as the LAAS architecture, CLARATY and HARPIC, have been developped to provide autonomy to robots. To achieve a robot's task, these control architectures plan sequences of sensorimotor behaviors. Currently carried out by roboticians, the design of sensorimotor behaviors is a truly complex task that can require many hours of hard work and intensive computations. In this paper, we propose a Constraint Programming-based framework to interact with roboticians during the sensorimotor behaviors design. A constraint network acquisition platform and a CSP-Based planner are used to automatically design sensorimotor behaviors. Moreover, our architecture exploits the propagation properties of the acquired CSPs to supervise the execution of a given sensorimotor behavior. Some experimental results are presented to validate our approach.

Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been known for sometime through the forward checking or the MAC search algorithms. Until recently, stronger forms of local consistency remained limited to those that change the structure of the constraint graph, and thus, could not be used in practice, especially on large networks. This paper focuses on the local consistencies that are stronger than arc consistency, without changing the structure of the network, i.e., only removing inconsistent values from the domains. In the last five years, several such local consistencies have been proposed by us or by others. We make an overview of all of them, and highlight some relations between them. We compare them both theoretically and experimentally, considering their pruning efficiency and the time required to enforce them.

Constraint programming techniques are widely used to solve real-world problems. It often happens that such problems are over-constrained and do not have any solution. In such a case, the goal is to find a good compromise. A simple theoretical framework is the Max-CSP, where the goal is to minimize the number of constraint violations. However, in real-life problems, complex rules are generally imposed with respect to violations. Solutions which do not satisfy these rules have no practical interest. Therefore, many frameworks derived from the Max-CSP have been introduced. In this paper, we classify the most usual types of rules, and we show that some of them are not expressible in existing frameworks. We introduce a new paradigm in which all these rules can be encoded, through meta-constraints. Moreover, we show that most of existing frameworks can be included in our model.

C. Bessiere and M.O. Cordier (1994) said that the AC-6 arc consistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are bidirectional. None of the previous algorithms achieving arc-consistency (AC-3, AC-4, AC-6) use constraint bidirectionality. We propose here an improved version of AC-6 which uses this property. Then, we claim that our new algorithm is optimal in the number of constraint checks performed (i.e. given a variable, value, and arc ordering, it performs the minimum possible number of constraint checks according to these orders).>