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.

Constraint Acquisition (CA) aims to widen the use of constraint programming by assisting users in the modeling process. However, most CA methods suffer from a significant drawback: they learn a single set of individual constraints for a specific problem instance, but cannot generalize these constraints to the parameterized constraint specifications of the problem. In this paper, we address this limitation by proposing GenCon, a novel approach to learn parameterized constraint models capable of modeling varying instances of the same problem. To achieve this generalization, we make use of statistical learning techniques at the level of individual constraints. Specifically, we propose to train a classifier to predict, for any possible constraint and parameterization, whether the constraint belongs to the problem. We then show how, for some classes of classifiers, we can extract decision rules to construct interpretable constraint specifications. This enables the generation of ground constraints for any parameter instantiation. Additionally, we present a generate-and-test approach that can be used with any classifier, to generate the ground constraints on the fly. Our empirical results demonstrate that our approach achieves high accuracy and is robust to noise in the input instances.

Program annotations in the form of function pre/postconditions play a crucial role in various software engineering and program verification tasks. However, the frequent unavailability of these annotations necessitates manual retrofitting. This paper shows how constraint acquisition, a learning framework derived from constraint programming and version space learning, can be extended for automatically inferring program preconditions. Our approach performs this inference in a black-box manner through automatic query generation and input-output observations of program executions. We introduce PreCA, the first-ever precondition inference framework leveraging query-based constraint acquisition. Notably, we specialize PreCA to handle memory-related preconditions on binary code, which pose significant challenges in data and information management systems. In contrast to prior black-box techniques, PreCA provides well-defined guarantees. Specifically, it employs a sound and complete method to generate preconditions consistent with all the observed input-output relationships of the program. Furthermore, empirical evaluations on our benchmark demonstrate that PreCA outperforms the results of state-of-the-art approaches, delivering comparable or superior results in 5s, as opposed to the 1-hour runtime of existing approaches on identical machines. We also present two successful use cases from the standard libc and the mbedtls cryptographic library. PreCA notably infers for the former one a more precise precondition than specified in the documentation.

Constraint Programming (CP) is a successful methodology for solving combinatorial problems from various domains. Efficiently modeling the problem at hand as a Constraint Satisfaction Problem is a crucial, but difficult task in CP. Toward this, a recent approach that is attracting increasing interest is Constraint Acquisition, i.e., the (semi)automatic learning of constraints through examples of solutions and non-solutions. This paper introduces a hybrid methodology that combines passive and active learning strategies to acquire both global and fixed arity constraints. This hybrid approach leverages the strengths of both techniques to address their individual limitations. Passive learning rapidly learns constraints from example solutions, while active learning refines and contextualizes constraints through user interaction. The core of the methodology consists of a passive learning module where subsets of variables are compared against global constraints and are validated using a CP solver. Constraints consistently present across multiple solution sets are identified as global constraints that belong to the model. Then, fixed arity constraints are refined through an active learning module with user input. Experiments across various problem types, from simple to complex, demonstrate the efficiency of the proposed hybrid methodology.

Constraint Programming (CP) has been successfully used to model and solve complex combinatorial problems. However, modeling is often not trivial and requires expertise, which is a bottleneck to wider adoption. In Constraint Acquisition (CA), the goal is to assist the user by automatically learning the model. In (inter)active CA, this is done by interactively posting queries to the user, e.g. does this partial solution satisfy your (unspecified) constraints or not. While interactive CA methods learn the constraints, the learning is related to symbolic concept learning, as the goal is to learn an exact representation. However, a large number of queries is required to learn the model, which is a major limitation. In this paper, we aim to alleviate this limitation by tightening the connection of CA and Machine Learning (ML), by, for the first time in interactive CA, exploiting statistical ML methods. We propose to use probabilistic classification models to guide interactive CA queries to the most promising parts. We discuss how to train classifiers to predict whether a candidate expression from the bias is a constraint of the problem or not, using both relation-based and scope-based features. We then show how the predictions can be used in all layers of interactive CA: the query generation, the scope finding, and the lowest-level constraint finding. We experimentally evaluate our proposed methods using different classifiers and show that our methods greatly outperform the state of the art, decreasing the number of queries needed to converge by up to 72%.

A constraint-based model represents knowledge about a domain by a set of constraints, which must be satisfied by solutions in that domain. These models may be used for reasoning, decision making and optimisation. Unfortunately, modelling itself is a hard and error-prone task that requires expertise. The automation of this process is often referred to as constraint acquisition and has been pursued for over 20 years. Methods typically learn constraints by testing candidates against a dataset of solutions and non-solutions, and often use some form of machine learning to decide which should be learned. However, few methods are robust under errors in the data, some cannot handle large sets of candidates, and most are computationally expensive even for small problems. We describe a statistical approach based on sequential analysis that is robust, fast and scalable to large biases. Its correctness depends on an assumption that does not always hold but which is, we show using Bayesian analysis, reasonable in practice.

Many planning, scheduling or multi-dimensional packing problems involve the design of subtle logical combinations of temporal or spatial constraints. Recently, we introduced GEQCA-I, which stands for Generic Qualitative Constraint Acquisition, as a new active constraint acquisition method for learning qualitative constraints using qualitative queries. In this paper, we revise and extend GEQCA-I to GEQCA-II with a new type of query, universal query, for qualitative constraint acquisition, with a deeper query-driven acquisition algorithm. Our extended experimental evaluation shows the efficiency and usefulness of the concept of universal query in learning randomly-generated qualitative networks, including both temporal networks based on Allen’s algebra and spatial networks based on region connection calculus. We also show the effectiveness of GEQCA-II in learning the qualitative part of real scheduling problems.

The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine learning. A more promising approach has been to perform program synthesis within an appropriately designed Domain Specific Language (DSL). However, these too have seen limited success. We propose Abstract Reasoning with Graph Abstractions (ARGA), a new object-centric framework that first represents images using graphs and then performs a search for a correct program in a DSL that is based on the abstracted graph space. The complexity of this combinatorial search is tamed through the use of constraint acquisition, state hashing, and Tabu search. An extensive set of experiments demonstrates the promise of ARGA in tackling some of the complicated object-centric tasks of the ARC rather efficiently, producing programs that are correct and easy to understand.

Abstract This paper studies the problem of geometric constraint acquisition from a given planar motion task using Fourier descriptor. In the previous work, we established a computational geometric framework for simultaneous type and dimensional synthesis of planar dyads by extracting line or circle constraints from a sequence of task poses. In cases where six or more poses are specified as the desired movement, the resulting optimal constraint may be nowhere in the accuracy neighborhood to be viewed as an approximate line or circle. The approach herein enhances the framework by exploiting Fourier transform to capture the feasible constraint of a continuous motion with a large set of poses. Theoretically, any arbitrary point trajectory on the task motion can be transformed to an array of harmonics and used as a constraint; on a practical level, only those with low number of harmonics could allow accurate realization by simple planar mechanisms suitable for real applications, e.g., four- and six-bar linkages, cams, and coupled serial chains. Therefore, the practical goal is to find the simple Fourier constraint defined with the least number of harmonics. Two examples of designing assistive mechanisms for upper- and lower-limb rehabilitation are provided in the end to illustrate the effectiveness of our approach.

Many planning, scheduling or multi-dimensional packing problems involve the design of subtle logical combinations of temporal or spatial constraints. On the one hand, the precise modelling of these constraints, which are formulated in various relation algebras, entails a number of possible logical combinations and requires expertise in constraint-based modelling. On the other hand, active constraint acquisition (CA) has been used successfully to support non-experienced users in learning conjunctive constraint networks through the generation of a sequence of queries. In this paper, we propose GEACQ, which stands for Generic Qualitative Constraint Acquisition, an active CA method that learns qualitative constraints via the concept of qualitative queries. GEACQ combines qualitative queries with time-bounded path consistency (PC) and background knowledge propagation to acquire the qualitative constraints of any scheduling or packing problem. We prove soundness, completeness and termination of GEACQ by exploiting the jointly exhaustive and pairwise disjoint property of qualitative calculus and we give an experimental evaluation that shows (i) the efficiency of our approach in learning temporal constraints and, (ii) the use of GEACQ on real scheduling instances.

Constraint acquisition systems assist the non-expert user in modelling her problem as a constraint network. QUACQ is a sequential constraint acquisition algorithm that generates queries as (partial) examples to be classified as positive or negative. The drawbacks are that the user may need to answer a great number of such examples, within a significant waiting time between two examples, to learn all the constraints. In this paper, we propose PACQ, a portfolio-based parallel constraint acquisition system. The design of PACQ benefits from having several users sharing the same target problem. Moreover, each user is involved in a particular acquisition session, opened in parallel to improve the overall performance of the whole system.We prove the correctness of PACQ and we give an experimental evaluation that shows that our approach improves on QUACQ.

Modeling a combinatorial problem is a hard and error-prone task requiring significant expertise. Constraint acquisition methods attempt to automate this process by learning constraints from examples of solutions and (usually) non-solutions. Active methods query an oracle while passive methods do not. We propose a known but not widely-used application of machine learning to constraint acquisition: training a classifier to discriminate between solutions and non-solutions, then deriving a constraint model from the trained classifier. We discuss a wide range of possible new acquisition methods with useful properties inherited from classifiers. We also show the potential of this approach using a Naive Bayes classifier, obtaining a new passive acquisition algorithm that is considerably faster than existing methods, scalable to large constraint sets, and robust under errors.

Ellipsoidal one-class constraint acquisition for quadratically constrained programming

Constraint acquisition systems such as QuAcq and MultiAcq can assist non-expert users to model their problems as constraint networks by classifying (partial) examples as positive or negative. For each negative example, the former focuses on one constraint of the target network, while the latter can learn a maximum number of constraints. Two bottlenecks of the acquisition process where both these algorithms encounter problems are the large number of queries required to reach convergence, and the high cpu times needed to generate queries, especially near convergence. In this paper we propose algorithmic and heuristic methods to deal with both these issues. We first describe an algorithm, called MQuAcq, that blends the main idea of MultiAcq into QuAcq resulting in a method that learns as many constraints as MultiAcq does after a negative example, but with a lower complexity. A detailed theoretical analysis of the proposed algorithm is also presented. %We also present a technique that boosts the performance of constraint acquisition by reducing the number of queries significantly. Then we turn our attention to query generation which is a significant but rather overlooked part of the acquisition process. We describe %in detail how query generation in a typical constraint acquisition system operates, and we propose heuristics for improving its efficiency. Experiments from various domains demonstrate that our resulting algorithm that integrates all the new techniques does not only generate considerably fewer queries than QuAcq and MultiAcq, but it is also by far faster than both of them, in average query generation time as well as in total run time, and also largely alleviates the premature convergence problem.

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.

Science Foundation Ireland ((Grant No. 12/RC/2289-P2 which is co-funded under the European Regional Development Fund); (CONFIRM Centre for Smart Manufacturing, Research Code 16/RC/3918))

In master slave manipulator, slave arm is controlled by an operator to manipulate the objects in remote environment using an iso-kinematic master arm which is located in the control room. In such a scenario, where the actual work environment is separated from the operator, formulation of techniques for assisting the operator to execute constrained motion (preferential inclusion or preferential exclusion of workspace zones) in the slave environment are not only helpful, but also essential. We had earlier demonstrated the efficacy of constraint motion with predefined geometrical constraints of various types. However, in a hot-cell scenario the generation of the constraint equations is difficult since we shall not have access to the cell for taking measurements. In this paper, a user friendly method is proposed for image based acquisition of the various constraint geometries thus eliminating the need to take in-cell measurements. For this purpose various hot cell tasks and required geometrical primitives pertaining to these tasks have been surveyed and an algorithm has been developed for generating the constraint geometry for each primitive. This methodology shall increase the efficiency and ease of use of the hot cell Tele-manipulator by providing real time constraint acquisition and subsequent assistive force based constrained motion.

Constraint acquisition

Constrained data clustering algorithms allow the incorporation of a priori knowledge for specific problems into the clustering task in the form of constraints. The quality of the constraints have great impact in the performance of the constrained clustering algorithms. Therefore, special care must be taken while building the sets of constraints. In order to take the maximum advantage of the constrained clustering algorithms, these constraints must be highly informative and non-redundant. We propose two constraint acquisition methods based on user-feedback. The first method searches for non-redundant intra-cluster and inter-cluster query-candidates supported by information contained in an initial partition of the data set, ranks the candidates by decreasing order of interest and, finally, prompts the user the most relevant query-candidates. The constraints may optionally be used for learning a new data representation, which may enhance the performance of clustering. The second method iterates between using the previous method for expanding the set of constraints, and producing an updated partition of the data. The motivation is to iteratively increment the set of constraints by including new informative and non-redundant constraints at each iteration. Experimental results advocate that the proposed constraint acquisition methods increase the performance of data clustering.

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.