Constraint Satisfaction

Large language models (LLMs) enable natural-language interaction in engineering modeling, but generated models may violate structural constraints, domain rules, or task requirements. We propose a metamodel-guided model generation method that coordinates generation-time constraints and post-generation validation. The method transforms metamodel information, uses its terminology to guide structured constraint extraction from specifications, and links constraints to metamodel elements while recording their sources in an Integrated Constraint Model (ICM). For each task, relevant constraints are bound to concrete objects, values, and references. The generation-time constraint layer (L1) restricts candidate content. The post-generation validation layer (L2) checks constructed models and serialized artifacts, and task acceptance checks retain the original requirements throughout repair. Deterministic procedures construct and serialize models, while LLMs propose candidate content and repairs. Validation uses existing domain tools and checkers written by humans with LLM assistance. Experiments cover AUTOSAR, railway models, and structured decisions in private international law. All 60 AUTOSAR generation runs passed acceptance within the declared task scope, and all 255 resulting ARXML files passed XSD validation. In a separate controlled AUTOSAR repair experiment, all 85 core fault units and 15 prespecified substitute units were restored within one repair round. A local AUTOSAR experiment recorded interventions during stepwise generation. The results support coordinating generation constraints, domain checks, and task acceptance to construct models and guide bounded repair.

Constraint Programming (CP) offers an intuitive, declarative framework for modeling Vehicle Routing Problems (VRP). While classical successor-based CP models can be adapted to handle optional visits or insertion-based heuristics, sequence variables provide a significantly more natural and elegant formulation for these requirements. Building upon our prior work that introduced the initial concept, the main contribution of this article is the complete semantic and operational formalization of sequence variables as a computational domain. Specifically, we formally define the sequence domain and its update operations, and detail the implementation and data structures required to integrate sequence variables into trail-based CP solvers. Furthermore, we introduce consistency levels for associated constraints on this domain alongside specialized global constraints tailored for routing problems. Finally, we demonstrate that sequence variables simplify problem modeling while achieving competitive computational performance on Pickup and Delivery Problems with and without Time Windows, the Dial-a-Ride Problem, and a Prize-Collecting Scheduling Problem.

Video Temporal Grounding (VTG) aims to localize specific video segments corresponding to natural language queries. While recent Large Vision-Language Models (LVLMs) employ Reinforcement Learning to generate Chains-of-Thought (CoT), they typically rely solely on outcome-based supervision. Consequently, this often leads to hallucinations, where the reasoning process becomes disconnected from the visual content and the final prediction. Existing attempts to mitigate this by relying on external supervision from larger models or separate reward models are computationally expensive and prone to rigid patterns. To address these challenges, we propose TAR (Temporal Anchor-Constrained Reasoning), a framework that introduces the temporal anchor (T-anchor) as a transparent and auditable checkpoint mechanism. T-anchor enforces progressive refinement within the CoT, compelling the model to continuously ground its intermediate thoughts in visual evidence and iteratively calibrate temporal predictions, thereby significantly enhancing the faithfulness and autonomy of the reasoning process and final accuracy. Furthermore, we introduce a bootstrapping paradigm that automatically harvests high-quality CoT data using only a standard 7B model, eliminating the dependency on ultra-large models. Extensive experiments demonstrate that TAR achieves state-of-the-art performance and generates faithful, autonomous, and progressively refined reasoning traces.

Modeling scheduling problems with conditional time intervals and cumulative functions has become a common approach when using modern commercial constraint programming solvers. This paradigm enables the modeling of a wide range of scheduling problems, including those involving producers and consumers. However, it is unavailable in existing open-source solvers and practical implementation details remain undocumented. In this work, we present an implementation of this modeling approach using a single, generic global constraint called the Generalized Cumulative. We also introduce a novel timetabling filtering algorithm specifically designed to handle tasks defined on conditional time-intervals. Experimental results demonstrate that this approach, combined with the new filtering algorithm, performs competitively with existing solvers enabling the modeling of producer and consumer scheduling problems and effectively scales to large-scale problems.

In this document, we introduce PyCSP$3$, a Python library that allows us to write models of combinatorial constrained problems in a declarative manner. Currently, with PyCSP$3$, you can write models of constraint satisfaction and optimization problems. More specifically, you can build CSP (Constraint Satisfaction Problem) and COP (Constraint Optimization Problem) models. Importantly, there is a complete separation between the modeling and solving phases: you write a model, you compile it (while providing some data) in order to generate an XCSP$3$ instance (file), and you solve that problem instance by means of a constraint solver. You can also directly pilot the solving procedure in PyCSP$3$, possibly conducting an incremental solving strategy. In this document, you will find all that you need to know about PyCSP$3$, with more than 50 illustrative models.

TCSPs (Temporal Constraint Satisfaction Problems) [Dechter et al. 1991] get rid of unary constraints by binarizing them after having added an "origin of the world" variable. In this work, we look at the constraints between the "origin of the world" variable and the other variables, as the (binarized) domains of these other variables. With this in mind, we define a notion of arc-consistency for TCSPs, which we will refer to as binarized-domains Arc-Consistency, or bdArc-Consistency for short. We provide an algorithm achieving bdArc-Consistency for a TCSP, which we will refer to as bdAC-3, for it is an adaptation of Mackworth's [1977] well-known arc-consistency algorithm AC-3. We show that if an STP is bdArc-Consistent, and connected, i.e., its "origin of the world" variable is disconnected from none of the other variables, its binarized domains are minimal. We provide two polynomial backtrack-free procedures: one for the task of getting a solution from a connected bdArc-Consistent STP; the other for the task of getting, from a bdArc-Consistent STP, either that it is inconsistent or, in case of consistency, a connected bdArc-Consistent STP refinement. We then show how to use our results both in a general TCSP solver and in a TCSP-based job shop scheduler. The work also provides an experimental comparison on STPs of bdAC-3 with an existing arc-consistency algorithm, ACSTP, restricted to STPs [Kong et al. 2018]; an experimental comparison of three TCSP-based job shop schedulers, two of which use weak versions of bdAC-3 as the filtering procedure during the search, the third [Schwalb and Dechter 1997] a weak version of path-consistency; and the swi-prolog source codes used by these comparisons. Last but not least, we provide an incremental version of bdAC-3.