Background: Counterexample-Guided Abstraction Refinement (CEGAR) is a prominent technique to generate Cartesian abstractions for guiding search in cost-optimal planning. The core idea is to start from the trivial abstraction—an abstract state representing all concrete states—and iteratively refine it in a loop by splitting one abstract state into two. Each iteration of the loop searches an optimal abstract plan and replicates it into the concrete state space until finding a flaw—and splitting such abstract state—or returning a plan for the task if no flaw is found. Previous work finds only a single flaw in progression, by executing the abstract plan from the initial state and stopping when execution cannot be continued. Objectives: A theoretical framework for identifying different flaws of abstract plans, analysing their properties and using them to refine abstractions in different ways leading to higher-quality heuristics. Methods: We show that alternative types of flaw can be defined. Specifically, we search flaws in regression from the goals—resulting in higher heuristic values—and identify sequence flaws along the whole abstract plan by searching them in a Cartesian relaxation of the task after the first flaw, which greatly increases the flexibility of refinements in CEGAR. Results: Our experiments show that across existing benchmarks numerous sequence flaws exist in most abstract plans. We observe that the selected flaw has a high impact on the heuristic, and we propose several strategies that generate more informed abstractions. Overall, this greatly improves the performance of the baseline that only used the first progression flaw. Conclusions: Guiding the CEGAR process by analysing multiple flaws of an abstract plan trace and selecting the best refinement can improve its performance as a tool to generate admissible heuristics in planning. Thus, using our new types of flaw and flaw selection strategies, we get stronger heuristics than the state-of-the-art planners based on Cartesian abstractions.
Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-experts GP models (GP-pro), which combine local GP models to capture global correlations, alleviate this computational burden. However, training local experts on disjoint data subsets can lead to overestimated posterior variances. We propose GP-pro-c, a product-of-experts GP model that calibrates these variances using an information-based method. The method exploits the monotonicity and submodularity of information gain in GPs to define a calibration ratio that reduces the posterior variance of individual local GP models. We evaluate GP-pro-c using negative log-likelihood (NLL), root mean squared error (RMSE), and expected normalised calibration error (ENCE). Experiments on four synthetic functions and six regression datasets show that GP-pro-c achieves average reductions of 2.3
Background: In declarative constraint solving, a user formulates a constraint model in terms of variables and constraints, and uses a generic, off-the-shelf solver to solve the problem. Constraint Programming (CP) is one such constraint-solving paradigm, which has a wide support for many types of constraints, including global constraints. Global constraints capture complex relations between several decision variables, and CP solvers have specialized propagators to solve them efficiently. Objectives: While CP solvers support a wide range of global constraints, few solvers support them in a reified or even halfreified context. Hence, for most CP solvers, reified global constraints must be decomposed into non-global constraints. This bypasses the global constraint propagator, which can considerably slow the solving process, suppressing one of the key benefits of modeling with global constraints: a faster solve-time. This is a problem for generic CP-modeling, as reified constraints are often introduced by the modeling system during translation and flattening of compound constraints. Additionally, half-reified global constraints are also used extensively in eXplainable Constraint Programming techniques (XCP). Therefore, XCP techniques suffer from scalability issues when global constraints occur in the model. In this paper, we aim to alleviate this bottleneck, allowing the use of the propagators of global constraints when modeling their half-reification, for all CP-solvers. Methods: We propose a set of reformulation rules that allow the use of half-reification of a global constraint with any CP solver that supports the “normal” global constraint propagator. This is achieved by introducing auxiliary variables for the decision variables in the global constraint and the use of a reified channeling constraint, which most CP solvers support. Additionally, we show how to reduce the overhead of these auxiliary variables, by limiting the number of variables introduced, and by fixing their value when unconstrained. Finally, we prove the propagation strength of our reformulation for a variety of global constraint families. Results: We experimentally evaluate the reformulations on a variety of global constraints and applications where reified constraints can occur. Our results show that this reformulation is much faster compared to decomposing the global constraint, and in some cases, even outperforms solver-level propagation routines for reified global constraints. Conclusions: Using the reformulations proposed in this paper, we make the use of reified global constraints easily available for any CP solver. Hence, we expand the range of available solvers and constraint models that can be used in XCP techniques or for solving CSPs with compound constraints.
Background: Large Language Model (LLM)-based systems, such as conversational agents, are usually designed with monolithic, static architectures that rely on a single, general-purpose LLM to handle all user queries. However, these systems may be inefficient as different queries may require different levels of reasoning, domain knowledge or pre-processing. While generalist LLMs (e.g. GPT-4o, Claude-Sonnet) perform well across a wide range of tasks, they may incur significant financial, energy and computational costs. These costs may be disproportionate for simpler queries, resulting in unnecessary resource utilisation. A routing mechanism can therefore be employed to route queries to more appropriate components, such as smaller or specialised models, thereby improving efficiency and optimising resource consumption. Objectives: This survey aims to provide a comprehensive overview of routing strategies in LLM-based systems. Specifically, it reviews when, why, and how routing should be integrated into LLM pipelines to improve efficiency, scalability, and performance. Methods: We structure the survey by defining the objectives to optimise, such as cost minimisation and performance maximisation; the timing of routing within the LLM workflow, whether it occurs before or after generation; and the various implementation strategies, including similarity-based, supervised, reinforcement learning-based, and generative methods. Practical considerations such as industrial applications and current limitations are also examined, like standardising routing experiments, accounting for non-financial costs, and designing adaptive strategies. Results: There is a wide range of routing strategies, from lightweight, similarity-based and supervised methods, to more complex approaches involving LLM fine-tuning and reinforcement learning. Most current strategies adopt a pre-generation approach, which is generally more resource-efficient. This survey demonstrates that some low-resource solutions can provide generalisation capabilities. Conclusions: Routing offers a practical way to improve the efficiency of LLM-based systems. By formalising routing as a performance-cost optimisation problem, this survey provides tools and directions to guide future research and development of adaptive low-cost LLM-based systems.
Designing Artificial Intelligence (AI)-based interactive systems for law enforcement poses unique socio-technical and ethical challenges, particularly when such systems must support real-time decision-making in dynamic, high-stakes environments. Despite their potential, AI-supported interactive systems in policing require carefully elicited domain-specific requirements to ensure effective use while being Ethical by Design. However, methods for such requirement elicitation remain limited. This paper presents a participatory approach for identifying the requirements of AI-driven Mixed Reality (MR) systems in law enforcement contexts. The introduced methodology builds on two of our previous EU projects: the Erasmus+ project "Trustworthy AI", which provided educational material to teach key principles of Trustworthy AI, and AI4EU, which developed an abbreviated assessment tool for evaluating AI systems. In collaboration with police education units and law enforcement agencies in Sweden and Catalonia, we conducted a multi-phase study involving two preparatory workshops—one focused on educating participants in Trustworthy AI, and another involving hands-on MR use in standard police training scenarios. This reflects the view that it is not enough to simply ask people about new technologies—they must also be educated to critically assess their implications. After the workshops, we collected structured feedback using quantitative and qualitative methods. To analyze risk levels of the elicited requirements, we applied the AI4EU-based assessment tool. Our findings highlight key challenges and opportunities for designing AI-based systems with MR interfaces that enhance decision-making in real-time police operations while ensuring transparency, safety, and human oversight.
