Modern society is full of computational challenges that rely on probabilistic reasoning, statistics, and combinatorics. Interestingly, many of these questions can be formulated by encoding them into propositional formulas and then asking for its number of models. With a growing interest in practical problem-solving for tasks that involve model counting, the community established the Model Counting (MC) Competition in fall of 2019 with its first iteration in 2020. The competition aims at advancing applications, identifying challenging benchmarks, fostering new solver development, and enhancing existing solvers for model counting problems and their variants. The first iteration, brought together various researchers, identified challenges, and inspired numerous new applications. In this paper, we present a comprehensive overview of the 2021-2023 iterations of the Model Counting Competition. We detail its execution and outcomes. The competition comprised four tracks, each focusing on a different variant of the model counting problem. The first track centered on the model counting problem (MC), which seeks the count of models for a given propositional formula. The second track challenged developers to submit programs capable of solving the weighted model counting problem (WMC). The third track was dedicated to projected model counting (PMC). Finally, we initiated a track that combined projected and weighted model counting (PWMC). The competition continued with a high level of participation, with seven to nine solvers submitted in various different version and based on quite diverging techniques.

A wide range of LM applications require generating text that conforms to syntactic or semantic constraints. Imposing such constraints can be naturally framed as probabilistic conditioning, but exact generation from the resulting distribution -- which can differ substantially from the LM's base distribution -- is generally intractable. In this work, we develop an architecture for controlled LM generation based on sequential Monte Carlo (SMC). Our SMC framework allows us to flexibly incorporate domain- and problem-specific constraints at inference time, and efficiently reallocate computational resources in light of new information during the course of generation. By comparing to a number of alternatives and ablations on four challenging domains -- Python code generation for data science, text-to-SQL, goal inference, and molecule synthesis -- we demonstrate that, with little overhead, our approach allows small open-source language models to outperform models over 8x larger, as well as closed-source, fine-tuned ones. In support of the probabilistic perspective, we show that these performance improvements are driven by better approximation to the posterior distribution. Our system builds on the framework of Lew et al. (2023) and integrates with its language model probabilistic programming language, giving users a simple, programmable way to apply SMC to a broad variety of controlled generation problems.

Conventional trajectory planning approaches for autonomous vehicles often assume a fixed vehicle model that remains constant regardless of the vehicle's location. This overlooks the critical fact that the tires and the surface are the two force-transmitting partners in vehicle dynamics; while the tires stay with the vehicle, surface conditions vary with location. Recognizing these challenges, this paper presents a novel framework for spatially resolving dynamic constraints in both offline and online planning algorithms applied to autonomous racing. We introduce the GripMap concept, which provides a spatial resolution of vehicle dynamic constraints in the Frenet frame, allowing adaptation to locally varying grip conditions. This enables compensation for location-specific effects, more efficient vehicle behavior, and increased safety, unattainable with spatially invariant vehicle models. The focus is on low storage demand and quick access through perfect hashing. This framework proved advantageous in real-world applications in the presented form. Experiments inspired by autonomous racing demonstrate its effectiveness. In future work, this framework can serve as a foundational layer for developing future interpretable learning algorithms that adjust to varying grip conditions in real-time.

Data cleaning is a long-standing challenge in data management. While powerful logic and statistical algorithms have been developed to detect and repair data errors in tables, existing algorithms predominantly rely on domain-experts to first manually specify data-quality constraints specific to a given table, before data cleaning algorithms can be applied. In this work, we propose a new class of data-quality constraints that we call Semantic-Domain Constraints, which can be reliably inferred and automatically applied to any tables, without requiring domain-experts to manually specify on a per-table basis. We develop a principled framework to systematically learn such constraints from table corpora using large-scale statistical tests, which can further be distilled into a core set of constraints using our optimization framework, with provable quality guarantees. Extensive evaluations show that this new class of constraints can be used to both (1) directly detect errors on real tables in the wild, and (2) augment existing expert-driven data-cleaning techniques as a new class of complementary constraints. Our extensively labeled benchmark dataset with 2400 real data columns, as well as our code are available at https://github.com/qixuchen/AutoTest to facilitate future research.

-- This paper introduces the Compliant Explicit Reference Governor (C-ERG), an extension of the Explicit Reference Governor that allows the robot to operate safely while in contact with the environment. The C-ERG is an intermediate layer that can be placed between a high-level planner and a low-level controller: its role is to enforce operational constraints and to enable the smooth transition between free-motion and contact operations. The C-ERG ensures safety by limiting the total energy available to the robotic arm at the time of contact. In the absence of contact, however, the C-ERG does not penalize the system performance. The emerging trend in the modern industry is to prioritize flexibility [1]. Until recently, robotics has been dominated by sampling-based motion planning which places an emphasis on "collision-free" paths to avoid harming itself or anything in its path [2].

Researchers recently extended Distributed Constraint Optimization Problems (DCOPs) to Communication-Aware DCOPs so that they are applicable in scenarios in which messages can be arbitrarily delayed. Distributed asynchronous local search and inference algorithms designed for CA-DCOPs are less vulnerable to message latency than their counterparts for regular DCOPs. However, unlike local search algorithms for (regular) DCOPs that converge to k-opt solutions (with k > 1), that is, they converge to solutions that cannot be improved by a group of k agents), local search CA-DCOP algorithms are limited to 1-opt solutions only. In this paper, we introduce Latency-Aware Monotonic Distributed Local Search-2 (LAMDLS-2), where agents form pairs and coordinate bilateral assignment replacements. LAMDLS-2 is monotonic, converges to a 2-opt solution, and is also robust to message latency, making it suitable for CA-DCOPs. Our results indicate that LAMDLS-2 converges faster than MGM-2, a benchmark algorithm, to a similar 2-opt solution, in various message latency scenarios.

Recent advances in deep neural language models combined wit h the capacity of large scale datasets have accelerated the development of natural langu age generation systems that produce fluent and coherent texts (to various degrees of succ ess) in a multitude of tasks and application contexts. However, controlling the output of t hese models for specific user and task needs is still an open challenge. This is crucial not onl y to customizing the content and style of the generated language, but also to their safe and re liable deployment in the real world. We present an extensive survey on the emerging topic o f constrained neural language generation in which we formally define and categorize the pro blems of natural language generation by distinguishing between conditions and constraints (the latter being testable conditions on the output text instead of the input), present constrained text generation tasks, and review existing methods and evaluation metrics for cons trained text generation. Our aim is to highlight recent progress and trends in this emergi ng field, informing on the most promising directions and limitations towards advancing th e state-of-the-art of constrained neural language generation research.

The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do not guarantee to avoid constraints violations; or constraint-specific model architectures (e.g., for monotonocity); or on output projection, which requires to solve an optimization problem that might be computationally demanding. We present the Hypersherical Constrained Representation, a novel method to enforce constraints in the output space for convex and bounded feasibility regions (generalizable to star domains). Our method operates on a different representation system, where Euclidean coordinates are converted into hyperspherical coordinates relative to the constrained region, which can only inherently represent feasible points. Experiments on a synthetic and a real-world dataset show that our method has predictive performance comparable to the other approaches, can guarantee 100% constraint satisfaction, and has a minimal computational cost at inference time.

Keywords: scheduling, RCPSP, bottlenecks, constraint relaxation Abstract: In realistic production scenarios, Advanced Planning and Scheduling (APS) tools often require manual intervention by production planners, as the system works with incomplete information, resulting in suboptimal schedules. Often, the preferable solution is not found just because of the too-restrictive constraints specifying the optimization problem, representing bottlenecks in the schedule. To provide computer-assisted support for decision-making, we aim to automatically identify bottlenecks in the given schedule while linking them to the particular constraints to be relaxed. In this work, we address the problem of reducing the tardiness of a particular project in an obtained schedule in the resource-constrained project scheduling problem by relaxing constraints related to identified bottlenecks. We develop two methods for this purpose. The second method identifies potential improvements in relaxed versions of the problem and proposes targeted relaxations. Surprisingly, the untargeted relaxations result in improvements comparable to the targeted relaxations. 1 INTRODUCTION In the modern manufacturing industry, Advanced Planning and Scheduling (APS) tools are used to schedule production automatically. However, not all parameters and information are available to the APS systems in practice.

Expressive range analysis is a visualization-based technique used to evaluate the performance of generative models, particularly in game level generation. It typically employs two quantifiable metrics to position generated artifacts on a 2D plot, offering insight into how content is distributed within a defined metric space. In this work, we use the expressive range of a generator as the conceptual space of possible creations. Inspired by the quality diversity paradigm, we explore this space to generate levels. To do so, we use a constraint-based generator that systematically traverses and generates levels in this space. To train the constraint-based generator we use different tile patterns to learn from the initial example levels. We analyze how different patterns influence the exploration of the expressive range. Specifically, we compare the exploration process based on time, the number of successful and failed sample generations, and the overall interestingness of the generated levels. Unlike typical quality diversity approaches that rely on random generation and hope to get good coverage of the expressive range, this approach systematically traverses the grid ensuring more coverage. This helps create unique and interesting game levels while also improving our understanding of the generator's strengths and limitations.