Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) are widely used in automated verification, but there is a lack of interactive tools designed for educational purposes in this field. To address this gap, we present EduSAT, a pedagogical tool specifically developed to support learning and understanding of SAT and SMT solving. EduSAT offers implementations of key algorithms such as the Davis-Putnam-Logemann-Loveland (DPLL) algorithm and the Reduced Order Binary Decision Diagram (ROBDD) for SAT solving. Additionally, EduSAT provides solver abstractions for five NP-complete problems beyond SAT and SMT. Users can benefit from EduSAT by experimenting, analyzing, and validating their understanding of SAT and SMT solving techniques. Our tool is accompanied by comprehensive documentation and tutorials, extensive testing, and practical features such as a natural language interface and SAT and SMT formula generators, which also serve as a valuable opportunity for learners to deepen their understanding. Our evaluation of EduSAT demonstrates its high accuracy, achieving 100% correctness across all the implemented SAT and SMT solvers. We release EduSAT as a python package in .whl file, and the source can be identified at https://github.com/zhaoy37/SAT_Solver.

Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP), which can be solved by general-purpose off-the-shelf MICP solvers. To mitigate the scalability challenge of solving these MICP problems, existing work focuses on devising efficient and strong formulations of the problems, while less effort has been spent on exploiting their specific structure to develop specialized solvers. The latter is the theme of our work. We focus on efficiently handling one-hot constraints, which are particularly relevant when encoding PWA dynamics. We have implemented our techniques in a tool, Soy, which organically integrates logical reasoning, arithmetic reasoning, and stochastic local search. For a set of PWA control benchmarks, Soy solves more problems, faster, than two state-of-the-art MICP solvers.

Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional solvers have had decades to build. We drew inspiration from the warm-start technique used in conventional solvers to address one of the major challenges faced by decision diagram based methods. Decision diagrams become more useful the wider they are allowed to be, but also become more costly to generate, especially with large numbers of variables. In the original version of this paper, we presented a method of peeling off a sub-graph of previously constructed diagrams and using it as the initial diagram for subsequent iterations that we call peel-and-bound. We tested the method on the sequence ordering problem, and our results indicate that our peel-and-bound scheme generates stronger bounds than a branch-and-bound scheme using the same propagators, and at significantly less computational cost. In this extended version of the paper, we also propose new methods for using relaxed decision diagrams to improve the solutions found using restricted decision diagrams, discuss the heuristic decisions involved with the parallelization of peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for sequencing problems. Furthermore, we test the new methods on the sequence ordering problem and the traveling salesman problem with time-windows (TSPTW), and include an updated and generalized implementation of the algorithm capable of handling any discrete optimization problem. The new results show that peel-and-bound outperforms ddo (a decision diagram based branch-and-bound solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking is easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes cardinality and parity (XOR) reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

Wave Function Collapse (WFC) is a widely used tile-based algorithm in procedural content generation, including textures, objects, and scenes. However, the current WFC algorithm and related research lack the ability to generate commercialized large-scale or infinite content due to constraint conflict and time complexity costs. This paper proposes a Nested WFC (N-WFC) algorithm framework to reduce time complexity. To avoid conflict and backtracking problems, we offer a complete and sub-complete tileset preparation strategy, which requires only a small number of tiles to generate aperiodic and deterministic infinite content. We also introduce the weight-brush system that combines N-WFC and sub-complete tileset, proving its suitability for game design. Our contribution addresses WFC's challenge in massive content generation and provides a theoretical basis for implementing concrete games.

We introduce a formal framework (called NCDC-ASP) for representing and reasoning about cardinal directions between extended spatial objects on a plane, using Answer Set Programming (ASP). NCDC-ASP preserves the meaning of cardinal directional relations as in Cardinal Directional Calculus (CDC), and provides solutions to all consistency checking problems in CDC under various conditions (i.e., for a complete/incomplete set of basic/disjunctive CDC constraints over connected/disconnected spatial objects). In particular, NCDC-ASP models a discretized version of the consistency checking problem in ASP, over a finite grid (rather than a plane), where we provide new lower bounds on the grid size to guarantee that it correctly characterizes solutions for the consistency checking in CDC. In addition, NCDC-ASP has the following two novelties important for applications. NCDC-ASP introduces default CDC constraints to represent and reason about background or commonsense knowledge that involves default qualitative directional relations (e.g., "the ice cream truck is by default to the north of the playground" or "the keyboard is normally placed in front of the monitor"). NCDC-ASP introduces inferred CDC constraints to allow inference of missing CDC relations and to provide them as explanations. We illustrate the uses and usefulness of NCDC-ASP with interesting scenarios from the real-world. We design and develop a variety of benchmark instances, and comprehensively evaluate NCDC-ASP from the perspectives of computational efficiency.

Crossword puzzles have traditionally served not only as entertainment but also as an educational tool that can be used to acquire vocabulary and language proficiency. One strategy to enhance the educational purpose is personalization, such as including more words on a particular topic. This paper focuses on the case of encouraging people's interest in news and proposes a framework for automatically generating news-centric crossword puzzles. We designed possible scenarios and built a prototype as a constraint satisfaction and optimization problem, that is, containing as many news-derived words as possible. Our experiments reported the generation probabilities and time required under several conditions. The results showed that news-centric crossword puzzles can be generated even with few news-derived words. We summarize the current issues and future research directions through a qualitative evaluation of the prototype. This is the first proposal that a formulation of a constraint satisfaction and optimization problem can be beneficial as an educational application.

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing causal discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series causal discovery, and event sequence causal discovery. However, most previous surveys are only focused on the time series causal discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data causal discovery.

Operational constraint violations may occur when deep reinforcement learning (DRL) agents interact with real-world active distribution systems to learn their optimal policies during training. This letter presents a universal distributionally robust safety filter (DRSF) using which any DRL agent can reduce the constraint violations of distribution systems significantly during training while maintaining near-optimal solutions. The DRSF is formulated as a distributionally robust optimization problem with chance constraints of operational limits. This problem aims to compute near-optimal actions that are minimally modified from the optimal actions of DRL-based Volt/VAr control by leveraging the distribution system model, thereby providing constraint satisfaction guarantee with a probability level under the model uncertainty. The performance of the proposed DRSF is verified using the IEEE 33-bus and 123-bus systems.

Many decision-making scenarios, e.g., public policy, healthcare, business, and disaster response, require accommodating the preferences of multiple stakeholders. We offer the first formal treatment of reasoning with multi-stakeholder qualitative preferences in a setting where stakeholders express their preferences in a qualitative preference language, e.g., CP-net, CI-net, TCP-net, CP-Theory. We introduce a query language for expressing queries against such preferences over sets of outcomes that satisfy specified criteria, e.g., $\mlangpref{\psi_1}{\psi_2}{A}$ (read loosely as the set of outcomes satisfying $\psi_1$ that are preferred over outcomes satisfying $\psi_2$ by a set of stakeholders $A$). Motivated by practical application scenarios, we introduce and analyze several alternative semantics for such queries, and examine their interrelationships. We provide a provably correct algorithm for answering multi-stakeholder qualitative preference queries using model checking in alternation-free $\mu$-calculus. We present experimental results that demonstrate the feasibility of our approach.