Constraint satisfaction is a simple but powerful tool. Constraints identify the impossible and reduce the realm of possibilities to effectively focus on the possible, allowing for a natural declarative formulation of what must be satisfied, without expressing how. The field of constraint reasoning and satisfiability has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics.

The purpose of this course is to familiarize students with the theory and techniques of constraint processing, using the constraint graphical model. This model offers a natural language for encoding world knowledge in areas such as scheduling, vision, diagnosis, prediction, design, hardware and software verification, and bio-informatics, and it facilitates many computational tasks relevant to these domains such as constraint satisfaction, constraint optimization, counting and sampling. The course will focus on techniques for constraint processing. It will cover search and inference algorithms, consistency algorithms, and structure based techniques, and will focus on properties that facilitate efficient solutions. Extensions to general graphical models such as probabilistic networks, cost networks, and satisfiability-based schemes will be discussed. This year we will explore the potential collaboration between Constraint Processing and Large Language Models. We ask: can LLM help in solving constraint processing, and vice-versa, can constraints representation and algorithms be relevant to training LLMs? Students will have an opportunity to address such questions through recent literatures in their projects.