Automated Reasoning: satisfiability

Go to Course: https://www.coursera.org/learn/automated-reasoning-sat

Introduction

### Course Review: Automated Reasoning: Satisfiability **Course Overview** "Automated Reasoning: Satisfiability" is an engaging and informative course on Coursera that dives into the intriguing world of satisfiability (SAT) and satisfiability modulo theories (SMT). The course is designed to equip learners with the knowledge and skills needed to utilize SAT/SMT tools effectively for solving a diverse set of problems. What sets this course apart is its balanced blend of theoretical foundations and practical applications, ranging from fitting rectangles for poster printing to tackling puzzles and addressing scheduling issues. For anyone interested in logic, computer science, mathematics, or artificial intelligence, this course provides essential insights into automated reasoning. **Syllabus Breakdown** 1. **SAT/SMT Basics and Examples** The course begins with a solid introduction to the concepts of SAT and SMT. You will start from the ground up, so even if you're a beginner, you'll find this section accessible. It presents numerous real-life examples demonstrating how SAT can be applied, enhancing your understanding and showing the versatility of the tools at your disposal. 2. **SMT Applications** Building on the basics, the course delves into practical applications of SMT, specifically focusing on satisfiability in the context of linear inequalities. This segment truly showcases the power of SMT in actual problem-solving scenarios. 3. **Theory and Algorithms for CNF-based SAT** This module introduces essential algorithms that are foundational to SAT solvers. You'll explore how the Resolution rule determines the unsatisfiability of propositional formulas expressed in conjunctive normal form (CNF). The DPLL algorithm—a key player in SAT solving—is explained, bridging concepts from the theoretical realm to practical implementations in contemporary SAT solvers. 4. **Theory and Algorithms for SAT/SMT** The final module is crucial for understanding complex SAT problems and their solutions. It discusses how to convert arbitrary propositional formulas to CNF and introduces the Tseitin Transformation, which optimally maintains formula size. Furthermore, you will learn how to expand SAT into SMT using methods such as the Simplex algorithm, which is extensively covered. **Course Experience** The course is thoughtfully structured, making it easy to follow for learners with varying levels of experience in mathematics and computer science. The instructors have done a wonderful job at balancing theory with applications, ensuring that concepts are not merely abstract but have practical relevance. The hands-on approach through examples and applications allows students to witness firsthand how powerful SAT/SMT tools can be in addressing real-world problems. **Study Materials & Resources** The course comes equipped with well-organized materials, including assignments and quizzes that reinforce learning and promote engagement. The resources available make the learning experience interactive and dynamic, giving students an opportunity to practice and implement the concepts they are being taught. **Recommendation** I highly recommend the Automated Reasoning: Satisfiability course for anyone eager to deepen their understanding of logic, algorithm design, or computational theory. It is particularly beneficial for students and professionals in computer science, mathematics, operations research, and artificial intelligence. The knowledge acquired here is not just theoretical; it has practical implications that are widely applicable in various industries, such as software engineering, optimization problems, and even complex logic puzzles. **Conclusion** In summary, Coursera's "Automated Reasoning: Satisfiability" is a well-rounded, comprehensive course that effectively bridges the gap between theoretical knowledge and practical application. Whether you are a seasoned professional or a curious learner, this course is a fantastic opportunity to delve into the fascinating field of automated reasoning. Enroll today to start your journey into SAT and SMT, and unlock a new dimension of problem-solving!

Syllabus

SAT/SMT basics, SAT examples

This module introduces SAT (satisfiability) and SMT (SAT modulo theories) from scratch, and gives a number of examples of how to apply SAT.

This module shows a number of applications of satisfiability modulo the theory of linear inequalities (SMT)

This module describes how a rule called Resolution serves to determine whether a propositional formula in conjunctive normal form (CNF) is unsatisfiable. It is shown how an approach called DPLL does the same job, and how it is related to resolution. Finally, it is shown how current SAT solvers essentially implement and optimize DPLL.

This module consists of two parts. The first part is about transforming arbitrary propositional formulas to CNF, leading to the Tseitin transformation doing this job such that the size of the transformed formula is linear in the size of the original formula. The second part is about extending SAT to SMT, in particular to dealing with linear inequalities. It is shown how the Simplex method for linear optimization serves for this job; the Simplex method itself is explained in detail.