3. SAT Problem - Discrete Mathematics - Vol 1
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

3. SAT Problem

3. SAT Problem

The chapter explores the Satisfiability Problem (SAT), defining satisfiable propositions and introducing Conjunctive Normal Form (CNF) as a crucial concept. It discusses methods to determine if a compound proposition is satisfiable and presents a practical application in solving Sudoku puzzles using propositional logic. The chapter emphasizes the complexity of SAT and highlights its relevance in computer science and AI.

17 sections

Enroll to start learning

You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

Navigate through the learning materials and practice exercises.

  1. 3

    The SAT problem, also known as the satisfiability problem, determines if a...

  2. 3.1
    Introduction To Satisfiability Problem

    The SAT problem explores whether a given compound proposition can be...

  3. 3.2
    Definition Of Satisfiability

    The satisfiability problem (SAT) involves determining whether a compound...

  4. 3.3
    Unsatisfiable Proposition

    This section introduces the SAT problem, defining satisfiability and...

  5. 3.4
    Practical Implications Of The Sat Problem

    This section introduces the SAT problem, explaining how satisfiability is...

  6. 3.5
    Conjunctive Normal Form (Cnf) Introduction

    This section introduces the satisfiability problem and the concept of...

  7. 3.6
    Definition Of Cnf

    This section introduces the concept of the satisfiability problem, focusing...

  8. 3.7
    Clause And Literal Definitions

    This section introduces the satisfiability problem (SAT) and the concepts of...

  9. 3.8
    Verification Of Cnf

    This section introduces the satisfiability problem (SAT problem) and...

  10. 3.9
    Conversion To Cnf

    This section discusses the satisfiability problem (SAT) and the importance...

  11. 3.2
    Application Of Sat Problem

    The section covers the concept of the Satisfiability Problem (SAT),...

  12. 3.2.1
    Sudoku Puzzle Solver

    This section introduces the SAT problem, explaining its significance and...

  13. 3.2.2
    Encoding Sudoku With Propositional Variables

    This section covers the SAT problem's introduction and the encoding of...

  14. 3.2.3
    Row, Column, And Block Constraints

    This section introduces the Satisfiability (SAT) problem, its significance...

  15. 3.2.4
    Unique Value Assignment Constraint

    The SAT problem revolves around determining the satisfiability of...

  16. 3.2.5
    Finding Truth Assignments

    This section discusses the SAT problem and its significance in determining...

  17. 3.2.6

    The SAT problem's concept is explored, emphasizing its significance and...

What we have learnt

  • A compound proposition is satisfiable if there exists at least one truth assignment that makes it true.
  • Conjunctive Normal Form (CNF) is a representation of a compound proposition as a conjunction of clauses, where each clause is a disjunction of literals.
  • The SAT problem can be applied to various practical scenarios, including solving Sudoku puzzles, by encoding the problem as a compound proposition.

Key Concepts

-- Satisfiability Problem (SAT)
A problem of determining whether a given compound proposition has at least one truth assignment that makes it true.
-- Conjunctive Normal Form (CNF)
A way of structuring a logical expression as a conjunction of clauses, where each clause consists of disjunctions of literals.
-- Clause
A disjunction of literals within a CNF, representing a part of the overall compound proposition.
-- Literal
A variable or the constants true or false, which can be used in clauses.

Additional Learning Materials

Supplementary resources to enhance your learning experience.