Discrete Mathematics - Vol 1 | 3. SAT Problem by Abraham | Learn Smarter
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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.

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Sections

  • 3

    Sat Problem

    The SAT problem, also known as the satisfiability problem, determines if a compounded proposition can be true for any assignment of its variables.

    Learning Practice

  • 3.1

    Introduction To Satisfiability Problem

    The SAT problem explores whether a given compound proposition can be satisfied by any assignment of truth values to its variables.

    Learning Practice

  • 3.2

    Definition Of Satisfiability

    The satisfiability problem (SAT) involves determining whether a compound proposition is true for any truth assignment of its variables.

    Learning Practice

  • 3.3

    Unsatisfiable Proposition

    This section introduces the SAT problem, defining satisfiability and unsatisfiability of compound propositions, and discusses their significance in computer science.

    Learning Practice

  • 3.4

    Practical Implications Of The Sat Problem

    This section introduces the SAT problem, explaining how satisfiability is defined and its significance in computer science, particularly through practical applications like Sudoku.

    Learning Practice

  • 3.5

    Conjunctive Normal Form (Cnf) Introduction

    This section introduces the satisfiability problem and the concept of Conjunctive Normal Form (CNF), explaining their importance in logic and computation.

    Learning Practice

  • 3.6

    Definition Of Cnf

    This section introduces the concept of the satisfiability problem, focusing on the conjunctive normal form (CNF) and its significance in determining the satisfiability of compound propositions.

    Learning Practice

  • 3.7

    Clause And Literal Definitions

    This section introduces the satisfiability problem (SAT) and the concepts of conjunctive normal forms (CNF), clauses, and literals.

    Learning Practice

  • 3.8

    Verification Of Cnf

    This section introduces the satisfiability problem (SAT problem) and explains the concept of conjunctive normal form (CNF).

    Learning Practice

  • 3.9

    Conversion To Cnf

    This section discusses the satisfiability problem (SAT) and the importance of converting expressions to conjunctive normal form (CNF).

    Learning Practice

  • 3.2

    Application Of Sat Problem

    The section covers the concept of the Satisfiability Problem (SAT), detailing its significance and introducing Conjunctive Normal Form (CNF) as a means to analyze logical propositions.

    Learning Practice

  • 3.2.1

    Sudoku Puzzle Solver

    This section introduces the SAT problem, explaining its significance and applications, primarily in solving Sudoku puzzles.

    Learning Practice

  • 3.2.2

    Encoding Sudoku With Propositional Variables

    This section covers the SAT problem's introduction and the encoding of Sudoku into propositional variables.

    Learning Practice

  • 3.2.3

    Row, Column, And Block Constraints

    This section introduces the Satisfiability (SAT) problem, its significance in computer science, and the concept of Conjunctive Normal Form (CNF).

    Learning Practice

  • 3.2.4

    Unique Value Assignment Constraint

    The SAT problem revolves around determining the satisfiability of propositional logic statements, highlighting its implications in computational fields.

    Learning Practice

  • 3.2.5

    Finding Truth Assignments

    This section discusses the SAT problem and its significance in determining the satisfiability of propositional variables, along with the introduction of Conjunctive Normal Form (CNF).

    Learning Practice

  • 3.2.6

    Conclusion

    The SAT problem's concept is explored, emphasizing its significance and applications in computer science, such as in Sudoku puzzle solving.

    Learning Practice

References

ch3.pdf

Class Notes

Memorization

What we have learnt

  • A compound proposition is s...
  • Conjunctive Normal Form (CN...
  • The SAT problem can be appl...

Final Test

Revision Tests