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Overview

As our first constraint language, we’ll use propositional satisfiability (SAT). The SAT problem is the first problem proven to be \( \NP \)-complete [Cook1971]. It has been studied intensively during the last decades, in both theory and practice view points. Highly efficient SAT solvers, that can solve many problem instances with hundreds of thousands of variables and millions of constraints, exist. However, due to the nature of NP-complete problems, on some hand-crafted instances with only hundreds of variables, the very same solvers can fail badly, meaning that their running times are so large that they do not terminate in practise.

High-level outline:

  • ​ Round 1:

    • ​ Propositional formulas, satisfiability

    • ​ Problem solving with SAT solvers

    • ​ Truth tables and normal forms

  • ​ Round 2:

    • ​ Fundamentals of SAT solvers

    • ​ Resolution proof system

Note

We will use Python when encoding problems to formulas. If you are not familiar with Python, please consult the Python3 tutorial and especially the list comprehension part in it.