An Introduction to SAT Solving - Computer Science
An Introduction to SAT Solving
Applied Logic for Computer Science UWO ? December 3, 2017
Applied Logic for Computer Science
An Introduction to SAT Solving
UWO ? December 3, 2017
1 / 46
Plan
1 The Boolean satisfiability problem 2 Converting formulas to conjunctive normal form 3 Tseytin's transformation 4 How SAT solvers work
Applied Logic for Computer Science
An Introduction to SAT Solving
UWO ? December 3, 2017
2 / 46
Plan
1 The Boolean satisfiability problem 2 Converting formulas to conjunctive normal form 3 Tseytin's transformation 4 How SAT solvers work
Applied Logic for Computer Science
An Introduction to SAT Solving
UWO ? December 3, 2017
3 / 46
Propositional formula
Definition Let V be a finite set of Boolean valued variables. A propositional formula on V is defined inductively as follows:
each of the constants false, true is a propositional formula on V , any element of V is a propositional formula on V , if and are propositional formulas on V then ?, (), , , , are propositional formulas on V as well.
Examples and counter-examples
p ?q is a propositional formula on V = {p, q}, p + ?q is not a propositional formula on V = {p, q}, p ?q is not a propositional formula on V = {p}, ( ) is not a propositional formula on V = {p, q}.
Applied Logic for Computer Science
An Introduction to SAT Solving
UWO ? December 3, 2017
4 / 46
Assignment
Definition
Let again V be a finite set of Boolean valued variables.
An assignment on V is any map from V to {false, true}. Any assignment v on V induces an assignment on the propositional formulas on V by applying the following rules: if and are propositional formulas on V then we have:
1 v(?) = ?v(), 2 v( ) = v() v(), 3 v( ) = v() v(), 4 v( ) = v() v(), 5 v( ) = v() v().
Example
For the set of Boolean variables V = {p, q}. define v(p) = false and v(q) = true. Then, we have:
v(p q) = true. v(p q) = false.
Applied Logic for Computer Science
An Introduction to SAT Solving
UWO ? December 3, 2017
5 / 46
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