Slides

The slides from the lectures.

Lecture 1 (21 Oct 2008)

Motivation, Propositional Logic (Syntax, Semantics, Validity/Satisfiability)

Lecture 2 (24 Oct 2008)

Decision Procedures for PL: Truth table, Semantic Argument, DPLL. Normal Forms.

Lecture 3 (28 Oct 2008)

DPLL with Learning

Lecture 4 (31 Oct 2008)

FOL: Syntax, Semantics.

Lecture 5 (4 Nov 2008)

Semantic Argument for First-Order-Logic Decidability of FOL

Lecture 6 (7 Nov 2008)

First Order Theories (Part 1): Theory of Equality, Peano Axioms

Lecture 7 (11 Nov 2008)

First Order Theories (2): Peano Arithmetic, Presburger Arithmetic, Reals, Rationals, Lisp like Lists

Lecture 8 (14 Nov 2008)

First Order Theories (3): Arrays, Combination of Theories

Lecture 9 (18 Nov 2008)

Induction (step-wise, complete, well-founded, structural)

Lecture 10 (21 Nov 2008)

Quantifier Elimination for Theory of Rationals

Lecture 11 (25 Nov 2008)

Quantifier Elimination for Presburger Arithmetic

Lecture 12 (28 Nov 2008)

Quantifier Free Rationals

Lecture 13 (2 Dec 2008)

Dutertre-de-Moura-Algorithm for Quantifier-Free Rationals (part two).

Lecture 14 (5 Dec 2008)

Quantifier-free Theory of Equality

Lecture 15 (12 Dec 2008)

Theory of Equality and Arrays

Lecture 16 (15 Dec 2008)

Theory of Arrays (cont), Nelson-Oppen combinations.

Lecture 17 (7 Jan 2009)

Theory of Arrays with Quantifiers.

Lecture 18 (12 Jan 2009)

Array Property Fragment for Arrays with Integer Indices

Lecture 19 (16 Jan 2009)

Program Correctness: Linear Search

Lecture 20 (20 Jan 2009)

Program Correctness: Binary Search and Bubble Sort

Lecture 21 (23 Jan 2009)

Total Correctness

Lecture 22 (27 Jan 2009)

DPLL(T) (Davis Putnam Loveland Logemann Algorithm with Theory-Reasoning).

Lecture 23 (30 Jan 2009)

DPLL Modulo Theories (Nelson-Oppen)

Lecture 24 (3 Feb 2009)

Craig Interpolants (with congruence closure diagrams)

Lecture 25 (10 Feb 2009)

Craig Interpolants for Theory of Rationals

Lecture 26 (13 Feb 2009)

Summary (Updated on 17 Feb 2009)