Slides

Introduction

Organization, Introduction to Decision Procedures

Propositional Logic

Syntax and Semantic of Propositional Logic, Truth Tables, Semantic Tableaux, DPLL/CDCL

First Order Logic

Syntax and Semantics of First Order Logic, Substitution, Semantic Tableaux, Soundness and Completeness, Normal Forms

Theories

Definition of Theories, T-Validity, T-Satisfiability. Theory of Equality, Natural Numbers, Integers, Rationals, Reals, Recursive Data Structures, Arrays, and Theory combination.

Quantifier Elimination

Quantifier Elimination, Ferrante-Rackow's Method (for rationals), Cooper's Method (for integers)

Quantifier-free Theory of Equality

Theory of Equality, Congruence closure algorithm, Theory of Lists

Quantifier-free Theory of Rationals

Dutertre-de Moura algorithm

Theory of Arrays

Quantifier-free Theory of Arrays, Array Property Fragment, Arrays with Integer Indices

DPLL(T)

DPLL/CDCL algorithm as a rule-based system. Extension of DPLL/CDCL to theories.

Program Correctness

Partial and Total Correctness. Basic Paths. Verification Conditions. PiVC.

Conclusion

Summary of the Lecture. Overview over theories, decidability results. Hints for the exam.

All Slides

All slides in a single PDF