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You are here: Home Teaching Winter Term 2016/17 Decision Procedures (Lecture) Slides
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Slides

Lecture notes

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
Nelson-Oppen theory combination
Nelson-Oppen combination of quantifier-free theories
DPLL(T)
DPLL/CDCL algorithm as a rule-based system. Extension of DPLL/CDCL to theories.
DPLL(T) (with annotations)
Program Correctness
Partial and Total Correctness. Basic Paths. Verification Conditions. PiVC.
Craig Interpolation
Craig Interpolation, Interpolation in Theories, Interpolation for DPLL, Interpolation for Nelson-Oppen proofs with mixed Literals.
Conclusion
Summary of the Lecture. Overview over theories, decidability results. Hints for the exam.
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