Slides
Lecture notes
- All Slides1
- All slides in a single PDF
- Quantifier-free Theory of Equality2
- Theory of Equality, Congruence closure algorithm, Theory of Lists
- Conclusion3
- Summary of the Lecture. Overview over theories, decidability results. Hints for the exam.
- DPLL(T)4
- DPLL/CDCL algorithm as a rule-based system. Extension of DPLL/CDCL to theories.
- First Order Logic5
- Syntax and Semantics of First Order Logic, Substitution, Semantic Tableaux, Soundness and Completeness, Normal Forms
- Craig Interpolation6
- Craig Interpolation, Interpolation in Theories, Interpolation for DPLL, Interpolation for Nelson-Oppen proofs with mixed Literals.
- Introduction7
- Organization, Introduction to Decision Procedures
- Nelson-Oppen theory combination8
- Nelson-Oppen combination of quantifier-free theories
- Program Correctness9
- Partial and Total Correctness. Basic Paths. Verification Conditions. PiVC.
- Propositional Logic10
- Syntax and Semantic of Propositional Logic, Truth Tables, Semantic Tableaux, DPLL/CDCL
- Quantifier Elimination11
- Quantifier Elimination, Ferrante-Rackow's Method (for rationals), Cooper's Method (for integers)
- Quantifier-free Theory of Rationals12
- Dutertre-de Moura algorithm
- Theories13
- Definition of Theories, T-Validity, T-Satisfiability. Theory of Equality, Natural Numbers, Integers, Rationals, Reals, Recursive Data Structures, Arrays, and Theory combination.
- Theory of Arrays14
- Quantifier-free Theory of Arrays, Array Property Fragment, Arrays with Integer Indices
