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