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Quantifier-free Theory of Equality
Theory of Equality, Congruence closure algorithm, Theory of Lists
Summary of the Lecture. Overview over theories, decidability results. Hints for the exam.
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
Craig Interpolation
Craig Interpolation, Interpolation in Theories, Interpolation for DPLL, Interpolation for Nelson-Oppen proofs with mixed Literals.
Organization, Introduction to Decision Procedures
Nelson-Oppen theory combination
Nelson-Oppen combination of quantifier-free theories
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
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