(Continuing Lecture 09)

QE for Presburger Arithmetic

Bounding Variables in Presburger Arithmetic

Small Solutions for Quantifier-Free Presburger Arithmetic

Deciding Boolean Algebra with Presburger Arithmetic

List of Theories Admitting QE

Applications of Quantifier Elimination

Remarks (also relevant for talk to come):

• Normal Forms for First-Order Logic
• Definition of Propositional Resolution
• Definition of Resolution for FOL
• SMT solvers: combine decision procedures (such as one for Presburger arithmetic) with DPLL (Lecture 08a)