 ## Lecture: SAT-Checking

Important Facts
Lecture Times: Monday, 14:15 – 15:45, 5056
Tuesday, 14:15 – 15:45, 5056
First Lecture: Obtober 13, 2014
Language: English or German (depending on the students’ preferences)
Exam: written or oral, to be announced
Prerequisites: for Bachelor or Master (“Wahlpflicht” in Theoretical Computer Science)
Basic knowledge about algorithms is required.
Credit Points: 6
First Exam: 28.02.2015, 10:00 – 12:00, Aula 1
Revision: 05.03.2015, 10:00 – 12:00, 5056
Second Exam: 28.03.2015, 10:00 – 12:00, AH I / AH II

News and materials can be found in the corresponding L2P learning room. For additional information see also the Campus page.

## Motivation

Different approaches in computer science involve tools (solvers) to check whether certain formulas are satisfiable. Examples can be found in the fields of hardware and software verification, counterexample generation, termination analysis of programs, and optimization algorithms, just to mention a few.

In this lecture we deal with the automatic check of satisfiability of formulas from different logics. Formulas of propositional logic can be checked for satisfiability using SAT-solvers (SAT=”satisfiability”). Extending the logic with different theories leads us to SMT-solvers (SMT=”satisfiability modulo theories”). During the semester we will discuss extensions of propositional logic with equalities, uninterpreted functions, and linear and non-linear constraints involving real- and integer-valued variables (linear/non-linear  real/integer arithmetic). To demonstrate practical relevance, we employ the above methods in the context of bounded model checking.

## Materials

For learning you can use the book

Daniel Kroening and Ofer Strichman: Decision Procedures: An Algorithmic Point of View, Springer-Verlag, Berlin, 2008.

which is available in the computer science library, the lecture slides and the lecture notes that will be made available in the L2P learning room.

### Lecture Content Nr. Theme Slides 1. Introduction 2. Propositonal logic 3. SAT solving SAT solving examples SAT solving examples 4. First order theories 5. Decidability 6. Eager SMT solving Equality logic Bit vectors 7. Lazy SMT solving Equality logic 8. Linear real arithmetic Fourier Motzkin elimination Simplex Simplex in SMT 9. Linear integer arithmetic Branch and bound Gomory cuts Omega test Omega test – example Application 10. Nonlinear real arithmetic Virtual substitution Cylindrical algebraic decomposition Groebner bases Interval constraint propagation 11. Applications for SMT  