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

Evaluations of past years