Satisfiability Checking

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Satisfiability Checking


Schedule WS 12/13

Prerequisites:

SWS:

V3 + ワ1

Lecture times:

Monday 15:30 - 17:00 (room 5056) (V2)


Thursday 10:00 - 11:30 (room 5056) (V1 + ワ1)

Start:

October 08, 2012

Language:

English or German (depending on the students' preferences)

Exam:

written or oral, to be announced

ECTS credits:

6

News and materials can be found in the corresponding L2P learning room. For additional information see also the Campus page. During the semester we record the lecture and work out lecture notes. Both the videos and the notes will be made available in the L2P room. For possible exam combinations with other lectures see here.


Motivation

Different approaches in computer science involve tools (solvers) to check if 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.


In this lecture we deal with the automatic check of satisfiability for 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''). To demonstrate practical relevance, we employ the above methods in the context of bounded model checking.


Prerequisites

This course can be attended by bachelor students (as Wahlpflicht in theoretical computer science) as well as by master/diploma students.


Basic knowledge about algorithms is required.


Materials

For learning you can use the book

Decision Procedures: An Algorithmic Point of View

by Daniel Kroening and Ofer Strichman

Springer-Verlag, Berlin, 2008

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


Lecture Content

The slides of the last lecture (WS 11/12):

Nr.



Theme



Slides


1.



Introduction




2.

First-order logic

3.



Propositional logic






Examples for propositional logic






SAT-solving






Examples for SAT-solving




4.

SAT-modulo-theories solving

5.



Equality logic




6.

Linear real algebra



Fourier-Motzkin variable elimination






Simplex




7.



Presburger arithmetic






The branch and bound method




Gomory cuts




The Omega test

8.



Applications




Bounded model checking

Minimal critical subsystems

9.



Nonlinear real arithmetic




Virtual substitution

Cylindrical Algebraic Decomposition


Evaluations

WS 10/11: Lecturer Lecture

WS 11/12: Lecturer Lecture

WS 12/13: Lecturer Lecture


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