After successful completion of the course, students are able to...

• make use of basic methods of computability theory in order to identify, for instance, undecidable problems
• apply formal methods from complexity theory to new problems in order to prove their tractability or NP-hardness,
• represent problems in the area of formal methods as satisfiability problems, to solve these problems with a SAT solver, and to formally argue the correctness of all involved techniques and reductions,
• formally establish partial and total correctness of software systems, by using  deductive verification approaches based on Hoare logic and predicate transformers. Students will also be able to formulate program semantics and prove program properties algorithmically,
• understand and apply the basic techniques of model checking: encoding specifications in temporal logic, reasoning about temporal logic formulae, model checking of temporal logic formulae on Kripke structures, using state space reduction techniques, and applying bounded model checking for verification tasks.

Introduction to complexity theory: problem reductions, P versus NP, undecidability; SAT solving and its applications in computer science; introduction to the formal semantics of programming languages; formal verification of programs; model checking and its applications in hard- and software verification.

The course is organized in four blocks. The course (and thus each block) consists of a lecture and a consolidation part.

The topics of the course are presented during the lectures.

The consolidation part includes two additional classes per block for discussing examples and their solutions. Students receive an exercise sheet for each block. The submissions will be corrected and returned to the students

Three additional classes will be offered to recall some basic principles of mathematical proofs.

Ects breakdown

  2 h introduction (first meeting)
 60 h lecture (20 dates à 2h + 1h preparation)
 40 h exercise sheets (4 sheets, 10 exercises/sheet, 1h/exercise)
 16 h discussion of exercises (8 dates à 2h)
 30 h preparation for written exam
  2 h written exam
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150 h = 6 Ects

The evaluation is based on a written exam.

For slides and other material see the TUWEL course.

Basic knowledge in mathematical logic and algorithms are required (to the extent taught in “Theoretische Informatik und Logik” and “Algorithmen und Datenstrukturen”).