Formal Analysis and Verification

• 39 hrs lectures
• 13 hrs projects

• 70 pts final exam (test part)
• 30 pts projects

Students are acquainted with principles and methods of formal analysis and verification and with their application within the process of designing safety-critical systems. Students know capabilities and the basic ways of using computer-aided tools for formal analysis and verification.
Acquired knowledge about the significance and possibilities of using formal methods within the development of various kinds of systems and about their growing use in practice.

The goal of the course is to introduce formal analysis and verification to students as a modern and promising  method of automated evaluation of properties of various kinds of safety-critical systems (such as drivers and other parts of operating systems, control software, workflow, communication protocols, parts of hardware, etc.). The course acquaints students both with the theoretical background of the given area, with computer-aided tools based on them as well as with successful applications of formal analysis and verification in practice (Microsoft, Intel, Nasa, Airbus, ...).

Knowledge of discrete mathematics, the theory of formal languages, and algorithmics on the bachelor's level is assumed.

• Aho, A.V., Lam, S., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques, and Tools. Addison Wesley, 2nd ed., 2006. The part devoted to static analysis.
• Bradley, A.R., Manna, Z.: The Calculus of Computation: Decision Procedures with Applications to Verification, Springer, 2007.
• Valmari, A.: The State Explosion Problem. In Reisig, W., Rozenberg, G.: Lectures on Petri Nets I: Basic Models, volume 1491 of Lecture Notes in Computer Science, pages 429-528. Springer-Verlag, 1998.
• Chess, B., West,J.: Secure Programming with Static Analysis. Addison-Wesley Professional, 2007.
• Kroening, D., Strichman, O.: Decision Procedures: An Algorithmic Point of View, Springer, 2008.
• Holzmann, G.J.: The SPIN Model Checker: Primer and Reference Manual, Addison-Wesley Professional, 2003.
• Ben-Ari, M.: Principles of the Spin Model Checker, Springer, 2008.
• Bertot Y., Castéran, P.: Interactive Theorem Proving and Program Development: Coq'Art: The Calculus of Inductive Constructions, Springer, 2010.
• Materials presented within the lectures and made accessible via the Internet.
• Materials freely accessible on the Internet, especially papers and documentation related to the various computer-aided tools for formal analysis and verification.
• Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, 2008.
• Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis, Springer-Verlag, 2005.
• Edmund, M.C., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, 2000.
• Khedker, U., Sanyal, A., Sathe, B.: Data Flow Analysis: Theory and Practice, CRC Press, 2009.

1. The meaning of the terms ``formal analysis and verification''. Capabilities and advantages of methods of formal analysis and verification. Various approaches to formal analysis and verification: model checking, static analysis, and theorem proving.
2. State spaces, state space paths, abstractions of states and transitions. Interleaving and true concurrency. Linear and branching time. Safety, liveness, and fairness.
3. Temporal logics CTL and CTL*, model checking systems whose properties are specified in CTL or CTL* using explicitly represented state spaces.
4. Binary decision diagrams for a compact, symbolic representation of state spaces and their implementation.
5. Lattices, fix points, and the Knaster-Tarski theorem as a formal basis for symbolic model checking.
6. Symbolic model checking for CTL and CTL*.
7. The temporal logic LTL, the correspondence between Büchi automata and LTL formulae, model checking systems whose properties are specified in LTL using Büchi automata.
8. The partial order state space reduction. The symmetry state space reduction. An overview of other state space reduction methods. Compositional verification.
9. Methods of automated abstraction of systems, the predicate abstraction, the counter-example guided abstraction refinement loop, Craig interpolation.
10. Decision procedures and modern methods of SAT and SMT solving and their use in formal verification (e.g., in the predicate abstraction).
11. Classical dataflow analyses (such as live variables, available expressions, etc.) as well as some selected, more advanced dataflow analyses (like some pointer analyses), their description via flow equations, and iterative methods of solving these methods.
12. Abstract interpretation and its use for defining static analyses.
13. Static analyses based on searching for bug patterns, a note on selected dynamic analyses, esp. those for detecting concurrency-related errors.

• A project including an installation of a selected tool for automated verification on a formal basis (Spin, Blast, ARMC, SMV, JPF, FindBugs, Invader, Uppaal aj.), experiments with this tool, and a preparation of an essay describing principles on which the chosen tool is built (10 pts.) and the performed experiments (10 pts. for experiments with existing case studies, 10 pts. for new case studies). It is possible to agree on studying a tool based on principles that are not a part of the lectures (theorem proving, real-time systems, etc.).

• An evaluated project for 30 points.
• A final examination for 70 points.
• To be allowed to sit for the written examination, a student is to earn at least 15 points during the semester.
• 
  Exam prerequisites:
  Having at least 50% of the possible point evaluation of the project.

Having at least 50% of the possible point evaluation of the project.