Formal Analysis and Verification

• 26 hrs lectures
• 26 hrs 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.

• 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.
• Aho, A.V., Lam, S., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques, and Tools. Addison Wesley, 2nd ed., 2006. (Část věnovaná statické analýze.)
• 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.
• Khedker, U., Sanyal, A., Sathe, B.: Data Flow Analysis: Theory and Practice, CRC Press, 2009.
• 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.
• Soubor materiálů prezentovaných na přednáškách a zveřejněných přes WWW.
• Materiály aktuálně volně dostupné na Internetu, a to zejména články a dokumentace týkající se počítačových nástrojů pro formální analýzu a verifikaci.

• 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. Symbolic model checking for CTL and CTL*.
6. The temporal logic LTL, the correspondence between Büchi automata and LTL formulae, model checking systems whose properties are specified in LTL using Büchi automata.
7. The partial order state space reduction. The symmetry state space reduction. An overview of other state space reduction methods. Compositional verification.
8. Methods of automated abstraction of systems, the predicate abstraction, the counter-example guided abstraction refinement loop, Craig interpolation.
9. Decision procedures and modern methods of SAT and SMT solving and their use in formal verification (e.g., in the predicate abstraction).
10. 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.
11. A brief note on abstract interpretation and its use for defining static analyses. Static analyses based on searching for bug patterns.
12. Formal verification of real-time systems, especially via methods based on timed automata and symbolic approaches using regions or zones.
13. Theorem proving. Principles, automated support (PVS, etc.), applications. Combining theorem proving and methods based on state spaces

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

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

• Two evaluated home assignments - each for 20 points.
• A final examination - 60 points.
• To be allowed to sit for the written examination, a student is to earn at least 20 points during the semester.
• The passing boundary w.r.t. the ECTS assessment - 50 points.