Model Checking
Winter 2007
Instructors:
Schedule:
-
Tuesday, 14:15-16:00
BC01: Lecture
-
Thursday, 10:15-12:00
INM200: Lecture
-
Friday, 13:15-15:00,
INM200: Exercises
Contact: Participants are asked to
subscribe to the mailing list
modelchecking2007_at_listes_dot_epfl_dot_ch to allow one to send
messages to all course participants. Instructions on how to subscribe
and how to use the mailing list are available in English
and French.
Objectives: The participants will become familiar with both the
theory and practice of model checking.
Motivation: Model checking concerns the use of algorithmic
methods in the temporal safety and performance assurance for software
and hardware systems. As our daily lives depend increasingly on digital
systems, the reliability of these systems becomes a concern of
overwhelming importance, and as the complexity of the systems grows,
their reliability can no longer be sufficiently controlled by the
traditional approaches of testing and simulation.
Syllabus:
- Reactive modules: a formal model for concurrent reactive
systems with software and hardware components.
- Verification algorithms: linear and branching temporal logics,
omega automata, equivalences and refinement, games.
- State explosion: symbolic data structures, automatic
abstraction, compositional reasoning.
- Advanced topics: safety-liveness hierarchy, real-time and hybrid
systems, probabilistic systems.
Prerequisites: The course is open to masters and doctoral
students. Familiarity with propositional logic, finite automata, basic
computational complexity classes, and basic graph algorithms is
assumed. For example, you should know what a tautology is, how to
determinize a finite automaton, what PSPACE stands for, and how to find
the strongly connected components of a graph. If you are not familiar
with these concepts, please see the instructor.
Lecture notes:
Exercises
Software: Some of the homework problems will involve
experimentation with the verification tool Mocha. Please find some notes on how to
install and use Mocha here.
Homework: There will be weekly problem sets. Some of the
homework problems will involve formal proofs, and other homework
problems will involve experimentation with verification tools. The
problem sets will be given on this web page every Thursday afternoon and
are due on the following Thursday at the beginning of the lecture.
Quizzes: Every second Tuesday there will be a 30 minute
written quiz at the beginning of the lecture (14:15).
The dates of
the quizzes are:
- Oct 2
- Oct 16
- Oct 30
- Nov 13
- Nov 27
- Dec 18 (instead of Dec 11)
Mini-projects: Every student is supposed to complete a
mini-project. A list of suggested mini-projects is available
here.
Suggestions for designing your own mini-projects according to your
interests are very welcome (e.g., adapting published results to reactive
modules, application of other external verification tools).
The time-line for mini-projects is:
- by Nov 20: choose the mini-project
- by Dec 4: hand-in a 1 page summary of what you plan to do
for the project
- by Jan 10: hand-in a 5 page write-up of the project for theory
projects, and 3 page summary and the source code for implementation
projects.
Grading: Grades will be awarded on the basis of attending
exercises, performance on quizzes, performance on homework, and
performance on the mini-project. Every attended exercise will yield 2
points, up to a possible maximum of 20 points. Every quiz will yield a
maximum of 5 points, and the best 4 out of the 6 quizzes are counted,
for a total maximum of 20 points. Every homework will yield a maximum
of 4 points, and the best 10 out of the 13 homeworks are counted, for a
total maximum of 40 points. At exercise, you may be asked to present
your solutions to the previous homework. If the presenter does not
understand his/her own solution, the homework may be graded as 0
points, and the maximum number of points achievable through homework
may be decreased by 4 points. The write-up and presentation of the
mini-project will yield a maximum of 20 points. There will be no final
exam. Excuses for missing exercises, quizzes, or homeworks will not be
accepted.
Summary:
- exercise attendance: 20 points
- quizzes (4 out of 6): 20 points
- homeworks (10 out of 13): 40 points
- mini-project: 20 points
Teamwork: Students may collaborate on homeworks, but each
student needs to individually write up a solution set and be prepared
to present it during exercises. Mini-projects must be done
individually, or as clearly identifiable parts of a larger effort with
individual write-ups and presentations.
Topic Summary of Lectures
Sep 18
- Introduction to verification
- Introduction to Reactive Modules
Sep 20
- Definition of Reactive Modules
- Operations on Reactive Modules
Sep 25
- Modeling synchronous hardware
- Modeling multi-threaded software
- From Reactive Modules to transition graphs
Sep 27
- Invariant verification and graph reachability
- Safety monitors
- Depth-first search
Oct 2
- Symbolic graph representation
- Symbolic search
- Translation of modules to symbolic representations (initial and
update predicate)
Oct 4
- Comparison of symbolic and enumerative representations
- Space optimizations
- Hardness and complexity of invariant verification
Oct 9
- Binary Decision Diagrams
- Symbolic search with BDDs
Oct 11
- Compositional verification
- Abstraction
Oct 16
- Graph minimization
- Stable partitions
- Graph symmetries
Oct 18
- Computing stable partitions
- Paige-Tarjan algorithm
Oct 23
- Reachable Partition Refinement (Lee-Yannakis algorithm)
- Real-time verification problem
- Real-time propositional modules
Oct 25
- Clock regions, clock constraints
- Enumerative and symbolic verification of real-time modules
- Difference-bound Matrices (DBM)
Oct 30
- Safe Temporal Logic (STL)
- Observation structure (Kripke structure)
Nov 1
- Model checking STL
- Comparing state logics (expressive and distinguishing power)
- State equivalences (Bisimilarity)
Nov 6
- STL distinguishing power
- Characterization of bisimilarity
- Safe Automata Logic (SAL)
Nov 8
- Distinguishing power of SAL
- Expressive power of SAL
- Model checking SAL
Nov 13
- Model checking SAL
- Operations on automata
- Complementation of an automaton
Nov 15
- Comparison of STL and SAL
- Simulation
Nov 20
- Bisimularity versus simulation
- Refinement checking
- Assume-guarantee rule
Nov 22
- Safety versus Liveness
- Language of infinite sequences
- Definition of safe, live, and machine-closed
Nov 27
- Topology
- Fair graphs
- Streett and Büchi fairness
Nov 29
- Strong and weak fairness constraints
- Recurrence verification problem
Dec 4
- Fair ω-trajectory problem
- Strong Connected Component (SCC)
- Tarjan's algorithm
Dec 6
- Computational Tree Logic (CTL)
- CTL model checking
- Syntax and semantics of μ-Calculus (CTμ)
Dec 11
- CTL in CT&mu
- Model Checking CT&mu
- Expressive power of CT&mu
Dec 13
- Expressive power of CT&mu
- ω-automata
- Büchi/Streett/Rabin automata
Dec 18
- Automata-theoretic Liveness Verification
- Complementation of NBA
Dec 20
- ω-regular languages
- Counterfree and not counterfree languages
- Linear Temporal Logic (LTL)
- LTL Model Checking
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