1. SS 2017 Software Verification Tableaus, CTL model checking
Prof. Dr. Holger Schlingloff 1,2
Dr. Esteban Pavese 1
(1) Institut für Informatik der Humboldt Universität
(2) Fraunhofer Institut für offene Kommunikationssysteme FOKUS

2. Excursion: Propositional Tableaus
Multimodal extension:

3. Temporal Tableaus

4. Example

5. Another Example

6. Recap What is an atom in LTL modelchecking? What is the atom graph ?
How is it built?
Why are SCCs important?
What does Tarjan‘s algorithm compute?
In which time complexity?

7. Eventualities
if m contains (φU+ψ), some m‘ containing ψ must be reachable
„reachable“ means „in the same strongly connected component“ (SCC)
self-fulfilling SCC: for any α=(w,m) and (φU+ψ) m there is a reachable α‘=(w‘,m‘) and ψm‘
we have to decompose the atom graph into SCCs
Tarjan’s algorithm is a clever solution to this
linear complexity (enumerates SCCs as they are encountered)
overall complexity: |M|*2|φ|
meaning: The model must be traversed only once

8. LTL Model Checking Algorithm

10. Improvements bitstate hashing incomplete hashing
partial order techniques
Remark: Wikipedia is amazing, it even has a page on translating LTL to BA: