## Diagram-based verification of reactive, real-time and hybrid systems, PhD thesis

*Henny Sipma*
This thesis proposes diagram-based formalisms to verify temporal
properties of reactive systems. Reactive systems maintain an ongoing
interaction with their environment and include discrete, real-time, and
hybrid systems. Diagrams integrate deductive and algorithmic techniques
for the verification of finite and
infinite-state systems, thus combining the
expressive power and flexibility of deduction with the automation
provided by algorithmic methods.

Generalized verification diagrams represent the temporal structure of
the program as relevant to the property they prove. The deductive
component of a verification diagram defines a set of first-order
verification conditions that, when proven valid, show that all
behaviors of the system are embedded in the diagram. The algorithmic
component is an automata-theoretic language inclusion check that
determines whether all behaviors of the diagram satisfy the property.

Falsification diagrams represent behaviors of the system that do
not satisfy the property. Deductive Model Checking incrementally
refines these diagrams, removing behaviors that the system cannot
exhibit, either until no behaviors remain, which proves the property,
or a counterexample is found.

We show how these methods can be used to verify not only discrete
systems, but real-time and hybrid systems as well. We also present two
specialized classes of diagrams for these systems: nonZenoness
diagrams represent a proof that a real-time or hybrid system is
time-divergent, that is, all behavior prefixes of the system can be extended
into behaviors in which time grows beyond any bound. Receptiveness
diagrams prove a related property of real-time and hybrid modules that
implies time divergence and is preserved by parallel composition.

Postscript,
PDF.
© 1999, Henny Sipma.

© Henny Sipma /
sipma@cs.stanford.edu
Last modified: Thu Mar 29 10:19:02 PST 2001