## A List by Author: Holger Hermanns

- e-mail:
- hermanns(a)cs.uni-saarland.de

### Probabilistic Bisimulation: Naturally on Distributions

by *
Holger Hermanns,
Jan Krčál,
Jan Křetínský,
* April 2014, 36 pages.

**FIMU-RS-2014-03.**
Available as *Postscript*,
**PDF**.

#### Abstract:

In contrast to the usual understanding of probabilistic systems as
stochastic processes, recently these systems have also been regarded
as transformers of probabilities. In this paper, we give a
natural definition of strong bisimulation for probabilistic
systems corresponding to this view that treats probability
distributions as first-class citizens. Our definition applies
in the same way to discrete systems as well as to systems with
uncountable state and action spaces. Several examples demonstrate
that our definition refines the understanding of behavioural
equivalences of probabilistic systems. In particular, it solves a
longstanding open problem concerning the representation of
memoryless continuous time by memoryfull continuous time. Finally,
we give algorithms for computing this bisimulation not only for
finite but also for classes of uncountably infinite systems.

### Verification of Open Interactive Markov Chains

by *
Tomáš Brázdil,
Holger Hermanns,
Jan Krčál,
Jan Křetínský,
Vojtěch Řehák,
* A full version of the paper presented at conference FSTTCS 2012. November 2012, 52 pages.

**FIMU-RS-2012-04.**
Available as *Postscript*,
**PDF**.

#### Abstract:

Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation. For this we embed the IMC into a game that is played with the environment. We devise algorithms that enable us to derive
bounds on reachability probabilities that are assured to hold in any composition context.