Parametric probabilistic transition systems for system design and analysis

Abstract

We develop a model of parametric probabilistic transition Systems (PPTSs), where probabilities associated with transitions may be parameters. We show how to find instances of the parameters that satisfy a given property and instances that either maximize or minimize the probability of reaching a certain state. As an application, we model a probabilistic non-repudiation protocol with a PPTS. The theory we develop allows us to find instances that maximize the probability that the protocol ends in a fair state (no participant has an advantage over the others).

Probabilistic reachability for parametric Markov models

“…Lanotte et al [27] considered parametric MCs, showing that the problem whether there exists a well-defined evaluation is in PSPACE and whether such an evaluation induces a given reachability probability c is however undecidable. Recently, Damman et al [9] have extended the approach of Daws [10] to generate counterexamples for MC.…”

“…PMCs have already been introduced in previous publications [10,27]. We now define the underlying graph of a PMC.…”

PARAM: A Model Checker for Parametric Markov Models

“…In the early design phase of a system or for the sake of robust modelling, it can be advantageous to leave certain aspects unspecified and use symbolic parameters rather than fixed values. We consider parametric Markov chains (PMCs) [1], where e.g., certain transition probabilities are symbolic parameters. As a result, the analysis of properties, such as the probability of reaching a set of goal states, yields symbolic expressions [2,3] rather than concrete values.…”

Probabilistic Reachability for Parametric Markov Models

“…In [19], Lanotte et al considered parametric MCs, showing that the problem whether there exists a well-defined evaluation is undecidable. Moreover, the problem to minimise or maximise unbounded probabilistic reachability is also shown to be undecidable.…”