Probabilistic and Nondeterministic Systems

Abstract

Probabilistic and nondeterministic systems are important to model systems such as distributed network protocols, concurrent systems and randomized algorithms, where nondeterminism is inherently present along with probabilistic choices. Probabilistic transition systems without any nondeterminism have been explored over the past decade. Several logics have been proposed to express the probabilistic behavior of systems. Nondeterministic systems differ from their probabilistic counterparts in that there behavior needs a notion of scheduler which resolves the nondeterministic choices. The probability space of observations of such systems is dependent on the choice of scheduler. In the absence of unique probability space the system properties can only be measured in intervals. The methods proposed in literature for quantitative analysis of nondeterministic systems use approximations for conjunction and disjunction to avoid the nonlinearity in the equations for measures. The contribution of this thesis is three fold. In the initial part we present a model checking method for quantitative analysis of nondeterministic systems. We generate a set of constraints and compute the minimum and maximum measure for the property without using any approximations. Secondly, we present an abstraction and probabilistic bi-simulation based approach to model and analyze randomized token stabilization protocol. In the end we present a method for compositional verification of PNS where in we describe weak predicate transformers which can be used to generate sub-specification for the unknown systems from the specification of the composite system.