We consider the problem of achieving a required level of confidence about safety-critical systems consisting of interacting components. Especially, we address restrictions in traditional A/G reasoning techniques which may cause false positives in contract compatibility analyses. Therefore, we introduce interface assertions, i. e., predicate logical formulae over the components' interfaces. We show how to compute interface assertions for architecture configurations based on the interface assertions of the corresponding components and show soundness and relative completeness of the method. Moreover, we introduce mode-based contracts, which - as a special kind of interface assertions - consist of dedicated assume and guarantee pairs. They provide a methodological guidance for developers and facilitate contract specification in contrast to e. g. traditional A/G reasoning. For this concept, we provide algorithms to check under-specification, over-specification, and the fulfillment of specifications. We also sketch how the checks can be operationalized using SMT solvers. Finally, an example demonstrates the approach.

In this paper we consider real counterparts of classical probabilistic complexity classes in the framework of real Turing machines as introduced by Blum, Shub, and Smale [2].We give an extension of the well-known "BPP ~P/poly" result from discrete complexity theory to a very general setting in the real number model.This result holds for real inputs, real outputs, and random elements drawn from an arbitrary probability distribution over lR~.Then we turn to the study of Boolean parts, that is, classes of languages of zero-one vectors accepted by real machines.In particular we show that the classes BPP, PP, PH, and PSPACE are not enlarged by allowing the use of real constants and arithmetic at unit cost provided we restrict branching to equality tests.