Model-based testing (MBT) is a well-known technology, which allows for automatic test case generation, execution and evaluation. To test non-functional properties, a number of test MBT frameworks have been developed to test systems with real-time, co
ntinuous behaviour, symbolic data and quantitative system aspects. Notably, a lot of these frameworks are based on Tretmans classical input/output conformance (ioco) framework. However, a model-based test theory handling probabilistic behaviour does not exist yet. Probability plays a role in many different systems: unreliable communication channels, randomized algorithms and communication protocols, service level agreements pinning down up-time percentages, etc. Therefore, a probabilistic test theory is of great practical importance. We present the ingredients for a probabilistic variant of ioco and define the {pi}oco relation, show that it conservatively extends ioco and define the concepts of test case, execution and evaluation.
A number of introductory textbooks for Haskell use calculations right from the start to give the reader insight into the evaluation of expressions and the behavior of functional programs. Many programming concepts that are important in the functional
programming paradigm, such as recursion, higher-order functions, pattern-matching, and lazy evaluation, can be partially explained by showing a stepwise computation. A student gets a better understanding of these concepts if she performs these evaluation steps herself. Tool support for experimenting with the evaluation of Haskell expressions is currently lacking. In this paper we present a prototype implementation of a stepwise evaluator for Haskell expressions that supports multiple evaluation strategies, specifically targeted at education. Besides performing evaluation steps the tool also diagnoses steps that are submitted by a student, and provides feedback. Instructors can add or change function definitions without knowledge of the tools internal implementation. We discuss some preliminary results of a small survey about the tool.
We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and termin
al operators of the family are conjugate by a bundle automorphism. This result is used to study conditions for the existence of nonzero spectral flow of a family of self-adjoint Dirac type operators with local boundary conditions in a two-dimensional domain with nontrivial topology. Possible physical realizations of nonzero spectral flow are discussed.
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
We study the spectrum of fermionic modes on cosmic string loops. We find no fermionic zero modes nor massive bound states - this implies that vortons stabilized by fermionic currents do not exist. We have also studied kink-(anti)kink and vortex-(anti
)vortex systems and find that all systems that have vanishing net topological charge do not support fermionic bound modes.
