Mike Stannett

Are there asymmetries in UK Consumption? A time series analysis

In this paper we use time series techniques in order to test for asymmetric dynamics in UK consumption. The notion that fluctuation over the business cycle are asymmetric has been put forward at various times in the last century. Nevertheless, the most common representations of aggregate time series in macroeconomies are usually smooth and sluggish. The use of time series methods should be considered as only the first stage of an empirical investigation of asymmetries. It is also essential to develop economic models of asymmetric behaviour and to employ tests of asymmetric adjustment at the level structural realtionship.

X-machines and the halting problem: building a super-Turing machine

We describe a novel machine model of computation, and prove that this model is capable of performing calculations beyond the capability of the standard Turing machine model. In particular, we demonstrate the ability of our model to solve the Halting problem for Turing machines. We discuss the issues involved in implementing the model as a physical device, and offer some tentative suggestions.

The case for hypercomputation

Abstract The weight of evidence supporting the case for hypercomputation is compelling. We examine some 20 physical and mathematical models of computation that are either known or suspected to have super-Turing or hypercomputational capabilities, and argue that there is nothing in principle to prevent the physical implementation of hypercomputational systems. Hypercomputation may indeed be intrinsic to physics; recursion ‘emerges’ from hypercomputation in the same way that classical physics emerges from quantum theory as scale increases. Furthermore, even if hypercomputation were one day shown to be physically infeasible, there would still remain a role for hypercomputation as an organising principle for advanced research.

Computation and Hypercomputation

Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently close computable approximations. In addition to considering the nature of computability relative to any given physical theory, we can consider the relationship between versions of computability corresponding to different models of physics. Deutsch and Penrose have argued on mathematical grounds that quantum computation and Turing computation have equivalent formal power. We suggest this equivalence is invalid when considered from the physical point of view, by highlighting a quantum computational behaviour that cannot meaningfully be considered feasible in the classical universe.

Addressing self-management in cloud platforms: a semantic sensor web approach

As computing systems evolve and mature, they are also expected to grow in size and complexity. With the continuing paradigm shift towards cloud computing, these systems have already reached the stage where the human effort required to maintain them at an operational level is unsupportable. Therefore, the development of appropriate mechanisms for run-time monitoring and adaptation is essential to prevent cloud platforms from quickly dissolving into a non-reliable environment. In this paper we present our approach to enable cloud application platforms with self-managing capabilities. The approach is based on a novel view of cloud platforms as networks of distributed data sources - sensors. Accordingly, we propose utilising techniques from the Sensor Web research community to address the challenge of monitoring and analysing continuously flowing data within cloud platforms in a timely manner.

Using Isabelle/HOL to Verify First-Order Relativity Theory

Logicians at the Rényi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first-order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally unsolvable questions such as the Halting Problem and the consistency of set theory. As part of a joint project, researchers at Sheffield have recently started generating rigorous machine-verified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate a first-order proof in Isabelle/HOL of the theorem “no inertial observer can travel faster than light”. This approach to physical theories and physical computability has several pay-offs, because the precision with which physical theories need to be formalised within automated proof systems forces us to recognise subtly hidden assumptions.

An Integrated Model Checking Toolset for Kernel P Systems

P systems are the computational models introduced in the context of membrane computing, a computational paradigm within the more general area of unconventional computing. Kernel P (kP) systems are defined to unify the specification of different variants of P systems, motivated by challenging theoretical aspects and the need to model different problems. kP systems are supported by a software framework, called kPWorkbench, which integrates a set of related simulation and verification methodologies and tools. In this paper, we present an extension to kPWorkbench with a new model checking framework supporting the formal verification of kP system models. This framework supports both LTL and CTL properties. To make the property specification an easier task, we propose a property language, composed of natural language statements. We demonstrate our proposed methodology with an example.

Computing the appearance of physical reality

The role of theoretical physics is to investigate, represent and thereby explain the nature of physical reality. We claim that this goal is unattainable using current standard mathematical models of physics, not just for practical reasons, but as a matter of logical necessity. Standard models of quantum theory and relativistic spacetime are logically equivalent to models in which the nature of classically observable motions is a form of necessary illusion. Consequently, no standard deductions as to the nature of space, time and motion can be deemed sound.

Faster than light motion does not imply time travel

Seeing the many examples in the literature of causality violations based on faster-than- light (FTL) signals one naturally thinks that FTL motion leads inevitably to the possibility of time travel. We show that this logical inference is invalid by demonstrating a model, based on (3+1)-dimensional Minkowski spacetime, in which FTL motion is permitted (in every direction without any limitation on speed) yet which does not admit time travel. Moreover, the Principle of Relativity is true in this model in the sense that all observers are equivalent. In short, FTL motion does not imply time travel after all.

P systems controlled by general topologies

In this paper we investigate the use of general topological spaces as control mechanisms for basic classes of membrane systems employing only rewrite and communication rules.