The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

In this paper we revisit one of the rst models of analog computation, Shannon's General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPACcomputability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial di erential equations then we show that all real computable functions can be de ned by such models

How to compare the power of computational models

Abstract. We argue that there is currently no satisfactory general framework for comparing the extensional computational power of arbitrary computational models operating over arbitrary domains. We propose a conceptual framework for comparison, by linking computational models to hypothetical physical devices. Accordingly, we deduce a mathematical notion of relative computational power, allowing the comparison of arbitrary models over arbitrary domains. In addition, we claim that the method commonly used in the literature for “strictly more powerful” is problematic, as it allows for a model to be more powerful than itself. On the positive side, we prove that Turing machines and the recursive functions are “complete ” models, in the sense that they are not susceptible to this anomaly, justifying the standard means of showing that a model is “hypercomputational.”

Evaluating accounting information systems that support multiple GAAP reporting using normalized systems theory

This paper uses a mixed methods approach of design science and case study research to evaluate structures of Accounting Information Systems (AIS) that report in multiple Generally Accepted Accounting Principles (GAAP), using Normalized Systems Theory (NST). To comply with regulation, many companies need to apply multiple GAAP. In case studies we identify AIS structures for multiple GAAP reporting. AIS need to cope with changes in GAAP and regulation in an evolvable way, the impact of the changes needs to be bounded. Since NST provides guidelines to design modular structures (in software) with an ex-ante proven degree of evolvability [1], we use NST to evaluate the identified AIS structures. We list violations of NST principles (combinatorial effects) and describe their manifestation in the cases. This application of NST in accounting demonstrates its relevance in non-software-specific domains. Moreover this is the first evaluation of an AIS with respect to evolvability

Problems and prospects for quantum computational speed-up

This paper studies the problems involved in the speed-up of the classical computational algorithms using the quantum computational paradigm. In particular, we relate the primitive recursive function approach used in computability theory with the harmonic oscillator basis used in quantum physics. Also, we raise some basic issues concerning quantum computational paradigm: these include failures in programmability and scalability, limitation on the size of the decoherence - free space available and lack of methods for proving quantum programs correct. In computer science, time is discrete and has a well-founded structure. But in physics, time is a real number, continuous and is infinitely divisible; also time can have a fractal dimension. As a result, the time complexity measures for conventional and quantum computation are incomparable. Proving properties of programs and termination rest heavily on the well-founded properties, and the transfinite induction principle. Hence transfinite induction is not applicable to reason about quantum programs