Zeno machines and hypercomputation

This paper reviews the Church-Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of "hypercomputation", concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is hinted that claims to have "broken the Turing barrier" could be toned down and that the important and well-founded role of Turing computability in the mathematical sciences stands unchallenged.Comment: 11 pages. First submitted in December 2004, substantially revised in July and in November 2005. To appear in Theoretical Computer Scienc

Scale-invariant cellular automata and self-similar Petri nets

Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.Comment: 35 pages, 5 figure

Can a computer be "pushed" to perform faster-than-light?

We propose to "boost" the speed of communication and computation by immersing the computing environment into a medium whose index of refraction is smaller than one, thereby trespassing the speed-of-light barrier.Comment: 7 pages, 1 figure, presented at the UC10 Hypercomputation Workshop "HyperNet 10" at The University of Tokyo on June 22, 201

Zeno-machines And The Metaphysics Of Time

This paper aims to explore the nature of Zeno-machines by examining their conceptual coherence, from the perspective of contemporary theories on the passage of time. More specifically, it will analyse the following questions: Are Zeno-machines and supertasks coherent if we adopt the eternalist theory of time? What conclusions can be drawn from choosing the eternalist thesis, or the presentist thesis, when examining Zeno-machines? To this end, an overview of the opposing theories of time is provided, alongside the usual objections to Zeno-machines and their theoretical foundations from Zeno's dichotomy paradox.17216116