General Topologies and P Systems

In this paper we investigate the use of general topological spaces as control mechanisms for membrane systems. For simplicity, we illustrate our approach by showing how arbitrary topologies can be used to study the behaviour of membrane systems with rewrite and communication rules

GROUPS OF WORLDVIEW TRANSFORMATIONS IMPLIED BY ISOTROPY OF SPACE

Given any Euclidean ordered field, Q, and any 'reasonable' group, G, of (1+3)-dimensional spacetime symmetries, we show how to construct a model M-G of kinematics for which the set W of worldview transformations between inertial observers satisfies W = G. This holds in particular for all relevant subgroups of Gal, cPoi, and cEucl (the groups of Galilean, Poincare and Euclidean transformations, respectively, where c is an element of Q is a model-specific parameter corresponding to the speed of light in the case of Poincare transformations).In doing so, by an elementary geometrical proof, we demonstrate our main contribution: spatial isotropy is enough to entail that the set W of worldview transformations satisfies either W subset of Gal, W subset of cPoi, or W subset of cEucl for some c > 0. So assuming spatial isotropy is enough to prove that there are only 3 possible cases: either the world is classical (the worldview transformations between inertial observers are Galilean transformations); the world is relativistic (the worldview transformations are Poincare transformations); or the world is Euclidean (which gives a nonstandard kinematical interpretation to Euclidean geometry). This result considerably extends previous results in this field, which assume a priori the (strictly stronger) special principle of relativity, while also restricting the choice of Q to the field R of reals.As part of this work, we also prove the rather surprising result that, for any G containing translations and rotations fixing the time-axis t, the requirement that G be a subgroup of one of the groups Gal, cPoi or cEucl is logically equivalent to the somewhat simpler requirement that, for all g is an element of G: g[t] is a line, and if g[t] = t then g is a trivial transformation (i.e. g is a linear transformation that preserves Euclidean length and fixes the time-axis setwise)

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

Three Different Formalisations of Einstein’s Relativity Principle

We present three natural but distinct formalisations of Einstein’s special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms

On the reaction time of some synchronous systems

This paper presents an investigation of the notion of reaction time in some synchronous systems. A state-based description of such systems is given, and the reaction time of such systems under some classic composition primitives is studied. Reaction time is shown to be non-compositional in general. Possible solutions are proposed, and applications to verification are discussed. This framework is illustrated by some examples issued from studies on real-time embedded systems.Comment: In Proceedings ICE 2011, arXiv:1108.014

Abstract The case for hypercomputation

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 ÔemergesÕ 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