Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

Complexity Measures from Interaction Structures

We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ units. We demonstrate that these measures are able to identify complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex

Cellular Automaton for Realistic Modelling of Landslides

A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is based on a lattice, in which debris can be transferred among nearest neighbors according to established empirical relationships for granular flows. The model is then validated by comparing a simulation with reported field data. Our model is in fact a realistic elaboration of simpler ``sandpile automata'', which have in recent years been studied as supposedly paradigmatic of ``self-organized criticality''. Statistics and scaling properties of the simulation are examined, and show that the model has an intermittent behavior.Comment: Revised version (gramatical and writing style cleanup mainly). Accepted for publication by Nonlinear Processes in Geophysics. 16 pages, 98Kb uuencoded compressed dvi file (that's the way life is easiest). Big (6Mb) postscript figures available upon request from [email protected] / [email protected]

1D Cellular Automata for Pulse Width Modulated Compressive Sampling CMOS Image Sensors

Compressive sensing (CS) is an alternative to the Shannon limit when the signal to be acquired is known to be sparse or compressible in some domain. Since compressed samples are non-hierarchical packages of information, this acquisition technique can be employed to overcome channel losses and restricted data rates. The quality of the compressed samples that a sensor can deliver is affected by the measurement matrix used to collect them. Measurement matrices usually employed in CS image sensors are recursive random-like binary matrices obtained using pseudo-random number generators (PRNG). In this paper we analyse the performance of these PRNGs in order to understand how their non-idealities affect the quality of the compressed samples. We present the architecture of a CMOS image sensor that uses class-III elementary cellular automata (ECA) and pixel pulse width modulation (PWM) to generate onchip a measurement matrix and high the quality compressed samples.Ministerio de Economía y Competitividad TEC2015-66878-C3-1-RJunta de Andalucía TIC 2338-2013Office of Naval Research N000141410355CONACYT (Mexico) MZO-2017-29106

Non-classical computing: feasible versus infeasible

Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are a range of possible architectures that could be implemented on silicon that are distinctly different from the von Neumann model. Beyond this, quantum simulators, which are the quantum equivalent of analogue computers, may be constructable in the near future

Cellular Structures for Computation in the Quantum Regime

We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking avoids the time-scale problems associated with ground-state relaxation schemes. For quantum computing, the architecture constitutes a novel paradigm whereby the algorithm is embedded in spatial, as opposed to temporal, structure. The architecture can be exploited to produce highly efficient algorithms: for example, a list of length N can be searched in time of order cube root N.Comment: 11 pages (LaTeX), 3 figure