Heterotic Computing Examples with Optics, Bacteria, and Chemicals

Unconventional computers can perform embodied computation that can directly exploit the natural dynamics of the substrate. But such in materio devices are often limited, special purpose machines. To be practically useful, unconventional devices are usually be combined with classical computers or control systems. However, there is currently no established way to do this, or to combine different unconventional devices. In this position paper we describe heterotic unconventional computation, an approach that focusses on combinations of unconventional devices. This will need a sound semantic framework defining how diverse unconventional computational devices can be combined in a way that respects the intrinsic computational power of each, whilst yielding a hybrid device that is capable of more than the sum of its parts. We also describe a suite of diverse physical implementations of heterotic unconventional computers, comprising computation performed by bacteria hosted in chemically built material, sensed and controlled optically and chemically.Ministerio de Ciencia e Innovación TIN2009–13192Ministerio de Ciencia e Innovación JCI-2010-0653

Formulating Oscillator-Inspired Dynamical Systems to Solve Boolean Satisfiability

Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many of which are still challenging to solve using conventional digital solvers. In this work, we formulate two oscillator-inspired dynamical systems to solve quintessential computationally intractable problems in Boolean satisfiability (SAT). The system dynamics are engineered such that they facilitate solutions to two different flavors of the SAT problem. We formulate the first dynamical system to compute the solution to the 3-SAT problem, while for the second system, we show that its dynamics map to the solution of the Max-NAE-3-SAT problem. Our work advances understanding of how this physics-inspired approach can be used to address challenging problems in computing

Classification of Complex Systems Based on Transients

In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method distinguishes between different asymptotic behaviors of a system's average computation time before entering a loop. When applied to elementary cellular automata, we obtain classification results, which correlate very well with Wolfram's manual classification. Further, we use it to classify 2D cellular automata to show that our technique can easily be applied to more complex models of computation. We believe this classification method can help to develop systems, in which complex structures emerge.Comment: 9 page

Co-designing the computational model and the computing substrate

Given a proposed unconventional computing substrate, we can ask: Does it actually compute? If so, how well does it compute? Can it be made to compute better? Given a proposed unconventional computational model we can ask: How powerful is the model? Can it be implemented in a substrate? How faithfully or efficiently can it be implemented? Given complete freedom in the choice of model and substrate, we can ask: Can we co-design a model and substrate to work well together? Here I propose an approach to posing and answering these questions, building on an existing definition of physical computing and framework for characterising the computing properties of given substrates

Computation in Dynamically Bounded Asymmetric Systems

Previous explanations of computations performed by recurrent networks have focused on symmetrically connected saturating neurons and their convergence toward attractors. Here we analyze the behavior of asymmetrical connected networks of linear threshold neurons, whose positive response is unbounded. We show that, for a wide range of parameters, this asymmetry brings interesting and computationally useful dynamical properties. When driven by input, the network explores potential solutions through highly unstable ‘expansion’ dynamics. This expansion is steered and constrained by negative divergence of the dynamics, which ensures that the dimensionality of the solution space continues to reduce until an acceptable solution manifold is reached. Then the system contracts stably on this manifold towards its final solution trajectory. The unstable positive feedback and cross inhibition that underlie expansion and divergence are common motifs in molecular and neuronal networks. Therefore we propose that very simple organizational constraints that combine these motifs can lead to spontaneous computation and so to the spontaneous modification of entropy that is characteristic of living systems

Complexity in Cellular Automata

In order to identify complex systems capable of modeling artificial life, we study the notion of complexity within a class of dynamical systems called cellu- lar automata. We present a novel classification of cellular automata dynamics, which helps us identify interesting behavior in large automaton spaces. We give a detailed comparison of our results to previous methods of dynamics classification. In the second part of the thesis, we study the backward dynamics of cellular au- tomata. We present a novel representation of one-dimensional cellular automata, which can be used to charcterize all their garden of eden configurations. We demonstrate the usefulness of this method on examples. 1Naším dlouhodobým cílem je identifikovat komplexní systémy vhodné k mod- elování umělého života. Tento problém je obtížný zčásti kvůli chybějící formální definici komplexního chování. V této práci proto zkoumáme pojem komplexity dynamických systémů známých jako celulární automaty. Představujeme novou klasifikaci jejich dynamiky, kterou využíváme k automatickému rozpoznávání zajímavého chování ve velkých prostorech celulárních automatů. Naše výsledky dále porovnáváme s dříve navrhnutými metodami klasifikace. Ve druhé části práce se zameřujeme na zkoumání dozadné dynamiky celulárních automatů, tedy studujeme vzory daných automatů. V tomto kontextu zavádíme novou metodu reprezentace jednodimenzionálních automatů, pomocí které lze charakterizovat všechny jejich garden of eden konfigurace. Využití této metody demonstrujeme na příkladech. 1Department of AlgebraKatedra algebryMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Complexity in Cellular Automata

In order to identify complex systems capable of modeling artificial life, we study the notion of complexity within a class of dynamical systems called cellu- lar automata. We present a novel classification of cellular automata dynamics, which helps us identify interesting behavior in large automaton spaces. We give a detailed comparison of our results to previous methods of dynamics classification. In the second part of the thesis, we study the backward dynamics of cellular au- tomata. We present a novel representation of one-dimensional cellular automata, which can be used to charcterize all their garden of eden configurations. We demonstrate the usefulness of this method on examples. 1Naším dlouhodobým cílem je identifikovat komplexní systémy vhodné k mod- elování umělého života. Tento problém je obtížný zčásti kvůli chybějící formální definici komplexního chování. V této práci proto zkoumáme pojem komplexity dynamických systémů známých jako celulární automaty. Představujeme novou klasifikaci jejich dynamiky, kterou využíváme k automatickému rozpoznávání zajímavého chování ve velkých prostorech celulárních automatů. Naše výsledky dále porovnáváme s dříve navrhnutými metodami klasifikace. Ve druhé části práce se zameřujeme na zkoumání dozadné dynamiky celulárních automatů, tedy studujeme vzory daných automatů. V tomto kontextu zavádíme novou metodu reprezentace jednodimenzionálních automatů, pomocí které lze charakterizovat všechny jejich garden of eden konfigurace. Využití této metody demonstrujeme na příkladech. 1Department of AlgebraKatedra algebryMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

A Bio-inspired Distributed Control Architecture: Coupled Artificial Signalling Networks

This thesis studies the applicability of computational models inspired by the structure and dynamics of signalling networks to the control of complex control problems. In particular, this thesis presents two different abstractions that aim to capture the signal processing abilities of biological cells: a stand-alone signalling network and a coupled signalling network. While the former mimics the interacting relationships amongst the components in a signalling pathway, the latter replicates the connectionism amongst signalling pathways. After initially investigating the feasibility of these models for controlling two complex numerical dynamical systems, Chirikov's standard map and the Lorenz system, this thesis explores their applicability to a difficult real world control problem, the generation of adaptive rhythmic locomotion patterns within a legged robotic system. The results highlight that the locomotive movements of a six-legged robot could be controlled in order to adapt the robot's trajectory in a range of challenging environments. In this sense, signalling networks are responsible for the robot adaptability and inter limb coordination as they self-adjust their dynamics according to the terrain's irregularities. More generally, the results of this thesis highlight the capacity of coupled signalling networks to decompose non-linear problems into smaller sub-tasks, which can then be independently solved

Reservoir Computing in Materio

Reservoir Computing first emerged as an efficient mechanism for training recurrent neural networks and later evolved into a general theoretical model for dynamical systems. By applying only a simple training mechanism many physical systems have become exploitable unconventional computers. However, at present, many of these systems require careful selection and tuning by hand to produce usable or optimal reservoir computers. In this thesis we show the first steps to applying the reservoir model as a simple computational layer to extract exploitable information from complex material substrates. We argue that many physical substrates, even systems that in their natural state might not form usable or "good" reservoirs, can be configured into working reservoirs given some stimulation. To achieve this we apply techniques from evolution in materio whereby configuration is through evolved input-output signal mappings and targeted stimuli. In preliminary experiments the combined model and configuration method is applied to carbon nanotube/polymer composites. The results show substrates can be configured and trained as reservoir computers of varying quality. It is shown that applying the reservoir model adds greater functionality and programmability to physical substrates, without sacrificing performance. Next, the weaknesses of the technique are addressed, with the creation of new high input-output hardware system and an alternative multi-substrate framework. Lastly, a substantial effort is put into characterising the quality of a substrate for reservoir computing, i.e its ability to realise many reservoirs. From this, a methodological framework is devised. Using the framework, radically different computing substrates are compared and assessed, something previously not possible. As a result, a new understanding of the relationships between substrate, tasks and properties is possible, outlining the way for future exploration and optimisation of new computing substrates