Toward a formal theory for computing machines made out of whatever physics offers: extended version

Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on unconventional physical effects, we need guidance from a formal theory that is different from the symbolic-algorithmic theory of today's computer science textbooks. We propose a general strategy for developing such a theory, and within that general view, a specific approach that we call "fluent computing". In contrast to Turing, who modeled computing processes from a top-down perspective as symbolic reasoning, we adopt the scientific paradigm of physics and model physical computing systems bottom-up by formalizing what can ultimately be measured in any physical substrate. This leads to an understanding of computing as the structuring of processes, while classical models of computing systems describe the processing of structures.Comment: 76 pages. This is an extended version of a perspective article with the same title that will appear in Nature Communications soon after this manuscript goes public on arxi

Unconventional programming: non-programmable systems

Die Forschung aus dem Bereich der unkonventionellen und natürlichen Informationsverarbeitungssysteme verspricht kontrollierbare Rechenprozesse in ungewöhnlichen Medien zu realisieren, zum Beispiel auf der molekularen Ebene oder in Bakterienkolonien. Vielversprechende Eigenschaften dieser Systeme sind das nichtlineare Verhalten und der hohe Verknüpfungsgrad der beteiligten Komponenten in Analogie zu Neuronen im Gehirn. Da aber Programmierung meist auf Prinzipien wie Modularisierung, Kapselung und Vorhersagbarkeit beruht sind diese Systeme oft schwer- bzw. unprogrammierbar. Im Gegensatz zu vielen Arbeiten über unkonventionelle Rechensysteme soll in dieser Arbeit aber nicht hauptsächlich nach neuen rechnenden Systemen und Anwendungen dieser gesucht werden. Stattdessen konzentriert sich diese Dissertation auf unkonventionelle Programmieransätze, die sowohl für unkonventionelle Computer als auch für herkommliche digitale Rechner neue Perspektiven eröffnen sollen. Hauptsächlich in Bezug auf ein Modell künstlicher chemischer Neuronen werden Ansätze für unkonventionelle Programmierverfahren, basierend auf Evolutionären Algorithmen, Informationstheorie und Selbstorganisation bis hin zur Selbstassemblierung untersucht. Ein spezielles Augenmerk liegt dabei auf dem Problem der Symbolkodierung: Oft gibt es mehrere oder sogar unendlich viele Möglichkeiten, Informationen in den Zuständen eines komplexen dynamischen Systems zu kodieren. In Neuronalen Netzen gibt es unter anderem die Spikefrequenz aber auch Populationskodes. In Abhängigkeit von den weiteren Eigenschaften des Systems, beispielsweise von der Informationsverarbeitungsaufgabe und dem gewünschten Eingabe-Ausgabeverhalten dürften sich verschiedene Kodierungen als unterschiedlich nützlich erweisen. Daher werden hier Methoden betrachtet um die verschiedene Symbolkodierungmethoden zu evaluieren, zu analysieren und um nach neuen, geeigneten Kodierungen zu suchen.Unconventional and natural computing research offers controlled information modification processes in uncommon media, for example on the molecular scale or in bacteria colonies. Promising aspects of such systems are often the non-linear behavior and the high connectivity of the involved information processing components in analogy to neurons in the nervous system. Unfortunately, such properties make the system behavior hard to understand, hard to predict and thus also hard to program with common engineering principles like modularization and composition, leading to the term of non-programmable systems. In contrast to many unconventional computing works that are often focused on finding novel computing substrates and potential applications, unconventional programming approaches for such systems are the theme of this thesis: How can new programming concepts open up new perspectives for unconventional but hopefully also for traditional, digital computing systems? Mostly based on a model of artificial wet chemical neurons, different unconventional programming approaches from evolutionary algorithms, information theory, self-organization and self-assembly are explored. A particular emphasis is given on the problem of symbol encodings: Often there are multiple or even an unlimited number of possibilities to encode information in the phase space of dynamical systems, e.g. spike frequencies or population coding in neural networks. But different encodings will probably be differently useful, dependent on the system properties, the information transformation task and the desired connectivity to other systems. Hence methods are investigated that can evaluate, analyse as well as identify suitable symbol encoding schemes

Exploring the landscapes of "computing": digital, neuromorphic, unconventional -- and beyond

The acceleration race of digital computing technologies seems to be steering toward impasses -- technological, economical and environmental -- a condition that has spurred research efforts in alternative, "neuromorphic" (brain-like) computing technologies. Furthermore, since decades the idea of exploiting nonlinear physical phenomena "directly" for non-digital computing has been explored under names like "unconventional computing", "natural computing", "physical computing", or "in-materio computing". This has been taking place in niches which are small compared to other sectors of computer science. In this paper I stake out the grounds of how a general concept of "computing" can be developed which comprises digital, neuromorphic, unconventional and possible future "computing" paradigms. The main contribution of this paper is a wide-scope survey of existing formal conceptualizations of "computing". The survey inspects approaches rooted in three different kinds of background mathematics: discrete-symbolic formalisms, probabilistic modeling, and dynamical-systems oriented views. It turns out that different choices of background mathematics lead to decisively different understandings of what "computing" is. Across all of this diversity, a unifying coordinate system for theorizing about "computing" can be distilled. Within these coordinates I locate anchor points for a foundational formal theory of a future computing-engineering discipline that includes, but will reach beyond, digital and neuromorphic computing.Comment: An extended and carefully revised version of this manuscript has now (March 2021) been published as "Toward a generalized theory comprising digital, neuromorphic, and unconventional computing" in the new open-access journal Neuromorphic Computing and Engineerin

Symmetry structure in discrete models of biochemical systems : natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.Interaction Computing (IC) is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are (1) to identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this, and (2) to use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in Systems Biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, Krebs cycle, and p53-mdm2 genetic regulation constructed from Systems Biology models have canonically associated algebraic structures { transformation semigroups. These contain permutation groups (local substructures exhibiting symmetry) that correspond to "pools of reversibility". These natural subsystems are related to one another in a hierarchical manner by the notion of "weak control ". We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-abelian groups (SNAGs) are found in biological examples and can be harnessed to realize nitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.Peer reviewe

Memristors for the Curious Outsiders

We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page

Cellular Automata Applications in Shortest Path Problem

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 201

East-West Paths to Unconventional Computing

Unconventional computing is about breaking boundaries in thinking, acting and computing. Typical topics of this non-typical field include, but are not limited to physics of computation, non-classical logics, new complexity measures, novel hardware, mechanical, chemical and quantum computing. Unconventional computing encourages a new style of thinking while practical applications are obtained from uncovering and exploiting principles and mechanisms of information processing in and functional properties of, physical, chemical and living systems; in particular, efficient algorithms are developed, (almost) optimal architectures are designed and working prototypes of future computing devices are manufactured. This article includes idiosyncratic accounts of ‘unconventional computing’ scientists reflecting on their personal experiences, what attracted them to the field, their inspirations and discoveries.info:eu-repo/semantics/publishedVersio