Computational Mechanisms and Models of Computation

In this article, after presenting the basic idea of causal accounts of implementation and the problems they are supposed to solve, I sketch the model of computation preferred by Chalmers and argue that it is too limited to do full justice to computational theories in cognitive science. I also argue that it does not suffice to replace Chalmers’ favorite model with a better abstract model of computation; it is necessary to acknowledge the causal structure of physical computers that is not accommodated by the models used in computability theory. Additionally, an alternative mechanistic proposal is outlined.

Emergence, Complexity and Computation, 2016

Achieving greater speeds and densities in the post-Moore's Law era will require computation to be more like the physical processes by which it is realized. Therefore we explore the essence of computation, that is, what distinguishes computational processes from other physical processes. We consider such issues as the topology of information processing, programmability, and universality. We summarize general characteristics of analog computation, quantum computation, and field computation, in which data is spatially continuous. Computation is conventionally used for information processing, but since the computation governs physical processes, it can also be used as a way of moving matter and energy on a microscopic scale. This provides an approach to programmable matter and programmed assembly of physical structures. We discuss artificial morphogenesis, which uses the formal structure of embryological development to coordinate the behavior of a large number of agents to assemble complex hierarchical structures. We explain that this close correspondence between computational and physical processes is characteristic of embodied computation, in which computation directly exploits physical processes for computation, or for which the physical consequences of computation are the purpose of the computation.

2013

We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics and neuroinformatics depends on the adequate models of computation. In this article we first present the current state of the art through systematisation of existing models and mechanisms, and outline basic structural framework of computation. We argue that defining computation as information processing, and given that there is no information without (physical) representation, the dynamics of information on the fundamental level is physical/ intrinsic/ natural computation. As a special case, intrinsic computation is used for designed computation in computing machinery. Intrinsic natural computation occurs on variety of levels of physical processes, containing the levels of computation of living organisms (including highly intelligent animals) as well as designed computational devices. The present article offers a typology of current models of computation and indicates future paths for the advancement of the field; both by the development of new computational models and by learning from nature how to better compute using different mechanisms of intrinsic computation.

Journal of Logic, Language and Information, 2011

This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring to digital computation simply adhere to Turing's notion of computability. Classical computability theory studies what functions on the natural numbers are computable, and what mathematical problems are undecidable. Whilst a mathematical formalism of computability may perform a methodological function of evaluating computational theories of certain cognitive capacities, concrete computation in physical systems seems to be required for explaining cognition as an embodied phenomenon. There are many non-equivalent accounts of digital computation in physical systems. I examine only a handful of those in this paper: 1. Turing's account; 2. The triviality "account"; 3. Reconstructing Smith's account of participatory computation; 4. The Algorithm Execution account. My goal in this paper is twofold. First, it is to identify and clarify some of the underlying key requirements mandated by these accounts. I argue that these differing requirements justify a demand that one commits to a particular account when employing the notion of computation in regard to physical systems. Second, it is to argue that despite the informative role that mathematical formalisms of computability may play in cognitive science, they do not specify the relationship between abstract and concrete computation.

Proceedings of the Royal Society A, 2014

Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however, no consensus on how to tell if a given physical system is acting as a computer or not; leading to confusion over novel computational devices, and even claims that every physical event is a computation. In this paper, we introduce a formal framework that can be used to determine whether a physical system is performing a computation. We demonstrate how the abstract computational level interacts with the physical device level, in comparison with the use of mathematical models in experimental science. This powerful formulation allows a precise description of experiments, technology, computation and simulation, giving our central conclusion: physical computing is the use of a physical system to predict the outcome of an abstract evolution. We give conditions for computing, illustrated using a range of non-standard computing scenarios. The framework also covers broader computing contexts, where there is no obvious human computer user. We introduce the notion of a ‘computational entity’, and its critical role in defining when computing is taking place in physical systems.

The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and sub-symbolic information processing levels.

2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512)

An explicit measure of the computation performed by general systems (electronic circuits, neurons, mechanical devices, etc.) is defined. We propose that the deeper nature of computation, and thus of any measure of computation, is in its reduction of complexity. The latter we understand as the "obstruction against prediction", experienced by an observer. We demonstrate the applicability and usefulness of this concept in different examples, which include some of the most studied families of dynamical systems. The measure can also be computed for higher-dimensional and experimental systems.

1998

s of the Poster Session Contributions to the First International Conference on Unconventional Models of Computation Centre for Discrete Mathematics and Theoretical Computer Science, NZ and Santa Fe Institute, USA 5 # 9 January 1998, Auckland, New Zealand Edited by Peter Hertling, University of Auckland Preface The First International Conference on Unconventional Models of Computation, UMC'98, organized by the Centre for Discrete Mathematics and Theoretical Computer Science, in cooperation with the Santa Fe Institute, was held at the University of Auckland from January 5#9, 1998. The proceedings of UMC'98 have appeared in the DMTCS Series of Springer#Verlag, Singapore. This CDMTCS Research Report contains the abstracts or extended abstracts of the poster session contributions to UMC'98. They cover engineering, physical, mathematical, and philosophical aspects of a broad range of unconventional models of computation: from evolutionary computation, quantum computation, D...

Lecture Notes in Computer Science, 2013

This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Oftentimes, cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there is a consensus on just what it takes for a physical system to compute. Some cognitive scientists in referring to digital computation simply adhere to Turing computability. But if cognition is indeed computational, then it is concrete computation that is required for explaining cognition as an embodied phenomenon. Three accounts of computation are examined here: 1. Formal Symbol Manipulation. 2. Physical Symbol Systems and 3. The Mechanistic account. I argue that the differing requirements implied by these accounts justify the demand that one commits to a particular account when employing the notion of digital computation in regard to physical systems, rather than use these accounts interchangeably.

Proceedings of ISIS Summit Vienna 2015—The Information Society at the Crossroads, 2015

Future progress of new information processing devices capable of dealing with problems such as big data, Internet of things, semantic web, cognitive robotics, neuroinformatics and similar, depends on the adequate and efficient models of computation. We argue that defining computation as information transformation, and given that there is no information without representation, the dynamics of information on the fundamental level is physical/ intrinsic/ natural computation (Dodig-Crnkovic, 2011) (Dodig-Crnkovic, 2014). Intrinsic natural computation occurs on variety of levels of physical processes, such as the levels of computation of living organisms as well as designed computational devices. The present article is building on our typology of models of computation as information processing (Burgin & Dodig-Crnkovic, 2013). It is indicating future paths for the advancement of the field, expected both as a result of the development of new computational models and learning from nature how to better compute using information transformation mechanisms of intrinsic computation.