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This paper presents taxonomy of models of computation. It includes Existential (Physical, Abstract and Cognitive), Organizational, Temporal, Representational, Domain/Data, Operational, Process-oriented and Level-based taxonomy. It is connected to more general notion of natural computation, intrinsic to physical systems, and particularly to cognitive computation in living organisms and artificial cognitive systems. Computation is often understood through the Turing machine model, in the fields of computability, computational complexity and even as a basis for the present-day computer hardware and software architectures. However, several aspects of computation, even those existing in today's applications, are left outside in this model, thus adequate models of real-time, distributed, self-organized, resource-aware, adaptive, learning computation systems are currently being developed.
A Taxonomy of Computation and Information Architecture
Mark Burgin
Department of Mathematics,
UCLA, Los Angeles, USA
Gordana Dodig-Crnkovic
Chalmers University of Technology
and University of Gothenburg
Nowadays computation is typically understood through the Turing
machine model, in the fields of computability, computational
complexity and even as a basis for present-day computer
hardware and software architectures. Those are technologies
designed in the first place to process data. Being description of
data manipulation, Turing model of computation presents only
one aspect of computation in the real world an abstraction of the
execution of an algorithm. However, several other possible
aspects of computation, even those existing in todays
applications, are left outside, thus adequate models in distributed,
self-organized, resource-aware, adaptive, learning computation
systems are needed. This paper presents taxonomy of existing
models of computation. It is connected to more general notion of
natural computation, intrinsic to physical systems, and particularly
cognitive computation in cognitive systems. We see Turing model
of computation as a basic mechanism which can be used to build
more complex computational architectures, that in combination
with interaction with the environment (learning) give advanced
information-processing behaviors in cognitive systems.
Computation, Information Processing, Algorithms, Turing
Machine, Computing Architecture, Computing Taxonomy,
Cognitive computing
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 systematization 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 taxonomy 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.
The question “What is computation?” is answered differently
by different researchers (cf., for example, [1][8]). Some did this
in an informal setting based on computational and research
practice, as well as on philosophical and methodological
considerations. Others strived to build exact mathematical models
to comprehensively describe computation. When the Turing
machine (or Logical Computing Machine as Turing originally
named his logical device) was constructed and accepted as a
universal computational model, it was considered as the complete
and exact definition of computation (Church-Turing thesis).
However, the absolute nature of the Turing machine was
disproved by adopting a more general definition of algorithm [4].
In the spirit of broadening of the concept of computation, the
following definition was proposed: “For a process to qualify as
computation a model must exist such as algorithm, network
topology, physical process or in general any mechanism which
ensures definability of its behavior.” [9]
Nevertheless, in spite of all efforts, the conception of
computation remains too vague and ambiguous. This vagueness of
the foundations of computing has resulted in a variety of
approaches, including approaches that contradict each other. For
instance, [3] writes “to compute is to execute an algorithm.
Active proponents of the Church-Turing Thesis, such as [10]
claim computation is bounded by what Turing machines are doing
(that is compute mathematical functions). For them the problem of
defining computation was solved long ago with the Turing
machine model. At the same time, Wegner and Goldin insist that
computation is an essentially broader concept than algorithm [11]
and propose interactive view of computing. While [12] argues that
computation is symbol manipulation, thus disregarding analog
computers computing over continuous signals, neuroscientists on
the contrary study sub-symbolic computation in neurons. [13]
Abramsky summarizes the process of successive changing of
computing models as follows:
“Traditionally, the dynamics of computing systems, their
unfolding behavior in space and time has been a mere means to
the end of computing the function which specifies the algorithmic
problem which the system is solving. In much of contemporary
computing, the situation is reversed: the purpose of the computing
system is to exhibit certain behaviour. (…) We need a theory of
the dynamics of informatic processes, of interaction, and
information flow, as a basis for answering such fundamental
questions as: What is computed? What is a process? What are the
analogues to Turing completeness and universality when we are
concerned with processes and their behaviors, rather than the
functions which they compute? [14]
Abramsky emphasizes that there is the need for second-generation
models of computation, and in particular process models. The first
generation models of computation originated from problems of
formalization of mathematics and logic, while processes or agents,
interaction, and information flow are results of recent
developments of computers and computing. In the second-
generation models of computation, previous isolated systems are
replaced by processes or agents for which the interactions with
each other and with the environment are fundamental. Hewitt too
advocates agent-type, Actor model of computation [8] which is
suitable for modeling of physical (intrinsic) computation.
Existence of various types and kinds of computation, as well as a
variety of approaches to the concept of computation, shows
remarkable complexity that makes communication of results and
ideas increasingly difficult. Our aim is to explicate present
diversity and so call attention to the necessity of common
understanding: different models of computation may have their
specific uses and applications. It is just necessary to understand
their mutual relationships and assumptions under which they
In this paper, we present methodological analysis of the concept
of computation before and after electronic computers and the
emergence of computer science, demonstrating that history brings
us to the conclusion that efforts in building such definitions by
traditional approaches would be inefficient. An effective
methodology is to find essential features of computation with the
goal to explicate its nature and to build adequate models for
research and technology. In addition, we perform structural
analysis of the concept of computation through explication of
various structures intrinsically related to computation, and in
particular cognitive computation.
One important question related to computation (information
processing) architecture is if cognition can be understood as
computation in the sense of Turing-Church thesis or if cognitive
computation needs additional constructs in case of self-managing
(autonomous) distributed computing systems such as human
brain. Cognition is taken to be the ability to process information,
apply knowledge, and act accordingly, with intent, and it s
accomplishment through various processes that monitor and
control a system and its environment. “Cognition is associated
with a sense of “self” (the observer) and the systems with which it
interacts (the environment or the “observed”). Cognition
extensively uses time and history in executing and regulating
tasks that constitute a cognitive process. In [15], [16] Mikkilineni
argues that “cognition requires more than mere book-keeping
provided by the Turing machines and certain aspects of cognition
such as self-identity, self-description, self-monitoring and self-
management can be implemented using parallel extensions to
current serial von-Neumann stored program control (SPC).”
The paper is organized in the following way. In Section 2 we
develop computational taxonomy, which allows us to extract basic
characteristics of computation and distinguish fundamental types
of computation. The suggested system of computational classes
allows us to reflect natural structures in the set of computational
processes. In Section 3 we study the structural context and
architecture of computation, illuminating the computational triad
and several other structures intrinsically related to computation. In
Section 4 we present the development of computational models in
natural computing (computing nature). Finally, we summarize and
present open questions in Section 5.
In his famous work [1] Turing presents his fundamental model,
which later was called the Turing machine model of computation.
Turing writes: “We may now construct a machine to do the work
of this computer.” Here a computer is a person performing
mechanical procedure executing an algorithm. Thus, algorithms
were the first models of computation. Algorithm was the practice
of algebra in the 18th century. In the 19th century, the term came to
mean any process of systematic calculation. In the 20th century,
Encyclopedia Britannica described algorithm as a systematic
mathematical procedure that produces in a finite number of
steps the answer to a question or the solution of a problem.
It is common that we talk about computation as if it would be a
uniquely defined concept. However some think of computation as
algorithm, others as symbol manipulation, while yet others may
have in mind a more general phenomenon of information
Currently there are so many kinds of concepts of computation and
its implementations that it is useful to make classification and
systematization so to better understand their mutual relationships.
In what follows we will present several main ttaxonomies of
computation: existential/substantial, organizational, temporal,
representational, data-oriented, operational, process-oriented and
2.1 Existential taxonomy
On the different levels of organisation of objects/agents (subjects)
(physical, structural, interpretant) we find different types of
computational processes. According to Burgin, [17] p. 93, reality
in the most abstract way can ben represented by the existential
triad (physical, structural, mental1) which corresponds to Plato’s
triad (material, ideas/forms, mental). This can also be related to
the Peirce's triad of (object, sign, interpretant).
The existential/substantial classification of computation based on
the existential triad [18] defines the following types:
1. Physical or embodied (object) computations
2. Abstract or structural (sign) computations
3. Mental or cognitive (interpretant) computations
The existential types from this taxonomy have definite subtypes.
The following are types of embodied computations, where each
next level emerges as a consequence of previous ones.
1.1. Physical computations
1.2. Chemical computations
1.3. Biological computations
1.4. Cognitive computations
1 Here mental denotes that which is of or relating to the mind. The
mind is a traditional and vague concept and in scientific terms it
corresponds to an emergent process that emerges from
cognition. Unlike mind, which is ascribed primarily to humans,
cognition can be attributed to both animals and machines and is
therefore a more useful concept in the context of computational
With respects to the structures (objects) that are processed by
computations, it is possible to discern the following types:
2.1 Subsymbolic computations - data/signal processing
2.2 Symbolic computations - data structures processing
2.3 Hybrid/mixed subsymbolic and symbolic computations.
There are connections between the above types. For instance [19]
differentiates between verbal (linguistic) (symbolic and
subsymbolic) and non-verbal (non-linguistic) (symbolic and
subsymbolic) mental (cognitive) processes. He suggests that the
principle of object formation may be an example of the transition
from a stream of massively parallel subsymbolic micro-functional
events to symbol-type, serial processing through subsymbolic
integration. Even [20] suggests similar connection between
symbolic and subsymbolic (connectionist) computations.
Mental (cognitive, interpretive) computations can be observed at
the following levels:
3.1 Individual (computational network of the brain)
3.2 Group (computational networks of individuals)
3.3 Social (computational networks of groups)
A taxonomy of computation in relation to cognition is provided by
Fresco [21], who notes that, depending on the specific kind of
“information” used, information-processing accounts of
computation may differ greatly. Four main types of information in
this context are given:
3.a Syntactic (Shannon) information
3.b Algorithmic information
3.c Semantic information
3.d Instructional information
2.2 Organizational taxonomy
Organization of computation can be characterized as:
1. Centralized computations where computation is controlled
by a single algorithm.
2. Distributed computations where there are separate algorithms
that control computation in some neighbourhood that is
represented by a node in the computational network.
3. Clustered computations where there are separate algorithms
that control computation in clusters of neighbourhoods.
Turing machines, partial recursive functions and limit Turing
machines are models of centralized computations. Neural
networks, Petri nets and Cellular automata are models of
distributed computations. Grid automata in which some nodes
represent networks with the centralized control and the World
Wide Web are systems that perform clustered computations [4].
Grid automaton is the most advanced abstract model of distributed
computing systems, which performs concurrent computations,
while being a physical distributed computing system.
2.3 Temporal taxonomy
With respect to temporal characteristics, computations can be:
1. Sequential computations, which are performed in linear time.
2. Parallel or branching computations, in which separate steps
(operations) are synchronized in time.
3. Concurrent computations, which do not demand
synchronization in time.
While parallel computation is completely synchronized, branching
computation is not completely synchronized because separate
branches acquire their own time and become synchronized only in
Classical models of computation, such as the classical Turing
machine or partial recursive functions, perform only sequential
computations. Models that appeared later, such as Turing
machines with several heads and tapes or cellular automata,
provide means for parallel computations. There are also various
models for concurrent computations, according to [22].
In this context, the most advanced device model is grid
automaton, while the most advanced operational model, which
also is a process model, is the EAP (event-action-process) model.
All these models form three classes:
3.1 Device models (Petri nets, Kahn process networks,
dataflow process networks, discrete event simulators, grid
automata, the Linda model and the Actors model).
3.2 Operational models (ACP (algebra of communicating
processes), VCR (extended view-centric reasoning),
EVCR (view-centric reasoning) and ESP (event-signal-
process) model).
3.3 Process models (CSP (communicating sequential
processes) model and CCS (composite current source
delay) model.
2.4 Representational taxonomy
With respect to the data representation on which computations are
performed, there are following types of computation:
1. Discrete computations, which include interval computations.
2. Continuous computations, which include fuzzy continuous
3. Hybrid/mixed computations, which include discrete and
continuous processes.
Digital computing devices and the majority of computational
models, such as finite automata, Turing machines, recursive
functions, inductive Turing machines, and cellular automata,
perform discrete computations.
Examples of continuous computations are given by abstract
models, such as general dynamical systems [23] and hybrid
systems [24], and special computing devices, such as the
differential analyzer [25][26].
Hybrid/Mixed computations include piecewise continuous
computations, combining both discrete computation and
continuous computation. Examples of mixed computations are
given by neural networks [27], finite dimensional machines and
general machines of [28].
It is possible to refine the representational taxonomy in the
following way, obtaining three additional classifications.
2.5 Data-based taxonomy
With respect to the data and the domain of computation, the
following possibility exist:
1. The domain of computation is discrete and data are finite.
For instance, data are words in some alphabet.
2. The domain of computation is discrete but data are infinite.
For instance, data are ω-words in some alphabet. This
includes interval computations because real numbers
traditionally are represented as ω-words.
3. The domain of computation is continuous.
2.6 Operational taxonomy
With respect to operations in computation, the following
taxonomy can be found:
1. Operations in computation are discrete and they transform
discrete data elements. For instance, addition or
multiplication of whole numbers.
2. Operations in computation are discrete but they transform
(operate with) continuous sets. For instance, addition or
multiplication of all real numbers or of real functions.
3. Operations in computation are continuous. For instance,
integration of real functions.
2.7 Process-oriented taxonomy
1. The process of computation is discrete, i.e. it consists of
separate steps in the discrete domain, and it transforms
discrete data elements. For instance, computation of a Turing
machine or a finite automaton.
2. The process of computation is discrete but it employs
continuous operations. An example is given by analogue
computations [25][26] as quoted in [4] p. 122.
3. The process of computation is continuous but it employs
discrete operations. For instance, computation of a limit
Turing machine [4] p. 140.
2.8 Computation levels taxonomy
In [6] three generality levels of computations are introduced:
1. At the top and most abstract/general level, computation is
perceived as any transformation of information and/or
information representation.
2. At the middle level, where computation is distinguished as a
discretized process of transformation of information and/or
information representation.
3. At the bottom, least general level, computation is defined as
a discretized process of symbolic transformation of
information and/or symbolic information representation.
There are also spatial levels or scales of computations. Even
though the highest levels subsume the lower ones, computation is
performed/interpreted at a given level, as follows:
1. Macro-level includes computations performed by mechanical
calculators as well as electromechanical devices.
2. Micro-level includes computations performed by integrated
3. Nano-level includes computations performed by fundamental
parts that are not bigger than a few nano meters.
4. Molecular level includes computations performed by
5. Quantum level includes computations performed by atoms
and subatomic particles.
At present there are no commercially available nano-computers,
molecular or quantum computers, but they are being developed.
The earliest idea of computation was application of an algorithm.
The Turing machine model of computation is equivalent to an
algorithm. Thus, the first and most commonly encountered
computational structure is the computational dyad [29]
(computation, algorithm). The computational dyad reflects the
existing duality between computations and algorithms. In 1971
Dijkstra in his A Short Introduction to the Art of Programming
[30] defined an algorithm as a static description of computation,
which is a dynamic state sequence induced in a machine by the
algorithm. Later a more systemic explication of the duality
between computations and algorithms was elaborated. Namely,
computation is a process of information transformation, which is
organized and controlled by an algorithm, while an algorithm is a
system of rules for a computation [4]. In this context, an algorithm
is a compressed informational/structural representation of a
process. A computer program is an algorithm written in
(represented by) a programming language.
Thus, an algorithm is an abstract structure and it is possible to
realize the same algorithm as different programs (in different
programming languages). It is important to understand the
difference between algorithm and its representation or
embodiment. An algorithm is an abstract structure, which can be
represented in a multiplicity of ways: as a computer program, a
control schema, a graph, a system of cell states in the memory of a
computer, a mathematical system, such as an abstract finite
automaton, etc. Interestingly, many people think that neural
networks perform computations without algorithms. However,
this is not true as neural networks algorithms have representations
even though very different from traditional representations of
algorithms as systems of rules/instructions. The neural networks
algorithms are represented by neuron weights and connections
between neurons. This is similar to hardware
representation/realization of algorithms in computers (analog
The computational dyad is a simplification and incomplete
because there is always a system that uses algorithms to organize
and control computation. This observation suggests that the
computational dyad has to be extended to the triangular basic
computational triad (algorithm, computation, device/agent) that
reflects that specifies computation is performed by a device, such
as a computer, or by an agent, such as a human being or bacteria.
Functioning of the device or work of the agent that/who performs
computation is directed or controlled by an algorithm embodied in
a program, plan, scenario or hardware. Consequently, the process
of computation is also directed/controlled by an algorithm.
Note that the computing device can be either a physical device,
such as a computer, or an abstract device, such as a Turing
machine, or a programmed (virtual or simulated) device when a
program simulates some physical or abstract device. For instance,
neural networks and Turing machines are usually simulated by
programs on conventional computers. A Java virtual machine can
be run on different operating systems and is processor- and
operating system- independent. Besides, with respect to
architecture, it can be an embracing device, in which computation
is embodied and exists as a process, or an external device, which
organize and control computation as an external process.
The basic computational triad reflects the structure of the world
represented by the existential triad [17].
In previous sections we presented concept of computation and its
models and developed computational taxonomies in the context of
information processing. Adopting the approach of structural
realism we provided structural framework of computation based
on Burgin’s existential triad (physical, structural, mental/
cognitive) of the world [17]. We have chosen triadic structures as
fundamental elements in our study of structures, based on the
classical triad of Plato (matter, structure, mind), Peirce's triad of
(object, sign, interpretant) and Poppers structural triad (physical
world, knowledge, mentality).
In what follows, we will concentrate on the first two elements of
the existential triad physical and structural in their cognitive
aspect, both of them addressed through the idea of computing
nature (natural computing), [7] [31].
According to the Handbook of Natural Computing [32] natural
computing is “the field of research that investigates both human-
designed computing inspired by nature and computing taking
place in nature.” In particular, it addresses: intrinsic computation
performed by natural materials and computational nature of
processes taking place in nature. Natural computing comprises,
among others, areas of cellular automata and neural computation,
evolutionary computation, molecular, quantum and organic
computing, biocomputing, nature-inspired algorithms.
Knowledge in natural computing is generated bi-directionally,
through the interaction between computer science and natural
sciences. As the natural sciences are promptly absorbing concepts,
tools and methodologies of information processing, computer
science on its side is broadening the notion of computation,
recognizing information processing found in nature as special type
of computation intrinsic, natural computation. [33] [34][35][36]
This development in understanding of computation led Denning to
argue that computer science today is a natural science [37] [38].
In his “Simulating Physics with Computers” Feynman argued that
the specific forms of computation are best carried out by the
physical substrate we are trying to describe [39]. Even though
DNA computation can be emulated in silico, the efficiency of
computing with DNA substrate instead of its digital representation
is higher by many orders of magnitude [40]. Similar view of
physical (material) computation is presented in [41] where it is
argued for clear benefits of intrinsic (material) computation, as in
the Brook’s famous observation that “the world is its own best
model” [42]. Cooper addresses the question of the relationship
between abstract mathematical models and physical computation
that underlies every real-world computation, suggesting that we
are under the spell of the “mathematician bias” and arguing for
the return to embodied computation [43] [44][46]showing how
nature can help us to compute.
4.1 Intrinsic vs. designed computation
We are used to quick increase of computational power, memory
and usability of our computers, but the limit of miniaturization is
approaching as we are getting close to quantum dimensions of
hardware components. We are also facing the explosive increase
in the amounts of data, “big data” and the emergence of the
“internet of things” where computers are becoming an integral
part of practically all devices and indeed of our physical
environment. All of this poses huge demands on effective
computation techniques. Ever since the time of Turing, one of the
ideals was intelligent computing, which would besides mechanical
symbol manipulation include even intelligent problem solving.
That would help us manage complexity and vast amounts of data
that have to be processed, often in real time. In that direction
currently, there is a development of cognitive computing [47]
[50] aimed towards human-level abilities of machines that
process/organize/ and even understand information.
At the same time the development of computational models of
human brain has for a goal to reveal the exact mechanisms of
human brain function ( that
will help us understand not only how humans actually perform
information processing when they follow an algorithm, but also
how humans create algorithms or models in a recursive cascades
of self-reflective computational processes from physical substrate
to information/patterns to mental states through cognitive
computing. Those new developments can be seen as a part of the
research within the field of natural computing, where natural
system performing computation is embodied and embedded
human brain.
The new understanding of computation as complex distributed
concurrent computational system of systems with inspiration in
natural information processing allows among others learning
about nondeterministic complex computational systems, such as
living organisms, with self-* properties (self-organization, self-
configuration, self-optimization, self-healing, self-protection, self-
explanation, and self-awareness). Natural computation has a
potential to provide a basis for a unified understanding of
phenomena of embodied cognition, intelligence and knowledge
generation. [51][47]
Recently, a focus issue of the journal Chaos was dedicated to the
intrinsic and designed computation under the title “Information
Processing in Dynamical SystemsBeyond the Digital
Hegemony” addressing challenges of intrinsic computing in
dynamical systems as complementary to designed computing in
digital systems. [36]
This relates to the view of a brain as a dynamical system
processing information (computing) at different levels of
organization from molecular/electro-chemical, cellular
processes (DNA, protein networks), through neural circuits,
cortical through columns (morphologically distinct regions of the
brain processing and exchanging information), and finally through
the level of whole-brain information integration that is considered
to provide the function of consciousness, [52]. Cellular and
whole-brain levels of computation correspond to the cognition
level of cells and the brain. In a biological sense, cognition is the
property of an autopoietic system, with self-production, self-
organisation and closure and in structural coupling with the
environment. [53]
At this point, there are several avenues of the future development
of computing both in the setting of physical devices and of
theoretical models. Natural computation promises new and
broader ways of understanding of computational processes that
can be found intrinsically in various physical systems. In
connection to that, the structure and its particular case -
architecture of computational processes becomes increasingly
important, especially in the case of cognitive computing.
4.2 Levels of physical organization in natural
computing as natural information processing
In the section on Taxonomy of computation, under the heading
Hierarchy of computation levels, we mentioned levels and scales
of physical organization at which computation is performed in
designed computation. In the case of cognitive computing, the
following levels of designed, nature-inspired computation are
distinguished: synapses, neurons, microcircuits (modeling brains
cortical columns), long range interconnections (modeling axons
function) and the whole-brain level integration of processes,
representing non-von-Neumann architecture:
“overarching cognitive computing architecture is an on-chip
network of light-weight cores, creating a single integrated system
of hardware and software. This architecture represents a critical
shift away from traditional von Neumann computing to a
potentially more power-efficient architecture that has no set
programming, integrates memory with processor, and mimics the
brain’s event-driven, distributed and parallel processing.”
Mikkillineni [15], [16] describes cognitive architectures based on
his Distributed Intelligent Computing Element (DIME)
computing model, consisting of a recursive managed distributed
computing network, which can be viewed as an interconnected
group of such specialized Oracle machinesthatprovides the
architectural resiliency, which is often associated with cellular
organisms, through auto-failover; auto-scaling; live-migration;
and end-to-end transaction security assurance in a distributed
system. Mikkillineni argues that the self-identity and self-
management processes of a DIME networkadd the elements of
cognition into Turing machine type computing. This approach
extends Burgin’s view of computing consisting of hardware,
software and infoware [4] with one more architectural layer
corresponding to cognitive function related to knowledge.
Present account suggests that the concept of computation as
information processing develops together with the constantly
increasing scientific knowledge and tools of analysis [54]. We
present the structural framework of information processing and
computation starting with existential triadic relationships between
(physical, structural, mental/cognitive) and taxonomies of
numerous aspects of computation that follow this basic existential
layered architecture that is paralleled by physico-chemical,
chemo-biological and bio-cognitive levels of information
processing [55]. As there is no information without (physical)
representation [18], the dynamics of information is implemented
on different levels of granularity by different physical processes,
including the level of computation performed by computing
machines (designed computation), as well as by living organisms
(cognitive computation).
We highlight several topics of importance for the development of
new understanding of computation and its role: natural
computation, interactivity as fundamental for computational
modeling of concurrent information processing systems such as
living organisms and their networks, and the new developments in
modeling needed to support this generalized framework for
cognitive architectures [4][16]. In such a way, we achieve better
understanding of computation as information processing on
different levels.
There are still many open problems related to the nature of
information and computation, as well as to their relationships.
How is information dynamics represented in computational
systems, in machines, as well as in living organisms? Are
computers capable of processing only data or information and
knowledge as well, as recent work of Mikkillineni suggests? What
can we know of computational processes in machines and living
organisms and how these processes are related to the
computational architectures? What can we learn from natural
computational processes in cognitive systems that can be useful
for engineered information systems and knowledge management?
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... Infware, that is, objects that are carriers and representations of the processed information, form an imperative constituent of information processing in general and computation in particular. Based on the computational infware, traditionally two pure forms of conventional computations are taken into consideration-symbolic computations and sub-symbolic computations [1]. With respect to infware, both are pure types of computations, while existing and new combined or amalgamated types and forms of computations are studied later. ...
... The combination of pure types produces mixed types of information processing. The first step in this direction gives us hybrid information processing, which comprises both symbolic and sub-symbolic information processing being a two-fold type of information processing and encompassing hybrid computations [1]. Hybrid information processing allows combining advantages of both symbolic and sub-symbolic information processing. ...
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The goal of the paper is the introduction and exploration of new types of information processing. Starting with the typology developed in such an important class of information processing as computation, we extend this typology by analyzing information representations used in computational processes and delineating novel forms of information representations. While the traditional approach deals only with two dimensions of information processing—symbolic and sub-symbolic, our analysis explicated one more dimension—super-symbolic information processing. Information processing in biological systems is both symbolic and sub-symbolic, having the form of genes and neural networks. Nevertheless, in their evolution, biological systems have advanced their abilities one step further by developing super-symbolic information processing and evolving symbiotic information processing that performs information processing on the combined knowledge in the brain from both symbolic, subsymbolic, and super-symbolic information processing to derive higher order autopoietic and cognitive behaviors. Performing all forms of information processing, biological systems achieve much higher cognitive and intelligence level. That is why here we also consider a new type of computing automata called structural machines with the goal of transferring these advantageous features of biological systems to the existing information processing technology.
... A broader understanding of computation that includes dynamical systems solves this apparent contradiction. For the arguments from the theory of computation, see [105,106]. The free energy principle addresses this challenge by developing a physics of sentience combining dynamical systems theory with the boundary separating self from nonself. ...
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Cognition, historically considered uniquely human capacity, has been recently found to be the ability of all living organisms, from single cells and up. This study approaches cognition from an info-computational stance, in which structures in nature are seen as information, and processes (information dynamics) are seen as computation, from the perspective of a cognizing agent. Cognition is understood as a network of concurrent morphological/morphogenetic computations unfolding as a result of self-assembly, self-organization, and autopoiesis of physical, chemical, and biological agents. The present-day human-centric view of cognition still prevailing in major encyclopedias has a variety of open problems. This article considers recent research about morphological computation, morphogenesis, agency, basal cognition, extended evolutionary synthesis, free energy principle, cognition as Bayesian learning, active inference, and related topics, offering new theoretical and practical perspectives on problems inherent to the old computationalist cognitive models which were based on abstract symbol processing, and unaware of actual physical constraints and affordances of the embodiment of cognizing agents. A better understanding of cognition is centrally important for future artificial intelligence, robotics, medicine, and related fields.
... There is a variety of techniques for composition of algorithms and computing devices [55]. These compositions induce corresponding compositions of computational information operators. ...
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Defining computation as information processing (information dynamics) with information as a relational property of data structures (the difference in one system that makes a difference in another system) makes it very suitable to use operator formulation, with similarities to category theory. The concept of the operator is exceedingly important in many knowledge areas as a tool of theoretical studies and practical applications. Here we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, processes, and their networks.
... Information and computation have been objects of extensive study in (Dodig-Crnkovic and Burgin, 2011). Parallel to the taxonomy of information, taxonomy of computation has been developed in (Burgin and Dodig-Crnkovic, 2015) to describe classification of the dynamical phenomena involved in information processes. ...
... Research has already elicited several aspects that are relevant in this context. An overview of existing approaches to computation and information architecture is provided by [1], distinguishing among others the different types of information that are processed, from subsymbolic computation focusing on data and signal processing to symbolic computation that processes data structures, thus reflecting different levels of abstraction. In [2], patterns for cognitive systems are investigated into, focusing on systems that process textual information, yet indicating that other kind of information, such as cognitively interpreted sensory data, will be addressed by cognitive systems in the near future, thus entering into new dimensions of machine cognition. ...
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Many technical work places, such as laboratories or test beds, are the setting for well-defined processes requiring both high precision and extensive documentation, to ensure accuracy and support accountability that often is required by law, science, or both. In this type of scenario, it is desirable to delegate certain routine tasks, such as documentation or preparatory next steps, to some sort of automated assistant, in order to increase precision and reduce the required amount of manual labor in one fell swoop. At the same time, this automated assistant should be able to interact adequately with the human worker, to ensure that the human worker receives exactly the kind of support that is required in a certain context. To achieve this, we introduce a multilayer architecture for cognitive systems that structures the system's computation and reasoning across well-defined levels of abstraction, from mass signal processing up to organization-wide, intention-driven reasoning. By partitioning the architecture into well-defined, distinct layers, we reduce complexity and thus facilitate both the implementation and the training of the cognitive system. On this basis, we outline the functional modules of a cognitive system supporting the execution of partially manual processes in technical work places.
At the time when the first models of cognitive architectures have been proposed, some forty years ago, understanding of cognition, embodiment and evolution was substantially different from today’s. So was the state of the art of information physics, information chemistry, bioinformatics, neuroinformatics, computational neuroscience, complexity theory, self-organization, theory of evolution, as well as the basic concepts of information and computation. Novel developments support a constructive interdisciplinary framework for cognitive architectures based on natural morphological computing, where interactions between constituents at different levels of organization of matter-energy and their corresponding time-dependent dynamics, lead to complexification of agency and increased cognitive capacities of living organisms that unfold through evolution. Proposed info-computational framework for naturalizing cognition considers present updates (generalizations) of the concepts of information, computation, cognition, and evolution in order to attain an alignment with the current state of the art in corresponding research fields. Some important open questions are suggested for future research with implications for further development of cognitive and intelligent technologies.
This book mainly focuses on the widely distributed nature of computational tools, models, and methods, ultimately related to the current importance of computational machines as mediators of cognition. An entirely new eco-cognitive approach to computation is offered, to underline the question of the overwhelming cognitive domestication of ignorant entities, which is persistently at work in our current societies. Eco-cognitive computationalism does not aim at furnishing an ultimate and static definition of the concepts of information, cognition, and computation, instead, it intends, by respecting their historical and dynamical character, to propose an intellectual framework that depicts how we can understand their forms of “emergence” and the modification of their meanings, also dealing with impressive unconventional non-digital cases. The new proposed perspective also leads to a clear description of the divergence between weak and strong levels of creative “abductive” hypothetical cognition: weak accomplishments are related to “locked abductive strategies”, typical of computational machines, and deep creativity is instead related to “unlocked abductive strategies”, which characterize human cognizers, who benefit from the so-called “eco-cognitive openness”.
In the first two chapters of this book we have stressed that eco-cognitive computationalism sees computation in context, following some of the main tenets advanced by the recent cognitive science views on embodied, situated, and distributed cognition. We have also described the new attention in computer science devoted to the relevance in computation of the morphological features. It is by further deepening and analyzing the perspective opened by these novel fascinating approach that we see ignorant bodies as domesticated to become useful “mimetic bodies” from a computational point of view.
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Eco-cognitive computationalism considers computation in context, following some of the main tenets advanced by the recent cognitive science views on embodied, situated, and distributed cognition. It is in the framework of this eco-cognitive perspective that we can usefully analyze the recent attention in computer science devoted to the importance of the simplification of cognitive and motor tasks caused in organic entities by the morphological features: ignorant bodies can be domesticated to become useful “mimetic bodies”, that is able to render an intertwined computation simpler, resorting to that “simplexity” of animal embodied cognition, which represents one of the main quality of organic agents. Through eco-cognitive computationalism we can clearly acknowledge that the concept of computation changes, depending on historical and contextual causes, and we can build an epistemological view that illustrates the “emergence” of new kinds of computations, such as the one regarding morphological computation. This new perspective shows how the computational domestication of ignorant entities can originate new unconventional cognitive embodiments. In the last part of the article I will introduce the concept of overcomputationalism, showing that my proposed framework helps us see the related concepts of pancognitivism, paniformationalism, and pancomputationalism in a more naturalized and prudent perspective, avoiding the excess of old-fashioned ontological or metaphysical overstatements.
The number of digital resources that exist in repositories and on the Internet in general is enormous. Recovering resources that fit with the user’s specific needs poses a problem. To solve this problem, metainformation is added to the resources. One type of metainformation is the classification of a resource using a classification system that is widely recognised and agreed upon by its users. In this way, each resource is assigned a precise place within the classification system, thus facilitating its location. This article proposes a taxonomy for the classification of the resources (notes, exercises, exams or programmes that could be stored within a digital repository) that are generated within the scope of a Mathematical Logic course for a computer science degree programme. It also describes how to represent the proposed taxonomy using the IMS-VDEX standard and how to integrate it in the LOM and Dublin Core metadata specifications and proposes a set of controlled vocabularies that make it possible to refine the taxonomic metainformation.
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This book is about nature considered as the totality of physical existence, the universe and our present day attempts to understand it. If we see the universe as a networks of networks of computational processes of many different levels of organization, we can learn from different sciences the processing of interacting elementary particles.
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The development of models of computation induces the development of technology and natural sciences and vice versa. Current state of the art of technology and sciences, especially networks of concurrent processes such as Internet or biological and sociological systems, calls for new computational models. It is necessary to extend classical Turing machine model towards physical/ natural computation. Important aspects are openness and interactivity of computational systems, as well as concurrency of computational processes. The development proceeds in two directions - as a search for new mathematical structures beyond algorithms as well as a search for different modes of physical computation that are not equivalent to actions of human executing an algorithm, but appear in physical systems in which concurrent interactive information processing takes place. The article presents the framework of infocomputationalism as applied on computing nature, where nature is an informational structure and its dynamics (information processing) is understood as computation. In natural computing, new developments in both understanding of natural systems and in their computational modelling are needed, and those two converge and enhance each other.
In recent years, classical computability has expanded beyond its original scope to address issues related to computability and complexity in algebra, analysis, and physics. The deep interconnection between "computation" and "proof" has originated much of the most significant work in constructive mathematics and mathematical logic of the last 70 years. Moreover, the increasingly compelling necessity to deal with computability in the real world (such as computing on continuous data, biological computing, and physical models) has brought focus to new paradigms of computation that are based on biological and physical models. These models address questions of efficiency in a radically new way and even threaten to move the so-called Turing barrier, i.e. the line between the decidable and the un-decidable. This book examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. The book opens with an introduction by Andrew Hodges, the Turing biographer, who analyzes the pioneering work that anticipated recent developments concerning computation’s allegedly new paradigms. The remaining material covers traditional topics in computability theory such as relative computability, theory of numberings, and domain theory, in addition to topics on the relationships between proof theory, computability, and complexity theory. New paradigms of computation arising from biology and quantum physics are also discussed, as well as the computability of the real numbers and its related issues. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.
Designing a New Class of Distributed Systems closely examines the Distributed Intelligent Managed Element (DIME) Computing Model, a new model for distributed systems, and provides a guide to implementing Distributed Managed Workflows with High Reliability, Availability, Performance and Security. The book also explores the viability of self-optimizing, self-monitoring autonomous DIME-based computing systems. Designing a New Class of Distributed Systems is designed for practitioners as a reference guide for innovative distributed systems design. Researchers working in a related field will also find this book valuable.
This book presents a study of digital computation in contemporary cognitive science. Digital computation is a highly ambiguous concept, as there is no common core definition for it in cognitive science. Since this concept plays a central role in cognitive theory, an adequate cognitive explanation requires an explicit account of digital computation. More specifically, it requires an account of how digital computation is implemented in physical systems. The main challenge is to deliver an account encompassing the multiple types of existing models of computation without ending up in pancomputationalism, that is, the view that every physical system is a digital computing system. This book shows that only two accounts, among the ones examined by the author, are adequate for explaining physical computation. One of them is the instructional information processing account, which is developed here for the first time."This book provides a thorough and timely analysis of differing accounts of computation while advancing the important role that information plays in understanding computation. Frescos two-pronged approach will appeal to philosophically inclined computer scientists who want to better understand common theoretical claims in cognitive science.Marty J. Wolf, Professor of Computer Science, Bemidji State University An original and admirably clear discussion of central issues in the foundations of contemporary cognitive science. Frances Egan, Professor of Philosophy, Rutgers, The State University of New Jersey
This volume, with a foreword by Sir Roger Penrose, discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays, representing a field that assumes information and computation to be key in understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's “Calculating Space” (the MIT translation), and a panel discussion transcription on the topic, featuring worldwide experts in quantum mechanics, physics, cognition, computation and algorithmic complexity. The volume is dedicated to the memory of Alan M Turing — the inventor of universal computation, on the 100th anniversary of his birth, and is part of the Turing Centenary celebrations. © 2013 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.