Computation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking. In a more narrow meaning, computation is a process following a well defined model that is understood and can be expressed in an algorithm, protocol, network topology, etc.

Classes of computation

In practice, digital computation is often used to simulate natural processes (for example, Evolutionary computation), including those that are more naturally described by analog models of computation (for example, Artificial neural network). In this situation, it is important to distinguish between the mechanism of computation and the simulated model.

Computations as a physical phenomenon

An even more drastic point of view is the postulate of digital physics that the evolution of the universe itself is a computation.

Mathematical models of computation

In the theory of computation, mathematical models of computers are defined. A computation is the evolution over discrete time epochs of this model. Typical mathematical models of computers are the following:

Different mathematical models of computers can be classified according to their expressive power, see the Chomsky hierarchy.

Human Media Interaction (HMI):

Intelligent Agents

Computational Intelligence

<http://hmi.ewi.utwente.nl/topic/Computational%20Intelligence>

Computational Intelligence is a research area within Artificial Intelligence opposing itself to the traditional, symbolic oriented, AI. The reason is that symbolic AI is applicable in formal defined domains such as chess, but not for every day problems such as vision, speech recognition, dealing with ambiguous data, natural language processing etc. New techniques and methods, inspired by nature were developed to tackle these problems. The techniques and methods include evolutionary computing, fuzzy computing, swarm intelligence, ant systems andneuro-computing.

The main difference is that classical artificial intelligence techniques are top-to-bottom where the structure of models, solutions, parameter settings are all imposed from above by the designer.

Computational intelligence techniques are in general bottom-up, where order and structure emerges from an unstructured beginning and is learned from data from, or interaction with, the environment.

Within the Parlevink group Computational Intelligent Techniques are used, among other things, in the development of Intelligent Embodied Agents situated in Virtual Environments, Conversational Agents and in Robot Soccer.

Information Engineering:

<http://hmi.ewi.utwente.nl/topic/Information%20Engineering>

Now information is available in electronic form, it's about time we let our machines do something useful with it.

Authors are constrained because traditionally they can only write a sequential narrative; readers are frustrated because they can only consume information the way it was written by the author, if they can find it at all. Information engineering can free them both.

Information Engineering is a technology strongly guided by the social and economic environment in which information is exchanged. It studies ways to structure and store content and to make it accessible to others.

Important research subjects in information engineering are:

* Information retrieval: text retrieval, XML retrieval, retrieval interfaces, multimedia retrieval, retrieval for scientists

* Information representation, both for humans and machines: information visualisation, knowledge representation, XML

* Security: digital rights management, encryption, intellectual property

* Information in a business perspective: organisational aspects, business models, value chains

At HMI, important application areas are: bioinformatics and chemoinformatics, medical information, information for education, publishing industry.

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Theory of computation

From Wikipedia, the free encyclopedia

<http://en.wikipedia.org/wiki/Theory_of_computation>

The theory of computation is the branch of computer science that deals with whether and how efficiently problems can be solved on a computational model, using an algorithm. The field is divided into two major branches: computability theory and complexity theory, but both branches deal with formal models of computation.

In order to perform a rigorous study of computation, computer scientists work with a mathematical abstractions of computers called a model of computation. There are several formulations in use, but the most commonly examined is the Turing machine. A Turing machine can be thought of as a desktop PC with an infinite memory capacity, though it can only access this memory in small discrete chunks. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" model of computation. While the infinite memory capacity might be considered an unphysical attribute, for any problem actually solved by a Turing machine the memory used will always be finite, so any problem that can be solved on a Turing machine could be solved on a desktop PC which has enough memory installed.

Other formal definitions of computation

Aside from a Turing machine, other equivalent (See: Church-Turing thesis) models of computation are in use.

lambda calculus: A computation is an initial lambda expression (or two if you want to separate the function and its input) plus a finite sequence of lambda terms, each deduced from the preceding term by one application of Beta reduction.

Combinatory logic: is a concept which has many similarities to $Î»$ -calculus, but also important differences exist (e.g. fixed point combinator Y has normal form in combinatory logic but not in $Î»$ -calculus). Combinatory logic was developed with great ambitions: understanding the nature of paradoxes, making foundations of mathematics more economic (conceptually), eliminating the notion of variables (thus clarifying their role in mathematics).

mu-recursive functions: a computation is a mu-recursive function, i.e. its defining sequence, any input value(s) and a sequence of recursive functions appearing in the defining sequence with inputs and outputs. Thus, if in the defining sequence of a recursive function $f (x)$ the functions $g (x)$ and $h (x, y)$ appear, then terms of the form 'g(5)=7' or 'h(3,2)=10' might appear. Each entry in this sequence needs to be an application of a basic function or follow from the entries above by using composition, primitive recursion or mu recursion. For instance if $f (x) = h (x, g (x))$ , then for 'f(5)=3' to appear, terms like 'g(5)=6' and 'h(3,6)=3' must occur above. The computation terminates only if the final term gives the value of the recursive function applied to the inputs.

Markov algorithm: a string rewriting system that uses grammar-like rules to operate on strings of symbols.

Register machine

is a theoretically interesting idealization of a computer. There are more variants. In most of them, each register can hold a natural number (of unlimited size), and the instructions are simple (and few in number), e.g. only decrementation (combined with conditional jump) and inrementation exist (and halting). The lack of the infinite (or dynamically growing) external store (seen at Turing machines) can be understood by replacing its role with GÃ¶del numbering techniques: the fact that each register holds a natural number allows the possibility of representing a complicated thing (e.g. a sequence, or a matrix etc.) by an appropriate huge natural number â€” unambiguity of both representation and interpretation can be established by number theoretical foundations of these techniques.

P~: Like Turing machines, P~uses an infinite tape of symbols (without random access), and a rather minimalistic set of instructions. But these instructions are very different, thus, unlike Turing machines, Pâ€²â€² does not need to maintain a distinct state, because all "memory-like" functionality can be provided only by the tape. Instead of rewriting the current symbol, it can perform a modular arithmetic incrementation on it. Pâ€²â€² has also a pair of instructions for a cycle, inspecting the blank symbol. Despite its minimalistic nature, it has become the parental formal language of an implemented and (for entertainment) used programming language called Brainfuck.

In addition to the general computational models, some simpler computational models are useful for special, restricted applications. Regular expressions, for example, specify string patterns in many contexts, from office productivity software to programming languages. Another formalism mathematically equivalent to regular expressions, Finite automata are used in circuit design and in some kinds of problem-solving. Context-free grammars specify programming language syntax. Non-deterministic pushdown automata are another formalism equivalent to context-free grammars. Primitive recursive functions are a defined subclass of the recursive functions.

Different models of computation have the ability to do different tasks. One way to measure the power of a computational model is to study the class of formal languages that the model can generate; this leads to the Chomsky hierarchy of languages.

Further information: Introduction to Automata Theory, Languages, and Computation

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Fitzpatrick compares history of scientific computing in the United States, former Soviet Union

<http://www.unm.edu/news/Releases/02-09-11fitzpatrick.htm>

Fitzpatrick’s research will also examine how information technology has evolved and will continue to develop into the early 21st century. The goal of the grant is to produce a manuscript tentatively titled, “The Simulation Revolution,” scheduled for late 2004 or early 2005.

“Computing is now a central means of inquiry into the natural world, ubiquitous everywhere from astrophysics to complexity studies to molecular biology, yet we understand very little about both its history and the present impact it is having on the way science is conducted,” she said.

“The Soviet Union treated computing in a very different way than was the case here, given that commercial for-profit computing was antithetical to communism, and other factors. Soviet computer science generally (like many Soviet scientific fields) took on a more theoretical character than the Americans’ and they made some remarkable achievements,” she says.

For the 21st century, it is crucial to sort out as clearly as possible the role that computing will play, she says. At present, Japan claims to have the world’s fastest supercomputer in Yokohama. The Russians have no domestic computer industry (and about 80 percent of all software sold is pirated). Much of American software and low-end computing is for entertainment purposes.

Many factors motivated Fitzpatrick to do this project. At an early age she was fascinated by rockets, space travel and especially nuclear weapons. “I remember the furor over Three Mile Island, when I was still a child, and the duck-and-cover drills even as late as third grade, when we hid lined up in the school hallways with faces to the wall and hands locked behind our heads, pretending that Griffiss Air Force Base, nearby, had been hit by the Soviets. I wanted to know why nuclear energy and technology was both wonderful and dangerous, and why my father, a U.S. Marine who had fought in the Pacific during the second world war, vehemently insisted that Fat Man and Little Boy had saved his life and therefore mine.”

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Computational Models:

Computation

From Wikipedia, the free encyclopedia

Classes of computation

Computations as a physical phenomenon

Mathematical models of computation

Human Media Interaction (HMI):

Intelligent Agents

Computational Intelligence

Information Engineering:

Theory of computation

From Wikipedia, the free encyclopedia

Other formal definitions of computation

Fitzpatrick compares history of scientific computing in the United States, former Soviet Union

A Critical Review of the Notion of the Algorithm in Computer Science