One of the most common ways used to prove algorithmic correctness is mathematical induction, isn't it? Sarad. --- "R.A. Hettinga" wrote:

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iTWire -

Want to be a computer scientist? Forget maths

By Stuart Corner

Thursday, 05 July 2007

A new book seeks to demolish the concept that computer science is rooted in mathematics and, in particular that the notion of the algorithm is fundamental to computer science.

In particular, he says the notion of the algorithm, "has been largely ineffective as a paradigm for computer science." Fant argues that, because mathematicians, notably John Von Neumann and Alan Turing, were intimately involved with the early development of digital electronic computers in the 1940s they transplanted a mathematical model of computation, including the algorithm - commonly understood to be an exact prescription, defining a computational process, leading from various initial data to the desired result - into the fledgling science of computers.

He claims that "What is essentially a discipline of pure mathematics has come to be called "the theory of computer science," and "the notion of the algorithm has been decreed to be a fundamental paradigm of computer science" However, he says this mathematical perspective "is the wrong point of view" and is asking the wrong questions.

"Mathematicians and computer scientists are pursuing fundamentally different aims, and the mathematician's tools are not as appropriate as was once supposed to the questions of the computer scientist. The primary questions of computer science are not of computational possibilities but of expressional possibilities. Computer science does not need a theory of computation; it needs a comprehensive theory of process expression."

This concept of 'process expression' is, he says, a common thread running through the various disciplines of computer science. "A logic circuit is an expression of a logical process; an architecture is an expression of a continuously acting process to interpret symbolically expressed processes; a program is a symbolic expression of a process; a programming language is an environment within which to create symbolic process expression; a compiler is an expression of a process that translates between symbolic process expressions in different languages; an operating system is an expression of a process that manages the interpretation of other process expressions; any application is an expression of the application process."

And, he argues, important process expressions do not qualify as algorithms. "A logic circuit is not a sequence of operations. An operating system is not supposed to terminate, nor does it yield a singular solution. An operating system cannot be deterministic because it must relate to uncoordinated inputs from the outside world. Any program utilising random input to carry out its process, such...is not an algorithm."

"The notion of the algorithm," he concludes "simply does not provide conceptual enlightenment for the questions that most computer scientists are concerned with."

Fant is the founder and CEO of Theseus Research, a consulting firm specialising in the design and implementation of real-time image processing systems as well as ongoing research into the theory of computers. "Computer Science Reconsidered: The Invocation Model of Process Expression" is published by John Wiley.

-- ----------------- R. A. Hettinga The Internet Bearer Underwriting Corporation http://www.ibuc.com/ 44 Farquhar Street, Boston, MA 02131 USA "... however it may deserve respect for its usefulness and antiquity, [predicting the end of the world] has not been found agreeable to experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire'

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