What is the Fundamental Theorem of Computer Science?

In summary, the conversation discusses various fields within computer science such as information theory, information processing, and artificial neural networks. The concept of sigmoid transfer functions is identified as a common attribute between digital processing and processing by ANNs and is also mentioned in relation to quantum computers. However, there is no formally named Fundamental Theorem of Computer Science, though there are various important theorems in different fields within computer science.
  • #1
Phrak
4,267
6
What is the Fundamental Theorem of Computer Science?

No such formally named theorem exists if I do a google search. But I'm very curious as to what students and professors of Computer Science might think it should be.

Anyone?
 
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  • #3
Thanks story645, you've put some thought into this. And I'm suprised by your response.

I was uncertain as to what to ask, and still am--as far as category: should it be computer science, information theory, information processing, and belatedly information science. I'll look over your links
 
  • #4
That has to be Lubarsky's Law of Cybernetic Entomology (which itself is a consequence of Murphy's Sixth Law), and its two corollaries.
 
  • #5
Phrak said:
should it be computer science, information theory, information processing, and belatedly information science
They're all sort of different fields, with the latter three sort of being subsets of the first and connected to each other. Information theory has it's own big theorems, one of them having to do with thermodynamic entropy.
 
  • #6
story645 said:
They're all sort of different fields, with the latter three sort of being subsets of the first and connected to each other. Information theory has it's own big theorems, one of them having to do with thermodynamic entropy.

One day I'll have to pick-up information theory again.

In studying artificial neuro-networks, I asked what is in common between digital processing and processing by ANNs? --and perhaps biological processing as well? The one common attribute I could discover is that they both rely on sigmoid transfer functions.

In a software implementation of ANN's, the inputs to a gate are first summed than passed to a nonlinear transfer function such as arctan. In hardware, a saturation characteristics of an amplifier can be used.

In digital processing the reliance on sigmoid transfer functions is not so obvious. But without it, the state of ones and zeros would ultimately become mixed by noise. I don't believe one could implement a two input gate without saturation conditions.

Quantum computers are another matter. They may not fit into the scheme.
 

What is the Fundamental Theorem of Computer Science?

The Fundamental Theorem of Computer Science states that any algorithmic problem can be solved using a computer as long as it can be represented in a formal way and is computable.

Why is the Fundamental Theorem of Computer Science important?

The Fundamental Theorem of Computer Science is important because it proves the universality of computers, meaning that any problem that can be solved can be solved using a computer. This has led to the development of advanced technology and has greatly impacted fields such as mathematics, engineering, and artificial intelligence.

How does the Fundamental Theorem of Computer Science relate to Turing machines?

The Fundamental Theorem of Computer Science is derived from the concept of Turing machines, which are theoretical machines that can solve any computable problem. The theorem states that any problem that can be solved by a Turing machine can also be solved using a computer.

What are some examples of problems that can be solved using the Fundamental Theorem of Computer Science?

Some examples of problems that can be solved using the Fundamental Theorem of Computer Science include sorting algorithms, graph theory problems, and mathematical calculations. Essentially, any problem that can be represented in a formal way and is computable can be solved using a computer.

Is the Fundamental Theorem of Computer Science applicable to all types of computers?

Yes, the Fundamental Theorem of Computer Science is applicable to all types of computers, including classical computers, quantum computers, and even future technologies that may be developed. As long as the problem is computable, it can be solved using a computer according to this theorem.

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