Algorthm help required

Hi

Can someone explain to me or point me in the right direction in answering the following question? Please dont just say Yes/No

Can we always find an algorithm to solve a problem?


any help is appreciated.
thanks alot

You can't find an algorithm to solve a problem.
Algorithm is to formulate solution of a past-problem
for easing programming.
But the moment you get solution of a problem
It's no more a problem.
More accurately, you don't have solution of any problem.
Hope this clears ur question !
Anupam

i interpreted this question as meaning, is every problem solvable? i dont know if that's u meant, but the obvious answer is no. an example? write an algorithm that can factor numbers as large as X * 10^100! (in a reasonable amount of time please). if u can do this you'll be a rich rich rich riiiiiiiich person,(or be kidnapped by the NSA)

An answer is not so simple... In fact ther's a subject that studies this question, it's theoretical computer science.

However the right answer is no, cause we never can solve the HALT problem.
HALT is (should be) a predicate that for every y (y is a number that identifies a program in an univocal way) can says if y stop or not on input x.
Well, HALT(x,y) is not a computable predicate.

Proof:
Suppose that HALT(x,y) were computable, then we could construnct the program

Let y0 thne number of the program so constructed, then we have:
HALT(x,y0) <=> ~HALT(x,x)
but if we set x=y0
HALT(y0,y0) <=> ~HALT(y0,y0)
that is a contradiction.

This is only a small proof of this sucx... hem... beautiful and useful subject

You've been reading CRYPTONOMICON, haven't you?

No, I've not read CRYPTONOMICON, I've only done an examination of theoretical computer science (BLEAHHH...).