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Subject: Re: Never Say "Impossible"

Author: Robert Hyatt

Date: 07:07:06 05/09/01

Go up one level in this thread


On May 09, 2001 at 03:39:42, Uri Blass wrote:

>On May 09, 2001 at 01:11:50, Dann Corbit wrote:
>
>>On May 09, 2001 at 00:41:38, Uri Blass wrote:
>>[snip]
>>>No
>>>Chess is clearly polynomial and even O(1) like every solvable problem that is a
>>>practical problem.
>>>
>>>You need constant time to solve chess when the problem is only that the constant
>>>is large.
>>>
>>>The only problems that are exponential are problems when the size of the input
>>>has no finite upper bound.
>>>You can see the input of every practical problem in the world as something that
>>>has an upper bound so saying that an algorithm is not O(1) has only mathematical
>>>meaning and not practical meaning.
>>
>>Unbelievable that you also do not understand Big-O notation.
>
>I responded to the sentence of Hyatt:
>"In the case of chess it is clearly exponential, which is _not_ any form of a
>polynomial."
>
>I did not say that O(1) is not also O(exp(n)).
>I understand from the sentence of Hyatt that chess is not O(1) and even not
>O(n^500000)
>


You understood correctly.


><snipped>
>>I suggest that you read my other posts on the topic.
>>
>>Anyone who says that an O(1) process is not O(exp(n)) does not know what the
>>notation means!!!
>>
>>Anyway, you can say what O(f(n)) is by looking only at the algorithms not the
>>data.  Do you really understand this!?
>
>I understand what you mean but
>Every algorithm when there is a bound on the size of the data is practically
>O(1) because exp(constant) is another constant.
>
>Algorithms to solve problem like sort can be described theoretically
>as not O(1) because there is not a finite upper bound for the number of elemnts
>by definition.

This is not the definition of bit-Oh.  It is a notation that tells you how hard
you have to work as you increase the number of inputs.  If the work increases
linearly with the inputs, it is a linear function.  If it increases
exponentially with the number of inputs it is an exponential function.



>
>For practical purposes you can say that there is a finite upper bound so you can
>say that Solving the practical problems can be done in O(1) when the only
>problem is the constant.

That would be true of _any_ algorithm and would make big-Oh notation
worthless.

We just say everything is O(1) because _no_ algorithm can terminate when given
an infinite number of input values.




>
>Algorithms to solve problem like chess,go or other games can be described as
>O(1).
>
>Uri


Only by someone that hasn't had a complexity theory class.




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