If all else fails, assume good faith. If people are trying to upset you, they will be thwarted by your reaction. If people really are acting in good faith, then your reaction is correct.

> It sounds like you know exactly what
> I'm asking, but are being intentionally
> obtuse.

No, I really don't know what you're asking. It sounds like you're asking people simply to give you big, hard instances of problems that are known to be NPC. If that's what you're asking, why don't you just say so? What's the nonsense with "theoretical" and other things? If it's not what you're asking, then what are you asking?

>> ... and there is no way I can give you that data.

> Can't give because it's physically and/or logically
> impossible? Or, because you or your superior authority
> prefer not to?

It's commercially sensitive data. People are paying us money to provide systems that solve problems like this. We do it better than anyone else currently does, and we get paid for it. We are contractually obliged to keep the data secure, and we are obliged by commercial concerns not to pass it on anyway.

>>> Further, I'm not sure of the precise way
>>> to measure the complexity of the algorithm
>>> when just given a list of integers in ASCII.
>>> I assume you really need to analyze things
>>> at the bit level, instead of just the number
>>> of ASCII characters.

>> Largely it's the same thing.

> Largely, but not precisely. A proof would need
> to be formulated in terms of bits.

If you have it in terms of bytes, multiply by eight. Scalar factors simply don't matter in this field, they really don't. If you can put the instance in a file, simply count the bytes in the file. In the end it comes to the same thing because we are talking about big-Oh-type things - worst cases and limits

>> If marketed properly, people will throw
>> money at you to solve their instances.

> I think part of my question implies, "How
> do you market such an algorithm? At the
> end of the day, you need instances to feed
> the solver. How you get those instances
> into the solver?"

So is this your problem/question:

We have a program that solves instances of
problem X, which is NPC. We claim it's
polynomial, but need to test it. Please
can someone give us instances they believe
are difficult so we can prove our program
is worth looking at.

Is that what you're asking?

Which NPC problem does the algorithm/program solve?

> Assume you have everyone throwing money
> at you. Which instances do you solve given
> the resources you have? Picking the largest
> bundle of cash headed your way doesn't seem
> like it would necessarily give you the 'best
> results' (in terms of benefit, as described
> previously).

I don't understand why you're asking about "best results" - the market will sort that for you. Get a reputation for solving instances of problems believed to be hard, and the people who will derive the best benefit will have the greatest incentive to offer you the most money. Or just solve the one that gets you the most money and buy another machine.

Understand this - what you're asking, and this entire conversation - just doesn't make sense to me. Either you're not being honest, or there is a complete mis-match between our respective understandings of the whole problem area. Going back to my first paragraph I'll assume the latter. I just don't understand why you are saying what you're saying.

So let me ask this. Is this your question:

I claim to have solved P=NP by constructing
a program/machine that solves hard instances
problem X - known to be NPC. I need to test
it and prove to people that it works. How
do I do that?

If that's your question then

* I have no idea why you were ever talking about "theoretical" problems,

* I have some suggestions,

* I'd like to know what problem X is.

If that's not your question, perhaps you should re-read this thread and simply start again with a simple, single, clear question.