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To produce a software formally, you must first do a requirement analysis
and write requirement document:
IN your requirement, you will have all of the questions, like:
What are you going to do?
Are these requirements possible?
How are these requirements imlemented?
How much time are allocated for each task?
Requirement analysis is a must process in software engineering.
As a matter of fact, good software Co. have a good specification in every customer requirement
and implememtation. It can make everything clear to avoid many unnecessary works.
After this, the software engineers will follow the requirement documents to implement
the specification.
For P and NP problem, Sat. function f (X 1, X 2, ..., X i, ... X n) evaluate to true, this require minimum
2 ^ n calculation or data items. Each calculation complexity depend on the Sat. function f itself.
So the overall complexity is at least as complex as exponential.
No one can break this minimum for 'NP compleness' because if you do not even see every data item
once, how can you produce your products.
There is no magic, this is a self-evident axiom or natural law.
If , however, each data item need to be processed polynomially, the overall time complexity will
increase to 2 ^ p, where p is polynomial.
Sat. problem require most efficient, and most difficult format as its representative function,
otherwise if you take an easy Xs combination as its function, the time complexity can be polynomial
or even constant, and you can get P = NP but the answer is wrong due to losing 'complete' meaning.
Therefore, don't overlook a 'simple' Sat. function, it can contain enormous amount of data,
this function is not easy to built. However, for a fixed number of Xs, its complexity
and format can and should have fixed form.
After the software is built, the validation time is of course P (polynormial), however,
its building time is at least 2 ^ n (=! P), therefore P =! NP.
This has strickly proved P != NP as Sat. function need at least 2 ^ n time complexity to implement
if it is a 'NP complete' problem.
After this proof, it become a theorem, next blog will give a more complete typical sample of this proof.
There are many practical problems in P and NP problem and its related definitions.
Some problems are typical NP 'complete' while others are not as they are claimed to be.
Nevertheless, this is a very good problem for IT professionals to practice to some standards.
The next stages in software engineering are:
Software development;
Software test;
Software deployment;
Software maintenance.
I don't know why some IT professinals can firmly stuck on P = NP. Can anyone give an answer?
As you can reason, there is no way to reduce the minimum time.
Wrong implementation will lose lots of works or money, how can you say 'win'? Don't be a 'vampire'.
'Qualification' is not university, or anything else, a large number of doctor degree theses are actually
not over passing degree. This happen to your imported 'professionals'.
There exist big problems in 'telants plan' in every respect.
Hope this will save you lot of time in future. Taking some time to do analysis will eventually save
much more time.
I read a book about plasma by Mr. Chen, a very good book but unfortunately, contain many or too many
errors.
Anyway, thanks Mr. Chen and many others.
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