Abstract
P vs. NP problem is very important research direction in computation complexity theory. In this paper author, by an engineer’s viewpoint, establishes universal multiple-tape Turing-machine and k-homogeneous multiple-tape Turing-machine, and by them we can obtain an unified mathematical model for algorithm-tree, from the unified model for algorithm-tree, we can conclude that computation complexity for serial processing NP problem if under parallel processing sometimes we can obtain P=NP  in time-complexity, but that will imply another NP, non-deterministic space-complexity NP, i.e., under serial processing P≠NP  in space-complexity, and the result is excluded the case of NP problem that there exists a faster algorithm to replace the brute-force algorithm, and hence we can proof that under parallel processing time-complexity is depended on space-complexity, and vice verse, within P vs. NP problem, this point is just the natural property of P vs. NP problem so that “P≠NP ”.
Highlights
P vs. NP problem is an important problem in computation complexity theory
The complexity is main property of an algorithm, the complexity becomes to an important standard in algorithm analysis
Many NP problems have to waste so long time, or so many processors, that the problem is unsolvable in actual fact
Summary
P vs NP problem is an important problem in computation complexity theory. It is from both time-complexity and space-complexity of deterministic/non-deterministic Turing-machine. The complexity is main property of an algorithm, the complexity becomes to an important standard in algorithm analysis. To these/this algorithms/algorithm we must do the algorithm analysis to optimize it. Complexity, includes time-complexity and space-complexity, is just main method to estimate algorithm cost. P vs NP problem is yielded from complexity analysis of algorithm. The hard point of NP is that whether it is natural difficulty, intrinsic difficulty, or artificial imposed difficulty, i.e., whether exponential time-complexity or exponential space-complexity can be transformed into polynomial time-complexity or polynomial space-complexity by algorithm optimization, so that NP can be become into P
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