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1. Synthesis Algorithms of Models of Hybrid Systems | |||
ZHANG Haibin | |||
Computer Science and Technology 01 February 2014 | |||
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Abstract:In this paper, a computational model for hybrid systems is introduced. Based on this model, a partial order relation of hybrid systems is given and a lattice of hybrid systems is formalized. Armed with these notations, synthesis of hybrid systems is discussed. The synthesis can be seen as the operation of solving the least upper bound of members of the lattice. | |||
TO cite this article:ZHANG Haibin. Synthesis Algorithms of Models of Hybrid Systems[OL].[ 1 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4583958 |
2. Aujin Algorithm: A Deterministic Polynomial Algorithm for SAT | |||
Zhu-Jin Zhang | |||
Computer Science and Technology 24 June 2009 | |||
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Abstract:We discover a new object in the nature --- Aujin. Based on Aujin, we prove several important theorems, and build this deterministic polynomial algorithm for SAT(the NP-complete satisfiability problem). We also propose three conjectures such that the proof of any one of them will lead to the proof that P=NP. Millions of CNFs (conjunctive normal form) have been tested, and there is no counter-example. And thus experts in computational complexity may abandon the old mind --- NP≠P. Moreover, even if all these three conjectures were incorrect, Aujin Algorithm still is a deterministic polynomial algorithm in any case, and can be used to handle practical problems. | |||
TO cite this article:Zhu-Jin Zhang. Aujin Algorithm: A Deterministic Polynomial Algorithm for SAT[OL].[24 June 2009] http://en.paper.edu.cn/en_releasepaper/content/33376 |
3. A second proof of the conjecture that the class P is a proper subset of the class NP | |||
Xu Wandong | |||
Computer Science and Technology 12 February 2008 | |||
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Abstract:The problem of deciding whether an arbitrary undirected planar graph $G$ is a Hamiltonian (HC) is one of six best important {bf NP}-complete problems. In current paper, by the necessary and sufficient condition of HC, one turned the problem HC into the one of determining whether there does not have any one of forbidden subgraphs in each of spanning subgraphs of $G$. It can be completed in the polynomial time for determining whether there does not have any one of forbidden subgraphs in a spanning subgraph, but it never be completed in the polynomial time for determining whether there exists at least a spanning subgraph in which there never have any forbidden subgraph in infinite many of spanning subgraphs. Such that one can deduced that the time complexity of algorithm for solving the problem HC is $mathcal{O}(n^2 2^{1.5n+Delta})$, here $n$ is the order of $G$ and $Delta$ is $>0$, that is, it is extra exponential of $n$. So one can conclude that HC $NOTIN$ {bf P} and {bf P} $subset$ {bf NP}. | |||
TO cite this article:Xu Wandong . A second proof of the conjecture that the class P is a proper subset of the class NP[OL].[12 February 2008] http://en.paper.edu.cn/en_releasepaper/content/18638 |
4. A proof of the conjecture that the class P is a proper subset of the class NP | |||
Xu Wandong | |||
Computer Science and Technology 15 November 2007 | |||
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Abstract:The planar graph 3-colorability (P3C) is one of {bf NP}-complete problem. Duo to probably appearing the second type of mistake in setting colors, a computational algorithm might repeat many times to decide whether it can correct wrong coloring in many examined subgraphs. Then one can turn P3C by means of analyzing some actual graphs (not with theoretically transformation in polynomial time) into the problem of determining whether there is a planar in infinitely many of arbitrary subgraphs. The problem of determining whether an arbitrary graph is a planar is in the class {bf P} and it can be solved with a polynomial time algorithm. But the problem of determining whether there is a planar in arbitrary subgraphs, which have identical order, of $sumlimits_{nu=1}^{L}dbinom{L}{nu}nu!$, or of $sumlimits_{k=1}^{L}sum limits_{nu=1}^{k}dbinom{k}{nu}nu!$, where $L=lceil n/3 rceil-2$ and $n$ is the order of these graphs, isn\ | |||
TO cite this article:Xu Wandong . A proof of the conjecture that the class P is a proper subset of the class NP[OL].[15 November 2007] http://en.paper.edu.cn/en_releasepaper/content/16366 |
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