The stability of Non-Linear Feedback Shift Registers(NFSRs)plays an important role in the cryptographic security.Due to the complexity of nonlinear systems and the lack of efficient algebraic tools,the theorems relate...The stability of Non-Linear Feedback Shift Registers(NFSRs)plays an important role in the cryptographic security.Due to the complexity of nonlinear systems and the lack of efficient algebraic tools,the theorems related to the stability of NFSRs are still not well-developed.In this paper,we view the NFSR with periodic inputs as a Boolean control network.Based on the mathematical tool of semi-tensor product(STP),the Boolean network can be mapped into an algebraic form.Through these basic theories,we analyze the state space of non-autonomous NFSRs,and discuss the stability of an NFSR with periodic inputs of limited length or unlimited length.The simulation results are provided to prove the efficiency of the model.Based on these works,we can provide a method to analyze the stability of the NFSR with periodic input,including limited length and unlimited length.By this,we can efficiently reduce the computational complexity,and its efficiency is demonstrated by applying the theorem in simulations dealing with the stability of a non-autonomous NFSR.展开更多
We study queueing networks with instantaneous transitions of sequential batch departures and sequential batch arrivals. Unlike most of the existing models, this network is shown not to have a product form solution. An...We study queueing networks with instantaneous transitions of sequential batch departures and sequential batch arrivals. Unlike most of the existing models, this network is shown not to have a product form solution. An "extra arrival condition" is introduced under which the network is shown to possess a product form stationary distribution. Fur- thermore, the product form solution serves as a stochastic upper bound for the original network without the extra arrival process. The results include many queueing network models reported in the literature, e.g. the assembly transfer networks recently introduced by Miyazawa and Taylor, as special cases. We show that the network with the extra arrival process is "structurally reversible" in the sense that its reversed process has the same network structure. Local balances for this network are presented and discussed.展开更多
基金This work is supported by the National Natural Science Foundation of China(Grants Nos.61672020,U1803263,61662069,61762068,31560622,31260538,30960246,31672385,71761029)Project funded by China Postdoctoral Science Foundation(2013M542560,2015T81129)+6 种基金A Project of Shandong Province Higher Educational Science and Technology Program(No.J16LN61)Inner Mongolia Colleges and Universities Scientific and Technological Research Projects(Grant No.NJZC17148)CERNET Innovation Project(No.NGII20161209)Natural Science Foundation of Inner Mongolia Autonomous Region of china(No.2017MS0610,No.2017MS717)Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(No.NJYT-18-A13)Inner Mongolia Key Laboratory of economic data analysis and mining China-Mongolia Scientific Research Capacity Building of Incubator,Joint Laboratory and Technology Transfer Center,Education research project of national finance and economics(No.MZCJYB1803)Postgraduate research and innovation project of Inner Mongolia university of finance and economics.
文摘The stability of Non-Linear Feedback Shift Registers(NFSRs)plays an important role in the cryptographic security.Due to the complexity of nonlinear systems and the lack of efficient algebraic tools,the theorems related to the stability of NFSRs are still not well-developed.In this paper,we view the NFSR with periodic inputs as a Boolean control network.Based on the mathematical tool of semi-tensor product(STP),the Boolean network can be mapped into an algebraic form.Through these basic theories,we analyze the state space of non-autonomous NFSRs,and discuss the stability of an NFSR with periodic inputs of limited length or unlimited length.The simulation results are provided to prove the efficiency of the model.Based on these works,we can provide a method to analyze the stability of the NFSR with periodic input,including limited length and unlimited length.By this,we can efficiently reduce the computational complexity,and its efficiency is demonstrated by applying the theorem in simulations dealing with the stability of a non-autonomous NFSR.
基金Research partially supported by NSF under grants DMI-9908294 and DMI-0196084.
文摘We study queueing networks with instantaneous transitions of sequential batch departures and sequential batch arrivals. Unlike most of the existing models, this network is shown not to have a product form solution. An "extra arrival condition" is introduced under which the network is shown to possess a product form stationary distribution. Fur- thermore, the product form solution serves as a stochastic upper bound for the original network without the extra arrival process. The results include many queueing network models reported in the literature, e.g. the assembly transfer networks recently introduced by Miyazawa and Taylor, as special cases. We show that the network with the extra arrival process is "structurally reversible" in the sense that its reversed process has the same network structure. Local balances for this network are presented and discussed.
