| 关于二元延迟3步前馈逆有限自动机的结构 |
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| 引用本文： | 王鸿吉,姚刚.关于二元延迟3步前馈逆有限自动机的结构[J].软件学报,2007,18(1):40-49. |
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| 作者姓名： | 王鸿吉 姚刚 |
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| 作者单位： | 中国科学院,软件研究所,北京,100080;中国科学院,研究生院,北京,100049;信息安全国家重点实验室(中国科学院,软件研究所),北京,100080 |
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| 基金项目： | 国家自然科学基金;国家自然科学基金 |
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| 摘 要： | 前馈逆有限自动机的结构是有限自动机可逆性理论中的基本问题.对延迟步数≥3的前馈逆结构的刻划,则是一个长期的未解决问题.研究了二元延迟3步前馈逆有限自动机的结构.对于自治有限自动机Ma的状态图为圈的二元延迟3步弱可逆半输入存储有限自动机C(Maf ),给出了其长3极小输出权分别为1,2,8三种情形下结构的一种刻画.由于C(Maf )延迟3步弱可逆当且仅当它是延迟3步弱逆,因此,得到了二元延迟3步前馈逆有限自动机结构的一种部分刻画.
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| 关 键 词： | 有限自动机 半输入存储 前馈逆 可逆性 |
| 收稿时间： | 2005-01-26 |
| 修稿时间： | 2005-04-18 |
On the Structure of Binary Feedforward Inverse Finite Automata with Delay 3 |
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| WANG Hong-Ji and YAO Gang.On the Structure of Binary Feedforward Inverse Finite Automata with Delay 3[J].Journal of Software,2007,18(1):40-49. |
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| Authors: | WANG Hong-Ji and YAO Gang |
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| Affiliation: | 1.Institute of Software, The Chinese Academy of Sciences, Beijing 100080, China;2.Graduate School, The Chinese Academy of Sciences, Beijing 100049, China; 3.The State Key Laboratory of Information Security (Institute of Software, The Chinese Academy of Sciences |
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| Abstract: | The structure of feedforward inverses is a fundamental problem in the invertibility theory of finite automata. The characterization of the structure of feedforward inverses with delay steps ≥3 is a long-term unsolved problem. This paper deals with this topic. For a binary weakly invertible semi-input memory finite automaton C(Ma,f) with delay 3, where the state graph of Ma is cyclic, the characterizations of the structures are given when its minimal 3-output weight is 1, 2, and 8, respectively. Because C(Ma,f) is weakly invertible with delay 3 iff it is weakly inverse with delay 3, a partial characterization of the structure of binary feedforward inverses with delay 3 is obtained. |
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| Keywords: | finite automata semi-input memory feedforward inverses invertibility |
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