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| 关于二元延迟3步前馈逆有限自动机的结构 |
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王鸿吉1,2, 姚刚3
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1.中国科学院,软件研究所,北京,100080;2.中国科学院,研究生院,北京,100049;3.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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| 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. |
| 关键词: 有限自动机 半输入存储 前馈逆 可逆性 |
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| 基金项目:Supported by the National Natural Science Foundation of China for Grand International Joint Project under Grant No.60310213 (国家自然科学基金重大国际(地区)合作研究项目); the National Natural Science Foundation for Distinguished Young Scholars of China under Grant No.60325206 (国家杰出青年科学基金) |
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| On the Structure of Binary Feedforward Inverse Finite Automata with Delay 3 |
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WANG Hong-Ji,YAO Gang
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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(Maf ) 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(Maf ) 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. |
| Key words: finite automata semi-input memory feedforward inverses invertibility |
