接受项链（Necklaces）的5'->3' Watson-Crick自动机
5' -> 3' Watson-Crick Automata accepting Necklaces
AI总结：
本文研究接受代表环状DNA的项链输入的5'->3' Watson-Crick自动机，提出弱、强两种接受模式，分析其语言类性质并给出受限变体的层次结果。
摘要：
Watson-Crick（WK）有限自动机在代表DNA分子的Watson-Crick磁带上工作，它们配备两个读头。在5'->3' WK自动机中，两个读头沿相反的物理方向移动并读取输入。本文研究的输入为项链（necklaces），即代表环状DNA分子的序列。在感知型5'->3' WK自动机中，当两个读头相遇时，输入上的计算即结束。由于原始模型能够接受线性上下文无关语言，本文研究的项链语言与该语言类存在紧密关联。\n本文采用两种不同的接受模式使用这类自动机。一方面，在弱接受模式下，读头以非确定方式从输入的任意位置启动（相当于项链在非确定选择的位置被切开），若输入被接受，则它属于被接受的项链语言。这类语言可视为线性上下文无关语言在循环移位运算下取闭包得到的语言。另一方面，在强接受模式下，要求读头从环的每个位置启动计算时输入都能被接受。这类语言可视为包含于某一线性语言中的最大循环移位封闭语言。此外，本文将证明这类强接受模式下的语言具有一种局部可检验性质。本文还基于WK自动机的受限变体（如无状态变体或全终态变体）给出了一些层次结构结果。
英文摘要：
Watson-Crick (WK) finite automata work on a Watson-Crick tape representing a DNA molecule. They have two reading heads. In 5'->3' WK automata, the heads move and read the input in opposite physical directions. In this paper, we consider such inputs which are necklaces, i.e., they represent circular DNA molecules. In sensing 5'->3' WK automata, the computation on the input is finished when the heads meet. As the original model is capable of accepting the linear context-free languages, the necklace languages we are investigating here have strong relations to that class. Here, we use these automata in two different acceptance modes. On the one hand, in weak acceptance mode the heads are starting nondeterministically at any point of the input, like the necklace is cut at a nondeterministically chosen point), and if the input is accepted, it is in the accepted necklace language. These languages can be seen as the languages obtained from the linear context-free languages by taking their closure under cyclic shift operation. On the other hand, in strong acceptance mode, it is required that the input is accepted starting the heads in the computation from every point of the cycle. These languages can be seen as the maximal cyclic shift closed languages included in a linear language. On the other hand, as it will be shown, they have a kind of locally testable property. We present some hierarchy results based on restricted variants of the WK automata, such as stateless or all-final variants.
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