DNA码的变换器描述及反形问题的不可判定性
Transducer Descriptions of DNA Code Properties and Undecidability of Antimorphic Problems
摘要：
这项工作涉及的DNA代码属性的正式描述，并建立在以前的工作上的经典代码属性的换能器描述和DNA代码属性的轨迹描述。这条研究路线允许我们将一个属性作为算法的输入，除了任何正则语言之外，算法可以回答关于语言和属性的问题。在这里，我们通过换能器定义DNA代码的属性，并表明这种方法是严格的更有表现力的轨迹，而不牺牲效率的满意度问题的决定。我们还表明，极大值问题可以是不可判定的。我们的不可判定性结果不仅适用于固定的DNA对合，而且适用于任何固定的反形排列。此外，我们还证明了反形版本的后对应问题的不可判定性，任何固定的反形置换。
英文摘要：
This work concerns formal descriptions of DNA code properties, and builds on previous work on transducer descriptions of classic code properties and on trajectory descriptions of DNA code properties. This line of research allows us to give a property as input to an algorithm, in addition to any regular language, which can then answer questions about the language and the property. Here we define DNA code properties via transducers and show that this method is strictly more expressive than that of trajectories, without sacrificing the efficiency of deciding the satisfaction question. We also show that the maximality question can be undecidable. Our undecidability results hold not only for the fixed DNA involution but also for any fixed antimorphic permutation. Moreover, we also show the undecidability of the antimorphic version of the Post Corresponding Problem, for any fixed antimorphic permutation.
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