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The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints
arXiv - CS - Computational Complexity Pub Date : 2019-04-02 , DOI: arxiv-1904.01381
Aleksejs Naumovs, Maksims Dimitrijevs, and Abuzer Yakary{\i}lmaz

It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized language with a cutpoint and then by using the fact that there are uncountably many cutpoints. In this note, we prove the same results for fixed cutpoints: each recognized language is associated with an automaton (i.e., algorithm), and the proofs use the fact that there are uncountably many automata. For each case, we present a new construction.

中文翻译:

识别无数具有固定切点的语言的最小概率和量子有限自动机

众所周知,二态二元和三态一元概率有限自动机和二态一元量子有限自动机可以识别无数种带有切点的语言。这些结果是通过将每种识别的语言与一个切点相关联,然后利用存在无数个切点的事实而获得的。在这篇笔记中,我们证明了固定分割点的相同结果:每种识别的语言都与一个自动机(即算法)相关联,并且证明使用了有无数自动机这一事实。对于每种情况,我们都提出了一个新的结构。
更新日期:2020-08-25
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