The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints
Formal Languages and Automata Theory
2023-06-22 v4 Computational Complexity
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1904.01381,
title = {The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints},
author = {Aleksejs Naumovs and Maksims Dimitrijevs and Abuzer Yakaryılmaz},
journal= {arXiv preprint arXiv:1904.01381},
year = {2023}
}
Comments
12 pages, minor revisions, changing the format to "dmtcs-episciences" style