Geodesic
New results on classical and quantum counter automata
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4.

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We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter automaton and one-way deterministic one-counter automaton. We also obtain new results on classical counter automata regarding language recognition. It was conjectured that one-way probabilistic one blind-counter automata cannot recognize Kleene closure of equality language [A. Yakaryilmaz: Superiority of one-way and realtime quantum machines. RAIRO - Theor. Inf. and Applic. 46(4): 615-641 (2012)]. We show that this conjecture is false, and also show several separation results for blind/non-blind counter automata. 
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     author = {Nakanishi, Masaki and Yakary{\i}lmaz, Abuzer and Gainutdinova, Aida},
     title = {New results on classical and quantum counter automata},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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Nakanishi, Masaki; Yakaryılmaz, Abuzer; Gainutdinova, Aida. New results on classical and quantum counter automata. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4. doi : 10.23638/DMTCS-21-4-12. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-12/

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