Geodesic
On the state complexity of semi-quantum finite automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 2, pp. 187-207

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Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata. This paper shows three results of such a type that are stronger in some sense than other ones because (a) they deal with models of quantum finite automata with very little quantumness (so-called semi-quantum one- and two-way finite automata); (b) differences, even comparing with probabilistic classical automata, are bigger than expected; (c) a trade-off between the number of classical and quantum basis states needed is demonstrated in one case and (d) languages (or the promise problem) used to show main results are very simple and often explored ones in automata theory or in communication complexity, with seemingly little structure that could be utilized.

DOI : 10.1051/ita/2014003
Keywords: quantum computing, quantum finite automata, semi-quantum finite automata, state complexity 
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     author = {Zheng, Shenggen and Gruska, Jozef and Qiu, Daowen},
     title = {On the state complexity of semi-quantum finite automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {187--207},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {2},
     year = {2014},
     doi = {10.1051/ita/2014003},
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     zbl = {1292.81027},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2014003/}
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Zheng, Shenggen; Gruska, Jozef; Qiu, Daowen. On the state complexity of semi-quantum finite automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 2, pp. 187-207. doi: 10.1051/ita/2014003

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