On the state complexity of semi-quantum finite automata^⋆,⋆⋆

¹ Faculty of Informatics, Masaryk University, Brno 60200, Czech Republic.
zhengshenggen@gmail.com; gruska@fi.muni.cz
² Department of Computer Science, Sun Yat-sen University, Guangzhou 510006, P.R. China.
issqdw@mail.sysu.edu.cn

Received: 20 June 2013
Accepted: 27 January 2014

Abstract

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.