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Abstract: We prove that two-way probabilistic and quantum finite automata 2PFA-s and2QFA-s can be considerably more concise than both their one-way versions1PFA-s and 1QFA-s, and two-way nondeterministic finite automata 2NFA-s. Forthis purpose, we demonstrate several infinite families of regular languageswhich can be recognized with some fixed probability greater than $ {1-2} $ byjust tuning the transition amplitudes of a 2QFA and, in one case, a 2PFA witha constant number of states, whereas the sizes of the corresponding 1PFA-s,1QFA-s and 2NFA-s grow without bound. We also show that 2QFA-s with mixedstates can support highly efficient probability amplification. The weakestknown model of computation where quantum computers recognize more languageswith bounded error than their classical counterparts is introduced.



Author: Abuzer Yakaryilmaz, A. C. Cem Say

Source: https://arxiv.org/







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