Lower Bounds for Generalized Quantum Finite Automata

We obtain several lower bounds on the language recognition power of Nayak's generalized quantum finite automata (GQFA)[12]. Techniques for proving lower bounds on Kondacs and Watrous' one-way quantum finite automata (KWQFA)were introduced by Ambainis and Freivalds [2], and were expanded in a series of papers. We show that many of these techniques can be adapted to prove lower bounds for GQFAs. Our results imply that the class of languages recognized by GQFAs is not closed under union. Furthermore, we show that there are languages which can be recognized by GQFAs with probability p> 1/2, but not with p> 2/3.

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