| Summary: | In the past year two different models of quantum finite automata have been proposed. The
first model, introduced by Moore and Crutchfield[MC98], makes one measurement on its
state at the end of its computation and is called a measure-once quantum finite automata.
The second model, introduced by Kondacs and Watrous[KW97], makes a measurement of
its state after every transition and is called a measure-many quantum finite automata. In
this thesis we investigate the characteristics of the two models.
We characterize measure-once quantum finite automata when they are restricted to acceptance
with bounded error, and we show that, when they are not so restricted, they can
solve the word problem over the free group. We show that they can be simulated by probabilistic
finite automata, which implies that they are no more powerful than probabilistic finite
automata. We also describe an algorithm that determines if two automata are equivalent.
We show that the class of languages accepted by measure-many quantum finite automata
is closed under quotient, complement, and inverse homomorphisms. We prove a necessary
condition for a language to be accepted by a measure-many automaton with bounded error
and we show that certain sets, including piecewise testable sets, can be accepted with
bounded error by this automata. === Science, Faculty of === Computer Science, Department of === Graduate
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