2,416 research outputs found
One-Way Reversible and Quantum Finite Automata with Advice
We examine the characteristic features of reversible and quantum computations
in the presence of supplementary external information, known as advice. In
particular, we present a simple, algebraic characterization of languages
recognized by one-way reversible finite automata augmented with deterministic
advice. With a further elaborate argument, we prove a similar but slightly
weaker result for bounded-error one-way quantum finite automata with advice.
Immediate applications of those properties lead to containments and separations
among various language families when they are assisted by appropriately chosen
advice. We further demonstrate the power and limitation of randomized advice
and quantum advice when they are given to one-way quantum finite automata.Comment: A4, 10pt, 1 figure, 31 pages. This is a complete version of an
extended abstract appeared in the Proceedings of the 6th International
Conference on Language and Automata Theory and Applications (LATA 2012),
March 5-9, 2012, A Coruna, Spain, Lecture Notes in Computer Science,
Springer-Verlag, Vol.7183, pp.526-537, 201
Unbounded-error quantum computation with small space bounds
We prove the following facts about the language recognition power of quantum
Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more
powerful than probabilistic Turing machines for any common space bound
satisfying . For "one-way" Turing machines, where the
input tape head is not allowed to move left, the above result holds for
. We also give a characterization for the class of languages
recognized with unbounded error by real-time quantum finite automata (QFAs)
with restricted measurements. It turns out that these automata are equal in
power to their probabilistic counterparts, and this fact does not change when
the QFA model is augmented to allow general measurements and mixed states.
Unlike the case with classical finite automata, when the QFA tape head is
allowed to remain stationary in some steps, more languages become recognizable.
We define and use a QTM model that generalizes the other variants introduced
earlier in the study of quantum space complexity.Comment: A preliminary version of this paper appeared in the Proceedings of
the Fourth International Computer Science Symposium in Russia, pages
356--367, 200
An Application of Quantum Finite Automata to Interactive Proof Systems
Quantum finite automata have been studied intensively since their
introduction in late 1990s as a natural model of a quantum computer with
finite-dimensional quantum memory space. This paper seeks their direct
application to interactive proof systems in which a mighty quantum prover
communicates with a quantum-automaton verifier through a common communication
cell. Our quantum interactive proof systems are juxtaposed to
Dwork-Stockmeyer's classical interactive proof systems whose verifiers are
two-way probabilistic automata. We demonstrate strengths and weaknesses of our
systems and further study how various restrictions on the behaviors of
quantum-automaton verifiers affect the power of quantum interactive proof
systems.Comment: This is an extended version of the conference paper in the
Proceedings of the 9th International Conference on Implementation and
Application of Automata, Lecture Notes in Computer Science, Springer-Verlag,
Kingston, Canada, July 22-24, 200
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