17,346 research outputs found
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
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
A Minimal Periods Algorithm with Applications
Kosaraju in ``Computation of squares in a string'' briefly described a
linear-time algorithm for computing the minimal squares starting at each
position in a word. Using the same construction of suffix trees, we generalize
his result and describe in detail how to compute in O(k|w|)-time the minimal
k-th power, with period of length larger than s, starting at each position in a
word w for arbitrary exponent and integer . We provide the
complete proof of correctness of the algorithm, which is somehow not completely
clear in Kosaraju's original paper. The algorithm can be used as a sub-routine
to detect certain types of pseudo-patterns in words, which is our original
intention to study the generalization.Comment: 14 page
Alternating, private alternating, and quantum alternating realtime automata
We present new results on realtime alternating, private alternating, and
quantum alternating automaton models. Firstly, we show that the emptiness
problem for alternating one-counter automata on unary alphabets is undecidable.
Then, we present two equivalent definitions of realtime private alternating
finite automata (PAFAs). We show that the emptiness problem is undecidable for
PAFAs. Furthermore, PAFAs can recognize some nonregular unary languages,
including the unary squares language, which seems to be difficult even for some
classical counter automata with two-way input. Regarding quantum finite
automata (QFAs), we show that the emptiness problem is undecidable both for
universal QFAs on general alphabets, and for alternating QFAs with two
alternations on unary alphabets. On the other hand, the same problem is
decidable for nondeterministic QFAs on general alphabets. We also show that the
unary squares language is recognized by alternating QFAs with two alternations
Quantum counter automata
The question of whether quantum real-time one-counter automata (rtQ1CAs) can
outperform their probabilistic counterparts has been open for more than a
decade. We provide an affirmative answer to this question, by demonstrating a
non-context-free language that can be recognized with perfect soundness by a
rtQ1CA. This is the first demonstration of the superiority of a quantum model
to the corresponding classical one in the real-time case with an error bound
less than 1. We also introduce a generalization of the rtQ1CA, the quantum
one-way one-counter automaton (1Q1CA), and show that they too are superior to
the corresponding family of probabilistic machines. For this purpose, we
provide general definitions of these models that reflect the modern approach to
the definition of quantum finite automata, and point out some problems with
previous results. We identify several remaining open problems.Comment: A revised version. 16 pages. A preliminary version of this paper
appeared as A. C. Cem Say, Abuzer Yakary{\i}lmaz, and \c{S}efika
Y\"{u}zsever. Quantum one-way one-counter automata. In R\={u}si\c{n}\v{s}
Freivalds, editor, Randomized and quantum computation, pages 25--34, 2010
(Satellite workshop of MFCS and CSL 2010
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