41 research outputs found
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
Undecidability of recognized by measure many 1-way quantum automata
Let and be the
languages recognized by {\em measure many 1-way quantum finite automata
(MMQFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)})
with strict, resp. non-strict cut-point . We consider the languages
equivalence problem, showing that
\begin{itemize}
\item {both strict and non-strict languages equivalence are undecidable;}
\item {to do this, we provide an additional proof of the undecidability of
non-strict and strict emptiness of MMQFA(EQFA), and then reducing the languages
equivalence problem to emptiness problem;}
\item{Finally, some other Propositions derived from the above results are
collected.}
\end{itemize}Comment: Readability improved, title change
The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints
It is known that 2-state binary and 3-state unary probabilistic finite
automata and 2-state unary quantum finite automata recognize uncountably many
languages with cutpoints. These results have been obtained by associating each
recognized language with a cutpoint and then by using the fact that there are
uncountably many cutpoints. In this note, we prove the same results for fixed
cutpoints: each recognized language is associated with an automaton (i.e.,
algorithm), and the proofs use the fact that there are uncountably many
automata. For each case, we present a new construction.Comment: 12 pages, minor revisions, changing the format to "dmtcs-episciences"
styl
Finite automata with advice tapes
We define a model of advised computation by finite automata where the advice
is provided on a separate tape. We consider several variants of the model where
the advice is deterministic or randomized, the input tape head is allowed
real-time, one-way, or two-way access, and the automaton is classical or
quantum. We prove several separation results among these variants, demonstrate
an infinite hierarchy of language classes recognized by automata with
increasing advice lengths, and establish the relationships between this and the
previously studied ways of providing advice to finite automata.Comment: Corrected typo
From Quantum Query Complexity to State Complexity
State complexity of quantum finite automata is one of the interesting topics
in studying the power of quantum finite automata. It is therefore of importance
to develop general methods how to show state succinctness results for quantum
finite automata. One such method is presented and demonstrated in this paper.
In particular, we show that state succinctness results can be derived out of
query complexity results.Comment: Some typos in references were fixed. To appear in Gruska Festschrift
(2014). Comments are welcome. arXiv admin note: substantial text overlap with
arXiv:1402.7254, arXiv:1309.773