504 research outputs found
Generalizations of the distributed Deutsch-Jozsa promise problem
In the {\em distributed Deutsch-Jozsa promise problem}, two parties are to
determine whether their respective strings are at the {\em
Hamming distance} or . Buhrman et al. (STOC' 98)
proved that the exact {\em quantum communication complexity} of this problem is
while the {\em deterministic communication complexity} is
. This was the first impressive (exponential) gap between
quantum and classical communication complexity.
In this paper, we generalize the above distributed Deutsch-Jozsa promise
problem to determine, for any fixed , whether
or , and show that an exponential gap between exact
quantum and deterministic communication complexity still holds if is an
even such that , where is given. We also deal with a promise version of the
well-known {\em disjointness} problem and show also that for this promise
problem there exists an exponential gap between quantum (and also
probabilistic) communication complexity and deterministic communication
complexity of the promise version of such a disjointness problem. Finally, some
applications to quantum, probabilistic and deterministic finite automata of the
results obtained are demonstrated.Comment: we correct some errors of and improve the presentation the previous
version. arXiv admin note: substantial text overlap with arXiv:1309.773
Potential of quantum finite automata with exact acceptance
The potential of the exact quantum information processing is an interesting,
important and intriguing issue. For examples, it has been believed that quantum
tools can provide significant, that is larger than polynomial, advantages in
the case of exact quantum computation only, or mainly, for problems with very
special structures. We will show that this is not the case.
In this paper the potential of quantum finite automata producing outcomes not
only with a (high) probability, but with certainty (so called exactly) is
explored in the context of their uses for solving promise problems and with
respect to the size of automata. It is shown that for solving particular
classes of promise problems, even those without some
very special structure, that succinctness of the exact quantum finite automata
under consideration, with respect to the number of (basis) states, can be very
small (and constant) though it grows proportional to in the case
deterministic finite automata (DFAs) of the same power are used. This is here
demonstrated also for the case that the component languages of the promise
problems solvable by DFAs are non-regular. The method used can be applied in
finding more exact quantum finite automata or quantum algorithms for other
promise problems.Comment: We have improved the presentation of the paper. Accepted to
International Journal of Foundation of Computer Scienc
On the state complexity of semi-quantum finite automata
Some of the most interesting and important results concerning quantum finite
automata are those showing that they can recognize certain languages with
(much) less resources than corresponding classical finite automata
\cite{Amb98,Amb09,AmYa11,Ber05,Fre09,Mer00,Mer01,Mer02,Yak10,ZhgQiu112,Zhg12}.
This paper shows three results of such a type that are stronger in some sense
than other ones because (a) they deal with models of quantum automata with very
little quantumness (so-called semi-quantum one- and two-way automata with one
qubit memory only); (b) differences, even comparing with probabilistic
classical automata, are bigger than expected; (c) a trade-off between the
number of classical and quantum basis states needed is demonstrated in one case
and (d) languages (or the promise problem) used to show main results are very
simple and often explored ones in automata theory or in communication
complexity, with seemingly little structure that could be utilized.Comment: 19 pages. We improve (make stronger) the results in section
Synthesis, structure and power of systolic computations
AbstractA variety of problems related to systolic architectures, systems, models and computations are discussed. The emphases are on theoretical problems of a broader interest. Main motivations and interesting/important applications are also presented. The first part is devoted to problems related to synthesis, transformations and simulations of systolic systems and architectures. In the second part, the power and structure of tree and linear array computations are studied in detail. The goal is to survey main research directions, problems, methods and techniques in not too formal a way
A few remarks on the index of context-free grammars and languages
A hierarchy of context-free grammars and languages with respect to the index of context-free grammars is established and the undecidability of the basic problems is proven
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