2,932 research outputs found
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
Succinctness of two-way probabilistic and quantum finite automata
We prove that two-way probabilistic and quantum finite automata (2PFA's and
2QFA's) can be considerably more concise than both their one-way versions
(1PFA's and 1QFA's), and two-way nondeterministic finite automata (2NFA's). For
this purpose, we demonstrate several infinite families of regular languages
which can be recognized with some fixed probability greater than by
just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with
a constant number of states, whereas the sizes of the corresponding 1PFA's,
1QFA's and 2NFA's grow without bound. We also show that 2QFA's with mixed
states can support highly efficient probability amplification. The weakest
known model of computation where quantum computers recognize more languages
with bounded error than their classical counterparts is introduced.Comment: A new version, 21 pages, late
Two-tape finite automata with quantum and classical states
{\it Two-way finite automata with quantum and classical states} (2QCFA) were
introduced by Ambainis and Watrous, and {\it two-way two-tape deterministic
finite automata} (2TFA) were introduced by Rabin and Scott. In this paper we
study 2TFA and propose a new computing model called {\it two-way two-tape
finite automata with quantum and classical states} (2TQCFA). First, we give
efficient 2TFA algorithms for recognizing languages which can be recognized by
2QCFA. Second, we give efficient 2TQCFA algorithms to recognize several
languages whose status vis-a-vis 2QCFA have been posed as open questions, such
as . Third, we show that
can be recognized by {\it -tape
deterministic finite automata} (TFA). Finally, we introduce {\it
-tape automata with quantum and classical states} (TQCFA) and prove that
can be recognized by TQCFA.Comment: 25 page
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