1,590 research outputs found
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
On equivalence, languages equivalence and minimization of multi-letter and multi-letter measure-many quantum automata
We first show that given a -letter quantum finite automata
and a -letter quantum finite automata over
the same input alphabet , they are equivalent if and only if they are
-equivalent where , , are the
numbers of state in respectively, and . By
applying a method, due to the author, used to deal with the equivalence problem
of {\it measure many one-way quantum finite automata}, we also show that a
-letter measure many quantum finite automaton and a
-letter measure many quantum finite automaton are
equivalent if and only if they are -equivalent
where , , are the numbers of state in respectively,
and .
Next, we study the language equivalence problem of those two kinds of quantum
finite automata. We show that for -letter quantum finite automata, the
non-strict cut-point language equivalence problem is undecidable, i.e., it is
undecidable whether
where
and are -letter quantum finite automata.
Further, we show that both strict and non-strict cut-point language equivalence
problem for -letter measure many quantum finite automata are undecidable.
The direct consequences of the above outcomes are summarized in the paper.
Finally, we comment on existing proofs about the minimization problem of one
way quantum finite automata not only because we have been showing great
interest in this kind of problem, which is very important in classical automata
theory, but also due to that the problem itself, personally, is a challenge.
This problem actually remains open.Comment: 30 pages, conclusion section correcte
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 Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)
Eilenberg correspondence, based on the concept of syntactic monoids, relates
varieties of regular languages with pseudovarieties of finite monoids. Various
modifications of this correspondence related more general classes of regular
languages with classes of more complex algebraic objects. Such generalized
varieties also have natural counterparts formed by classes of finite automata
equipped with a certain additional algebraic structure. In this survey, we
overview several variants of such varieties of enriched automata.Comment: In Proceedings AFL 2014, arXiv:1405.527
Computation with narrow CTCs
We examine some variants of computation with closed timelike curves (CTCs),
where various restrictions are imposed on the memory of the computer, and the
information carrying capacity and range of the CTC. We give full
characterizations of the classes of languages recognized by polynomial time
probabilistic and quantum computers that can send a single classical bit to
their own past. Such narrow CTCs are demonstrated to add the power of limited
nondeterminism to deterministic computers, and lead to exponential speedup in
constant-space probabilistic and quantum computation. We show that, given a
time machine with constant negative delay, one can implement CTC-based
computations without the need to know about the runtime beforehand.Comment: 16 pages. A few typo was correcte
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