21,881 research outputs found
On the descriptional complexity of iterative arrays
The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable
Quantum Cloning Machines and the Applications
No-cloning theorem is fundamental for quantum mechanics and for quantum
information science that states an unknown quantum state cannot be cloned
perfectly. However, we can try to clone a quantum state approximately with the
optimal fidelity, or instead, we can try to clone it perfectly with the largest
probability. Thus various quantum cloning machines have been designed for
different quantum information protocols. Specifically, quantum cloning machines
can be designed to analyze the security of quantum key distribution protocols
such as BB84 protocol, six-state protocol, B92 protocol and their
generalizations. Some well-known quantum cloning machines include universal
quantum cloning machine, phase-covariant cloning machine, the asymmetric
quantum cloning machine and the probabilistic quantum cloning machine etc. In
the past years, much progress has been made in studying quantum cloning
machines and their applications and implementations, both theoretically and
experimentally. In this review, we will give a complete description of those
important developments about quantum cloning and some related topics. On the
other hand, this review is self-consistent, and in particular, we try to
present some detailed formulations so that further study can be taken based on
those results.Comment: 98 pages, 12 figures, 400+ references. Physics Reports (published
online
An introduction to finite automata and their connection to logic
This is a tutorial on finite automata. We present the standard material on
determinization and minimization, as well as an account of the equivalence of
finite automata and monadic second-order logic. We conclude with an
introduction to the syntactic monoid, and as an application give a proof of the
equivalence of first-order definability and aperiodicity
Designing optimal- and fast-on-average pattern matching algorithms
Given a pattern and a text , the speed of a pattern matching algorithm
over with regard to , is the ratio of the length of to the number of
text accesses performed to search into . We first propose a general
method for computing the limit of the expected speed of pattern matching
algorithms, with regard to , over iid texts. Next, we show how to determine
the greatest speed which can be achieved among a large class of algorithms,
altogether with an algorithm running this speed. Since the complexity of this
determination make it impossible to deal with patterns of length greater than
4, we propose a polynomial heuristic. Finally, our approaches are compared with
9 pre-existing pattern matching algorithms from both a theoretical and a
practical point of view, i.e. both in terms of limit expected speed on iid
texts, and in terms of observed average speed on real data. In all cases, the
pre-existing algorithms are outperformed
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