1,520 research outputs found
A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton
We describe a simple n-dimensional quantum cellular automaton (QCA) capable
of simulating all others, in that the initial configuration and the forward
evolution of any n-dimensional QCA can be encoded within the initial
configuration of the intrinsically universal QCA. Several steps of the
intrinsically universal QCA then correspond to one step of the simulated QCA.
The simulation preserves the topology in the sense that each cell of the
simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International
Conference on Language and Automata Theory and Applications (LATA 2010),
Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382
1D Effectively Closed Subshifts and 2D Tilings
Michael Hochman showed that every 1D effectively closed subshift can be
simulated by a 3D subshift of finite type and asked whether the same can be
done in 2D. It turned out that the answer is positive and necessary tools were
already developed in tilings theory. We discuss two alternative approaches:
first, developed by N. Aubrun and M. Sablik, goes back to Leonid Levin; the
second one, developed by the authors, goes back to Peter Gacs.Comment: Journ\'ees Automates Cellulaires, Turku : Finland (2010
Hyperbolic tilings and formal language theory
In this paper, we try to give the appropriate class of languages to which
belong various objects associated with tessellations in the hyperbolic plane.Comment: In Proceedings MCU 2013, arXiv:1309.104
Model Checking Parse Trees
Parse trees are fundamental syntactic structures in both computational
linguistics and compilers construction. We argue in this paper that, in both
fields, there are good incentives for model-checking sets of parse trees for
some word according to a context-free grammar. We put forward the adequacy of
propositional dynamic logic (PDL) on trees in these applications, and study as
a sanity check the complexity of the corresponding model-checking problem:
although complete for exponential time in the general case, we find natural
restrictions on grammars for our applications and establish complexities
ranging from nondeterministic polynomial time to polynomial space in the
relevant cases.Comment: 21 + x page
Models of Quantum Cellular Automata
In this paper we present a systematic view of Quantum Cellular Automata
(QCA), a mathematical formalism of quantum computation. First we give a general
mathematical framework with which to study QCA models. Then we present four
different QCA models, and compare them. One model we discuss is the traditional
QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam.
We discuss also Margolus QCA, also discussed by Schumacher and Werner. We
introduce two new models, Coloured QCA, and Continuous-Time QCA. We also
compare our models with the established models. We give proofs of computational
equivalence for several of these models. We show the strengths of each model,
and provide examples of how our models can be useful to come up with
algorithms, and implement them in real-world physical devices
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