19,883 research outputs found
On the categories of L-Valued and Q-Valued 6 deterministic fuzzy automata
Automata and languages have been studied in the context of different lattice structures by several authors. This paper is toward the categorical study of deterministic lattice-valued (L-valued) fuzzy automata and deterministic quantale-valued (Q-valued)
fuzzy automata. The existence of initial and final objects in the subcategory of category of deterministic lattice-valued fuzzy automata is shown. We also show that there is an adjunction between the category of deterministic lattice-valued and quantale-valued
fuzzy automata
Celulární automat a CML systémy
The main aim of this thesis is the study of cellular automata and discrete dynamical systems on a lattice.
Both tools, cellular automata as well as dynamical systems on a lattice are introduced and elementary properties described.
The relation between cellular automata and dynamical system on lattice is derived.
The main goal of the thesis is also the use of the cellular automata as that mathematical tool of evolution visualization of discrete dynamical systems.
The theory of cellular automata is applied to the discrete dynamical systems on a lattice Laplacian type and implemented in Java language.Hlavním cílem práce je studium vztahu celulárních automatů a diskrétních dynamických systémů na mřížce. Oba nástroje, jak celulární automat tak dynamický systém na mřížce, jsou zavedeny a jejich základní vlastnosti popsány. Vztah mezi celulárními automaty a dynamickými systémy na mřížce je podrobně popsán. Hlavním cílem práce je dále použití nástroje celulárního automatu jako matematického vizualizačního prostředku evoluce diskrétních dynamických systémů. Teorie celulárních automatů je použita na dynamické systémy na mřížce Lamplaceova typu a implementována v prostředí Java.470 - Katedra aplikované matematikyvelmi dobř
Basic Ideas to Approach Metastability in Probabilistic Cellular Automata
Cellular Automata are discrete--time dynamical systems on a spatially
extended discrete space which provide paradigmatic examples of nonlinear
phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular
Automata, are discrete time Markov chains on lattice with finite single--cell
states whose distinguishing feature is the \textit{parallel} character of the
updating rule. We review some of the results obtained about the metastable
behavior of Probabilistic Cellular Automata and we try to point out
difficulties and peculiarities with respect to standard Statistical Mechanics
Lattice models.Comment: arXiv admin note: text overlap with arXiv:1307.823
Parrondo games as lattice gas automata
Parrondo games are coin flipping games with the surprising property that
alternating plays of two losing games can produce a winning game. We show that
this phenomenon can be modelled by probabilistic lattice gas automata.
Furthermore, motivated by the recent introduction of quantum coin flipping
games, we show that quantum lattice gas automata provide an interesting
definition for quantum Parrondo games.Comment: 12 pages, plain TeX, 10 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages); for related work see
http://math.ucsd.edu/~dmeyer/research.htm
Quantum mechanics of lattice gas automata. I. One particle plane waves and potentials
Classical lattice gas automata effectively simulate physical processes such
as diffusion and fluid flow (in certain parameter regimes) despite their
simplicity at the microscale. Motivated by current interest in quantum
computation we recently defined quantum lattice gas automata; in this paper we
initiate a project to analyze which physical processes these models can
effectively simulate. Studying the single particle sector of a one dimensional
quantum lattice gas we find discrete analogues of plane waves and wave packets,
and then investigate their behaviour in the presence of inhomogeneous
potentials.Comment: 19 pages, plain TeX, 14 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages), two additional large
figures available upon reques
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