1,870 research outputs found
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Conjugacy of one-dimensional one-sided cellular automata is undecidable
Two cellular automata are strongly conjugate if there exists a
shift-commuting conjugacy between them. We prove that the following two sets of
pairs of one-dimensional one-sided cellular automata over a full shift
are recursively inseparable: (i) pairs where has strictly larger
topological entropy than , and (ii) pairs that are strongly conjugate and
have zero topological entropy.
Because there is no factor map from a lower entropy system to a higher
entropy one, and there is no embedding of a higher entropy system into a lower
entropy system, we also get as corollaries that the following decision problems
are undecidable: Given two one-dimensional one-sided cellular automata and
over a full shift: Are and conjugate? Is a factor of ? Is
a subsystem of ? All of these are undecidable in both strong and weak
variants (whether the homomorphism is required to commute with the shift or
not, respectively). It also immediately follows that these results hold for
one-dimensional two-sided cellular automata.Comment: 12 pages, 2 figures, accepted for SOFSEM 201
Reversible Logic Elements with Memory and Their Universality
Reversible computing is a paradigm of computation that reflects physical
reversibility, one of the fundamental microscopic laws of Nature. In this
survey, we discuss topics on reversible logic elements with memory (RLEM),
which can be used to build reversible computing systems, and their
universality. An RLEM is called universal, if any reversible sequential machine
(RSM) can be realized as a circuit composed only of it. Since a finite-state
control and a tape cell of a reversible Turing machine (RTM) are formalized as
RSMs, any RTM can be constructed from a universal RLEM. Here, we investigate
2-state RLEMs, and show that infinitely many kinds of non-degenerate RLEMs are
all universal besides only four exceptions. Non-universality of these
exceptional RLEMs is also argued.Comment: In Proceedings MCU 2013, arXiv:1309.104
Turing degrees of limit sets of cellular automata
Cellular automata are discrete dynamical systems and a model of computation.
The limit set of a cellular automaton consists of the configurations having an
infinite sequence of preimages. It is well known that these always contain a
computable point and that any non-trivial property on them is undecidable. We
go one step further in this article by giving a full characterization of the
sets of Turing degrees of cellular automata: they are the same as the sets of
Turing degrees of effectively closed sets containing a computable point
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
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
- …