2,723 research outputs found
Computational Aspects of Asynchronous CA
This work studies some aspects of the computational power of fully
asynchronous cellular automata (ACA). We deal with some notions of simulation
between ACA and Turing Machines. In particular, we characterize the updating
sequences specifying which are "universal", i.e., allowing a (specific family
of) ACA to simulate any TM on any input. We also consider the computational
cost of such simulations
Intrinsic universality and the computational power of self-assembly
This short survey of recent work in tile self-assembly discusses the use of
simulation to classify and separate the computational and expressive power of
self-assembly models. The journey begins with the result that there is a single
universal tile set that, with proper initialization and scaling, simulates any
tile assembly system. This universal tile set exhibits something stronger than
Turing universality: it captures the geometry and dynamics of any simulated
system. From there we find that there is no such tile set in the
noncooperative, or temperature 1, model, proving it weaker than the full tile
assembly model. In the two-handed or hierarchal model, where large assemblies
can bind together on one step, we encounter an infinite set, of infinite
hierarchies, each with strictly increasing simulation power. Towards the end of
our trip, we find one tile to rule them all: a single rotatable flipable
polygonal tile that can simulate any tile assembly system. It seems this could
be the beginning of a much longer journey, so directions for future work are
suggested.Comment: In Proceedings MCU 2013, arXiv:1309.104
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
On the decomposition of stochastic cellular automata
In this paper we present two interesting properties of stochastic cellular
automata that can be helpful in analyzing the dynamical behavior of such
automata. The first property allows for calculating cell-wise probability
distributions over the state set of a stochastic cellular automaton, i.e.
images that show the average state of each cell during the evolution of the
stochastic cellular automaton. The second property shows that stochastic
cellular automata are equivalent to so-called stochastic mixtures of
deterministic cellular automata. Based on this property, any stochastic
cellular automaton can be decomposed into a set of deterministic cellular
automata, each of which contributes to the behavior of the stochastic cellular
automaton.Comment: Submitted to Journal of Computation Science, Special Issue on
Cellular Automata Application
Measuring Communication in Parallel Communicating Finite Automata
Systems of deterministic finite automata communicating by sending their
states upon request are investigated, when the amount of communication is
restricted. The computational power and decidability properties are studied for
the case of returning centralized systems, when the number of necessary
communications during the computations of the system is bounded by a function
depending on the length of the input. It is proved that an infinite hierarchy
of language families exists, depending on the number of messages sent during
their most economical recognitions. Moreover, several properties are shown to
be not semi-decidable for the systems under consideration.Comment: In Proceedings AFL 2014, arXiv:1405.527
Polynomial Synthesis of Asynchronous Automata
Zielonka's theorem shows that each regular set of Mazurkiewicz traces can be
implemented as a system of synchronized processes with a distributed control
structure called asynchronous automaton. This paper gives a polynomial
algorithm for the synthesis of a non-deterministic asynchronous automaton from
a regular Mazurkiewicz trace language. This new construction is based on an
unfolding approach that improves the complexity of Zielonka's and Pighizzini's
techniques in terms of the number of states.Comment: The MOdelling and VErification (MOVE) tea
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