8,846 research outputs found
Bounded Languages Meet Cellular Automata with Sparse Communication
Cellular automata are one-dimensional arrays of interconnected interacting
finite automata. We investigate one of the weakest classes, the real-time
one-way cellular automata, and impose an additional restriction on their
inter-cell communication by bounding the number of allowed uses of the links
between cells. Moreover, we consider the devices as acceptors for bounded
languages in order to explore the borderline at which non-trivial decidability
problems of cellular automata classes become decidable. It is shown that even
devices with drastically reduced communication, that is, each two neighboring
cells may communicate only constantly often, accept bounded languages that are
not semilinear. If the number of communications is at least logarithmic in the
length of the input, several problems are undecidable. The same result is
obtained for classes where the total number of communications during a
computation is linearly bounded
On two-way communication in cellular automata with a fixed number of cells
The effect of adding two-way communication to k cells one-way cellular automata (kC-OCAs) on their size of description is studied. kC-OCAs are a parallel model for the regular languages that consists of an array of k identical deterministic finite automata (DFAs), called cells, operating in parallel. Each cell gets information from its right neighbor only. In this paper, two models with different amounts of two-way communication are investigated. Both models always achieve quadratic savings when compared to DFAs. When compared to a one-way cellular model, the result is that minimum two-way communication can achieve at most quadratic savings whereas maximum two-way communication may provide savings bounded by a polynomial of degree k
Causal graph dynamics
We extend the theory of Cellular Automata to arbitrary, time-varying graphs.
In other words we formalize, and prove theorems about, the intuitive idea of a
labelled graph which evolves in time - but under the natural constraint that
information can only ever be transmitted at a bounded speed, with respect to
the distance given by the graph. The notion of translation-invariance is also
generalized. The definition we provide for these "causal graph dynamics" is
simple and axiomatic. The theorems we provide also show that it is robust. For
instance, causal graph dynamics are stable under composition and under
restriction to radius one. In the finite case some fundamental facts of
Cellular Automata theory carry through: causal graph dynamics admit a
characterization as continuous functions, and they are stable under inversion.
The provided examples suggest a wide range of applications of this mathematical
object, from complex systems science to theoretical physics. KEYWORDS:
Dynamical networks, Boolean networks, Generative networks automata, Cayley
cellular automata, Graph Automata, Graph rewriting automata, Parallel graph
transformations, Amalgamated graph transformations, Time-varying graphs, Regge
calculus, Local, No-signalling.Comment: 25 pages, 9 figures, LaTeX, v2: Minor presentation improvements, v3:
Typos corrected, figure adde
Complete Symmetry in D2L Systems and Cellular Automata
We introduce completely symmetric D2L systems and cellular automata by means of an additional restriction on the corresponding symmetric devices. Then we show that completely symmetric D2L systems and cellular automata are still able to simulate Turing machine computations. As corollaries we obtain new characterizations of the recursively enumerable languages and of some space-bounded complexity classes
Free fall and cellular automata
Three reasonable hypotheses lead to the thesis that physical phenomena can be
described and simulated with cellular automata. In this work, we attempt to
describe the motion of a particle upon which a constant force is applied, with
a cellular automaton, in Newtonian physics, in Special Relativity, and in
General Relativity. The results are very different for these three theories.Comment: In Proceedings DCM 2015, arXiv:1603.0053
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
Counter Machines and Distributed Automata: A Story about Exchanging Space and Time
We prove the equivalence of two classes of counter machines and one class of
distributed automata. Our counter machines operate on finite words, which they
read from left to right while incrementing or decrementing a fixed number of
counters. The two classes differ in the extra features they offer: one allows
to copy counter values, whereas the other allows to compute copyless sums of
counters. Our distributed automata, on the other hand, operate on directed path
graphs that represent words. All nodes of a path synchronously execute the same
finite-state machine, whose state diagram must be acyclic except for
self-loops, and each node receives as input the state of its direct
predecessor. These devices form a subclass of linear-time one-way cellular
automata.Comment: 15 pages (+ 13 pages of appendices), 5 figures; To appear in the
proceedings of AUTOMATA 2018
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