106 research outputs found
Limit sets of stable Cellular Automata
We study limit sets of stable cellular automata standing from a symbolic
dynamics point of view where they are a special case of sofic shifts admitting
a steady epimorphism. We prove that there exists a right-closing
almost-everywhere steady factor map from one irreducible sofic shift onto
another one if and only if there exists such a map from the domain onto the
minimal right-resolving cover of the image. We define right-continuing
almost-everywhere steady maps and prove that there exists such a steady map
between two sofic shifts if and only if there exists a factor map from the
domain onto the minimal right-resolving cover of the image. In terms of
cellular automata, this translates into: A sofic shift can be the limit set of
a stable cellular automaton with a right-closing almost-everywhere dynamics
onto its limit set if and only if it is the factor of a fullshift and there
exists a right- closing almost-everywhere factor map from the sofic shift onto
its minimal right- resolving cover. A sofic shift can be the limit set of a
stable cellular automaton reaching its limit set with a right-continuing
almost-everywhere factor map if and only if it is the factor of a fullshift and
there exists a factor map from the sofic shift onto its minimal right-resolving
cover. Finally, as a consequence of the previous results, we provide a
characterization of the Almost of Finite Type shifts (AFT) in terms of a
property of steady maps that have them as range.Comment: 18 pages, 3 figure
Sofic-Dyck shifts
We define the class of sofic-Dyck shifts which extends the class of
Markov-Dyck shifts introduced by Inoue, Krieger and Matsumoto. Sofic-Dyck
shifts are shifts of sequences whose finite factors form unambiguous
context-free languages. We show that they correspond exactly to the class of
shifts of sequences whose sets of factors are visibly pushdown languages. We
give an expression of the zeta function of a sofic-Dyck shift
Coding for the Optical Channel: the Ghost-Pulse Constraint
We consider a number of constrained coding techniques that can be used to
mitigate a nonlinear effect in the optical fiber channel that causes the
formation of spurious pulses, called ``ghost pulses.'' Specifically, if is a sequence of bits sent across an optical channel, such that
for some (not necessarily all distinct) but , then the ghost-pulse effect causes to change to 1, thereby
creating an error. We design and analyze several coding schemes using binary
and ternary sequences constrained so as to avoid patterns that give rise to
ghost pulses. We also discuss the design of encoders and decoders for these
coding schemes.Comment: 13 pages, 6 figures; accepted for publication in IEEE Transactions on
Information Theor
Open maps: small and large holes with unusual properties
Let be a two-sided subshift on a finite alphabet endowed with a mixing
probability measure which is positive on all cylinders in . We show that
there exist arbitrarily small finite overlapping union of shifted cylinders
which intersect every orbit under the shift map.
We also show that for any proper subshift of there exists a finite
overlapping unions of shifted cylinders such that its survivor set contains
(in particular, it can have entropy arbitrarily close to the entropy of ).
Both results may be seen as somewhat counter-intuitive.
Finally, we apply these results to a certain class of hyperbolic algebraic
automorphisms of a torus.Comment: 15 pages, no figure
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