487 research outputs found
Infinite Communication Complexity
Suppose that Alice and Bob are given each an infinite string, and they want
to decide whether their two strings are in a given relation. How much
communication do they need? How can communication be even defined and measured
for infinite strings? In this article, we propose a formalism for a notion of
infinite communication complexity, prove that it satisfies some natural
properties and coincides, for relevant applications, with the classical notion
of amortized communication complexity. More-over, an application is given for
tackling some conjecture about tilings and multidimensional sofic shifts.Comment: First Version. Written from the Computer Science PO
Revisiting the Rice Theorem of Cellular Automata
A cellular automaton is a parallel synchronous computing model, which
consists in a juxtaposition of finite automata whose state evolves according to
that of their neighbors. It induces a dynamical system on the set of
configurations, i.e. the infinite sequences of cell states. The limit set of
the cellular automaton is the set of configurations which can be reached
arbitrarily late in the evolution.
In this paper, we prove that all properties of limit sets of cellular
automata with binary-state cells are undecidable, except surjectivity. This is
a refinement of the classical "Rice Theorem" that Kari proved on cellular
automata with arbitrary state sets.Comment: 12 pages conference STACS'1
Sofic Trace of a Cellular Automaton
The trace subshift of a cellular automaton is the subshift of all possible
columns that may appear in a space-time diagram, ie the infinite sequence of
states of a particular cell of a configuration; in the language of symbolic
dynamics one says that it is a factor system. In this paper we study conditions
for a sofic subshift to be the trace of a cellular automaton.Comment: 10 pages + 6 for included proof
A compact topology for sand automata
In this paper, we exhibit a strong relation between the sand automata
configuration space and the cellular automata configuration space. This
relation induces a compact topology for sand automata, and a new context in
which sand automata are homeomorphic to cellular automata acting on a specific
subshift. We show that the existing topological results for sand automata,
including the Hedlund-like representation theorem, still hold. In this context,
we give a characterization of the cellular automata which are sand automata,
and study some dynamical behaviors such as equicontinuity. Furthermore, we deal
with the nilpotency. We show that the classical definition is not meaningful
for sand automata. Then, we introduce a suitable new notion of nilpotency for
sand automata. Finally, we prove that this simple dynamical behavior is
undecidable
Ultimate Traces of Cellular Automata
A cellular automaton (CA) is a parallel synchronous computing model, which
consists in a juxtaposition of finite automata (cells) whose state evolves
according to that of their neighbors. Its trace is the set of infinite words
representing the sequence of states taken by some particular cell. In this
paper we study the ultimate trace of CA and partial CA (a CA restricted to a
particular subshift). The ultimate trace is the trace observed after a long
time run of the CA. We give sufficient conditions for a set of infinite words
to be the trace of some CA and prove the undecidability of all properties over
traces that are stable by ultimate coincidence.Comment: 12 pages + 5 of appendix conference STACS'1
Projective subdynamics and universal shifts
International audienceWe study the projective subdynamics of two-dimensional shifts of finite type, which is the set of one-dimensional configurations that appear as columns in them. We prove that a large class of one-dimensional shifts can be obtained as such, namely the effective subshifts which contain positive-entropy sofic subshifts. The proof involves some simple notions of simulation that may be of interest for other constructions. As an example, it allows us to prove the undecidability of all non-trivial properties of projective subdynamics
Applied public-key steganography
International audienceWe consider the problem of hiding information in a steganographic framework, i.e. embedding a binary message within an apparently innocuous content, in order to establish a `suspicion-free' digital communication channel. The adversary is passive as no intentional attack is foreseen. The only threat is that she discovers the presence of a hidden communication. The main goal of this article is to find if the calar Costa Scheme, a recently published embedding method exploiting side information at the encoder, is suitable for that framework. We justify its use assessing its security level with respect to the Cachin's criterion. We derive a public-key stegosystem following the ideas of R. Anderson and P. Petitcolas. This technique is eventually applied to PCM audio contents. Experimental performances are detailed in terms of bit-rate and Kullback-Leibler distance
The generic limit set of cellular automata
In this article, we consider a topological dynamical system. The generic limit set is the smallest closed subset which has a comeager realm of attraction. We study some of its topological properties, and the links with equicontinuity and sensitivity. We emphasize the case of cellular automata, for which the generic limit set is included in all subshift attractors, and discuss directional dynamics, as well as the link with measure-theoretical similar notions
The generic limit set of cellular automata
In this article, we consider a topological dynamical system. The generic
limit set is the smallest closed subset which has a comeager realm of
attraction. We study some of its topological properties, and the links with
equicontinuity and sensitivity. We emphasize the case of cellular automata, for
which the generic limit set is included in all subshift attractors, and discuss
directional dynamics, as well as the link with measure-theoretical similar
notions
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