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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
On predictions of the first results from RHIC
In this talk, I will discuss the predictions of the first results from RHIC:
the charged particle multiplicity , its centrality
dependence and the elliptic flow .Comment: A plenary review talk at Quark Matter 2001, Stony Brook, USA, January
2001, 10 page
Note on proton-antiproton suppression in 200 AGeV Au-Au collisions
We discuss the measured nuclear suppression of p + pbar production in 200
AGeV Au-Au collisions at RHIC within radiative energy loss. For the AKK set of
fragmentation functions, proton production is dominated by gluons, giving rise
to the expectation that the nuclear suppression for p + pbar should be stronger
than for pions due to the stronger coupling of gluons to the quenching medium.
Using a hydrodynamical description for the soft matter evolution, we show that
this is indeed seen in the calculation. However, the expected suppression
factors for pions and protons are sufficiently similar that a discrimination
with present data is not possible. In the high p_T region above 6 GeV where the
contributions of hydrodynamics and recombination to hadron production are
negligible, the model calculation is in good agreement with the data on p +
pbar suppression.Comment: 3 pages, 2 figures, slightly expanded versio
On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures
We study the notion of limit sets of cellular automata associated with
probability measures (mu-limit sets). This notion was introduced by P. Kurka
and A. Maass. It is a refinement of the classical notion of omega-limit sets
dealing with the typical long term behavior of cellular automata. It focuses on
the words whose probability of appearance does not tend to 0 as time tends to
infinity (the persistent words). In this paper, we give a characterisation of
the persistent language for non sensible cellular automata associated with
Bernouilli measures. We also study the computational complexity of these
languages. We show that the persistent language can be non-recursive. But our
main result is that the set of quasi-nilpotent cellular automata (those with a
single configuration in their mu-limit set) is neither recursively enumerable
nor co-recursively enumerable
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