12,668 research outputs found
Forbidden Configurations: Finding the number predicted by the Anstee-Sali Conjecture is NP-hard
Let F be a hypergraph and let forb(m,F) denote the maximum number of edges a
hypergraph with m vertices can have if it doesn't contain F as a subhypergraph.
A conjecture of Anstee and Sali predicts the asymptotic behaviour of forb(m,F)
for fixed F. In this paper we prove that even finding this predicted asymptotic
behaviour is an NP-hard problem, meaning that if the Anstee-Sali conjecture
were true, finding the asymptotics of forb(m,F) would be NP-hard
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
Realization of aperiodic subshifts and uniform densities in groups
A theorem of Gao, Jackson and Seward, originally conjectured to be false by
Glasner and Uspenskij, asserts that every countable group admits a
-coloring. A direct consequence of this result is that every countable group
has a strongly aperiodic subshift on the alphabet . In this article,
we use Lov\'asz local lemma to first give a new simple proof of said theorem,
and second to prove the existence of a -effectively closed strongly
aperiodic subshift for any finitely generated group . We also study the
problem of constructing subshifts which generalize a property of Sturmian
sequences to finitely generated groups. More precisely, a subshift over the
alphabet has uniform density if for every
configuration the density of 's in any increasing sequence of balls
converges to . We show a slightly more general result which implies
that these subshifts always exist in the case of groups of subexponential
growth.Comment: minor typos correcte
Discrete symmetries from hidden sectors
We study the presence of abelian discrete symmetries in globally consistent
orientifold compactifications based on rational conformal field theory. We
extend previous work [1] by allowing the discrete symmetries to be a linear
combination of U(1) gauge factors of the visible as well as the hidden sector.
This more general ansatz significantly increases the probability of finding a
discrete symmetry in the low energy effective action. Applied to globally
consistent MSSM-like Gepner constructions we find multiple models that allow
for matter parity or Baryon triality.Comment: 20 page
Topological transition in disordered planar matching: combinatorial arcs expansion
In this paper, we investigate analytically the properties of the disordered
Bernoulli model of planar matching. This model is characterized by a
topological phase transition, yielding complete planar matching solutions only
above a critical density threshold. We develop a combinatorial procedure of
arcs expansion that explicitly takes into account the contribution of short
arcs, and allows to obtain an accurate analytical estimation of the critical
value by reducing the global constrained problem to a set of local ones. As an
application to a toy representation of the RNA secondary structures, we suggest
generalized models that incorporate a one-to-one correspondence between the
contact matrix and the RNA-type sequence, thus giving sense to the notion of
effective non-integer alphabets.Comment: 28 pages, 6 figures, published versio
On Derivatives and Subpattern Orders of Countable Subshifts
We study the computational and structural aspects of countable
two-dimensional SFTs and other subshifts. Our main focus is on the topological
derivatives and subpattern posets of these objects, and our main results are
constructions of two-dimensional countable subshifts with interesting
properties. We present an SFT whose iterated derivatives are maximally complex
from the computational point of view, a sofic shift whose subpattern poset
contains an infinite descending chain, a family of SFTs whose finite subpattern
posets contain arbitrary finite posets, and a natural example of an SFT with
infinite Cantor-Bendixon rank.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
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