4,068 research outputs found
Black-Box Complexity: Breaking the Barrier of LeadingOnes
We show that the unrestricted black-box complexity of the -dimensional
XOR- and permutation-invariant LeadingOnes function class is . This shows that the recent natural looking bound is
not tight.
The black-box optimization algorithm leading to this bound can be implemented
in a way that only 3-ary unbiased variation operators are used. Hence our bound
is also valid for the unbiased black-box complexity recently introduced by
Lehre and Witt (GECCO 2010). The bound also remains valid if we impose the
additional restriction that the black-box algorithm does not have access to the
objective values but only to their relative order (ranking-based black-box
complexity).Comment: 12 pages, to appear in the Proc. of Artificial Evolution 2011, LNCS
7401, Springer, 2012. For the unrestricted black-box complexity of
LeadingOnes there is now a tight bound, cf.
http://eccc.hpi-web.de/report/2012/087
Habit Formation and the Evolution of Social Communication Networks
Stochastic learning theory;game theory;network formation;social communication;replicator dynamics
Weighted Automata and Logics for Infinite Nested Words
Nested words introduced by Alur and Madhusudan are used to capture structures
with both linear and hierarchical order, e.g. XML documents, without losing
valuable closure properties. Furthermore, Alur and Madhusudan introduced
automata and equivalent logics for both finite and infinite nested words, thus
extending B\"uchi's theorem to nested words. Recently, average and discounted
computations of weights in quantitative systems found much interest. Here, we
will introduce and investigate weighted automata models and weighted MSO logics
for infinite nested words. As weight structures we consider valuation monoids
which incorporate average and discounted computations of weights as well as the
classical semirings. We show that under suitable assumptions, two resp. three
fragments of our weighted logics can be transformed into each other. Moreover,
we show that the logic fragments have the same expressive power as weighted
nested word automata.Comment: LATA 2014, 12 page
Conjugation of injections by permutations
Let X be a countably infinite set, and let f, g, and h be any three injective
self-maps of X, each having at least one infinite cycle. (For instance, this
holds if f, g, and h are not bijections.) We show that there are permutations a
and b of X such that h=afa^{-1}bgb^{-1} if and only if |X\Xf|+|X\Xg|=|X\Xh|. We
also prove a version of this statement that holds for infinite sets X that are
not necessarily countable. This generalizes results of Droste and Ore about
permutations.Comment: 27 pages, 4 figure
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