28,920 research outputs found
Guaranteeing the diversity of number generators
A major problem in using iterative number generators of the form
x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard
to analyze when the generator is designed, hard to detect in real time when the
generator is used, and can have devastating cryptanalytic implications. In this
paper we define a measure of security, called_sequence_diversity_, which
generalizes the notion of cycle-length for non-iterative generators. We then
introduce the class of counter assisted generators, and show how to turn any
iterative generator (even a bad one designed or seeded by an adversary) into a
counter assisted generator with a provably high diversity, without reducing the
quality of generators which are already cryptographically strong.Comment: Small update
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Permutation and sampling with maximum length CA for pseudorandom number generation
In this paper, we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata (CA). Dynamic permutation and sampling have not been explored in previous CA work and a suitable implementation is shown using a two CA model. Three different schemes that incorporate these two operations are suggested - Weighted Permutation Vector Sampling with Controlled Multiplexing, Weighted Permutation Vector Sampling with Irregular Decimation and Permutation Programmed CA Sampling. The experiment results show that the resulting sequences have varying degrees of improvement in DIEHARD results and linear complexity compared to the CA
Subclasses of Presburger Arithmetic and the Weak EXP Hierarchy
It is shown that for any fixed , the -fragment of
Presburger arithmetic, i.e., its restriction to quantifier alternations
beginning with an existential quantifier, is complete for
, the -th level of the weak EXP
hierarchy, an analogue to the polynomial-time hierarchy residing between
and . This result completes the
computational complexity landscape for Presburger arithmetic, a line of
research which dates back to the seminal work by Fischer & Rabin in 1974.
Moreover, we apply some of the techniques developed in the proof of the lower
bound in order to establish bounds on sets of naturals definable in the
-fragment of Presburger arithmetic: given a -formula
, it is shown that the set of non-negative solutions is an ultimately
periodic set whose period is at most doubly-exponential and that this bound is
tight.Comment: 10 pages, 2 figure
Measuring economic complexity of countries and products: which metric to use?
Evaluating the economies of countries and their relations with products in
the global market is a central problem in economics, with far-reaching
implications to our theoretical understanding of the international trade as
well as to practical applications, such as policy making and financial
investment planning. The recent Economic Complexity approach aims to quantify
the competitiveness of countries and the quality of the exported products based
on the empirical observation that the most competitive countries have
diversified exports, whereas developing countries only export few low quality
products -- typically those exported by many other countries. Two different
metrics, Fitness-Complexity and the Method of Reflections, have been proposed
to measure country and product score in the Economic Complexity framework. We
use international trade data and a recent ranking evaluation measure to
quantitatively compare the ability of the two metrics to rank countries and
products according to their importance in the network. The results show that
the Fitness-Complexity metric outperforms the Method of Reflections in both the
ranking of products and the ranking of countries. We also investigate a
Generalization of the Fitness-Complexity metric and show that it can produce
improved rankings provided that the input data are reliable
Low Density Lattice Codes
Low density lattice codes (LDLC) are novel lattice codes that can be decoded
efficiently and approach the capacity of the additive white Gaussian noise
(AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional
Euclidean space as a linear transformation of a corresponding integer message
vector b, i.e., x = Gb, where H, the inverse of G, is restricted to be sparse.
The fact that H is sparse is utilized to develop a linear-time iterative
decoding scheme which attains, as demonstrated by simulations, good error
performance within ~0.5dB from capacity at block length of n = 100,000 symbols.
The paper also discusses convergence results and implementation considerations.Comment: 24 pages, 4 figures. Submitted for publication in IEEE transactions
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