1,697 research outputs found
A Fibonacci analogue of the two's complement numeration system
Using the classic two's complement notation of signed integers, the
fundamental arithmetic operations of addition, subtraction, and multiplication
are identical to those for unsigned binary numbers. We introduce a
Fibonacci-equivalent of the two's complement notation and we show that addition
in this numeration system can be performed by a deterministic finite-state
transducer. The result is based on the Berstel adder, which performs addition
of the usual Fibonacci representations of nonnegative integers and for which we
provide a new constructive proof. Moreover, we characterize the
Fibonacci-equivalent of the two's complement notation as an increasing
bijection between and a particular language.Comment: v3: 21 pages, 3 figures, 3 tables. v4: 24 pages, added a new section
characterizing the Fibonacci's complement numeration system as an increasing
bijection. v5: changes after revie
Redundancy of minimal weight expansions in Pisot bases
Motivated by multiplication algorithms based on redundant number
representations, we study representations of an integer as a sum , where the digits are taken from a finite alphabet
and is a linear recurrent sequence of Pisot type with
. The most prominent example of a base sequence is the
sequence of Fibonacci numbers. We prove that the representations of minimal
weight are recognised by a finite automaton and obtain an
asymptotic formula for the average number of representations of minimal weight.
Furthermore, we relate the maximal order of magnitude of the number of
representations of a given integer to the joint spectral radius of a certain
set of matrices
A Comparative Study of Some Pseudorandom Number Generators
We present results of an extensive test program of a group of pseudorandom
number generators which are commonly used in the applications of physics, in
particular in Monte Carlo simulations. The generators include public domain
programs, manufacturer installed routines and a random number sequence produced
from physical noise. We start by traditional statistical tests, followed by
detailed bit level and visual tests. The computational speed of various
algorithms is also scrutinized. Our results allow direct comparisons between
the properties of different generators, as well as an assessment of the
efficiency of the various test methods. This information provides the best
available criterion to choose the best possible generator for a given problem.
However, in light of recent problems reported with some of these generators, we
also discuss the importance of developing more refined physical tests to find
possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables
2 and 7, and in the text, correspondingly
On the character variety of the three-holed projective plane
We study the (relative) SL(2,C) character varieties of the three-holed
projective plane and the action of the mapping class group on them. We describe
a domain of discontinuity for this action, which strictly contains the set of
primitive stable representations defined by Minsky, and also the set of
convex-cocompact characters. We consider the relationship with the previous
work of the authors and S. P. Tan on the character variety of the four-holed
sphere.Comment: 27 page
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