20 citations · 60 across the 10 of their papers we have counts for
12 papers
The carry propagation of the successor function
Valérie Berthé, Christiane Frougny, Michel Rigo +1
Given any numeration system, we call carry propagation at a number the number of digits that are changed when going from the representation of to the one of , and amor…
Minimal digit sets for parallel addition in non-standard numeration systems
Christiane Frougny, Edita Pelantova, Milena Svobodova
We study parallel algorithms for addition of numbers having finite representation in a positional numeration system defined by a base in and a finite digit set $\m…
On-line algorithms for multiplication and division in real and complex numeration systems
Christiane Frougny, Marta Pavelka, Edita Pelantova +1
A positional numeration system is given by a base and by a set of digits. The base is a real or complex number such that , and the digit set is a finite set of digit…
Two applications of the spectrum of numbers
Christiane Frougny, Edita Pelantová
Let the base be a complex number, , and let $A \subset \C$ be a finite alphabet of digits. The \emph{-spectrum} of is the set $S_{A}(β) = \{\sum_{k=0}^n a_kβ^k \m…
-block parallel addition versus -block parallel addition in non-standard numeration systems
Christiane Frougny, Pavel Heller, Edita Pelantová +1
Parallel addition in integer base is used for speeding up multiplication and division algorithms. -block parallel addition has been introduced by Kornerup in 1999: instead of ma…
Negative bases and automata
Christiane Frougny, Anna Chiara Lai
We study expansions in non-integer negative base -β introduced by Ito and Sadahiro. Using countable automata associated with (-β)-expansions, we characterize the case where the (-β…