k -Block parallel addition versus 1-block parallel addition in non-standard numeration systems
نویسندگان
چکیده
منابع مشابه
k-Block parallel addition versus 1-block parallel addition in non-standard numeration systems
Parallel addition in integer base is used for speeding up multiplication and division algorithms. k-block parallel addition has been introduced by Kornerup in [14]: instead of manipulating single digits, one works with blocks of fixed length k. The aim of this paper is to investigate how such notion influences the relationship between the base and the cardinality of the alphabet allowing block ...
متن کاملParallel addition in non-standard numeration systems
We consider numeration systems where digits are integers and the base is an algebraic number β such that |β| > 1 and β satisfies a polynomial where one coefficient is dominant in a certain sense. For this class of bases β, we can find an alphabet of signed-digits on which addition is realizable by a parallel algorithm in constant time. This algorithm is a kind of generalization of the one of Av...
متن کاملMinimal Digit Sets for Parallel Addition in Non-Standard Numeration Systems
We study parallel algorithms for addition of numbers having finite representation in a positional numeration system defined by a base β in C and a finite digit set A of contiguous integers containing 0. For a fixed base β, we focus on the question of the size of the alphabet that permits addition in constant time, independently of the length of representation of the summands. We produce lower b...
متن کاملOstrowski Numeration Systems, Addition and Finite Automata
We present an elementary three pass algorithm for computing addition in Ostrowski numerations systems. When a is quadratic, addition in the Ostrowski numeration system based on a is recognizable by a finite automaton. We deduce that a subset of X ⊆Nn is definable in (N,+,Va), where Va is the function that maps a natural number x to the smallest denominator of a convergent of a that appears in t...
متن کاملParallel Multi-Block ADMM with o(1 / k) Convergence
This paper introduces a parallel and distributed extension to the alternating direction method of multipliers (ADMM) for solving convex problem: minimize f1(x1) + ∙ ∙ ∙ + fN (xN ) subject to A1x1 + ∙ ∙ ∙ + ANxN = c, x1 ∈ X1, . . . , xN ∈ XN . The algorithm decomposes the original problem into N smaller subproblems and solves them in parallel at each iteration. This Jacobian-type algorithm is we...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2014.06.001