Parallel addition in non-standard numeration systems

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Parallel 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 کامل

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 کامل

Minimal 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 کامل

Ostrowski 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 کامل

On-line finite automata for addition in some numeration systems

We consider numeration systems where the base is a negative integer, or a complex number which is a root of a negative integer. We give parallel algorithms for addition in these numeration systems, from which we derive on-line algorithms realized by finite automata. A general construction relating addition in base β and addition in base β is given. Results on addition in base β = m √ b, where b...

متن کامل

ذخیره 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: 2011

ISSN: 0304-3975

DOI: 10.1016/j.tcs.2011.06.028