Minimal Digit Sets for Parallel Addition in Non-Standard Numeration Systems
نویسندگان
چکیده
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 bounds on the size of such an alphabet A. For several types of well-studied bases (negative integer, complex
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