TY - JOUR

T1 - Fast exponentiation using the truncation operation

AU - Bshouty, Nader H.

AU - Mansour, Yishay

AU - Schieber, Baruch

AU - Tiwari, Prasson

PY - 1992/9

Y1 - 1992/9

N2 - Given an integer k, and an arbitrary integer greater than {Mathematical expression}, we prove a tight bound of {Mathematical expression} on the time required to compute {Mathematical expression} with operations {+, -, *, /, ⌊·⌋, ≤}, and constants {0, 1}. In contrast, when the floor operation is not available this computation requires Ω(k) time. Using the upper bound, we give an {Mathematical expression} time algorithm for computing ⌊log log a⌋, for all n-bit integers a. This upper bound matches the lower bound for computing this function given by Mansour, Schieber, and Tiwari. To the best of our knowledge these are the first non-constant tight bounds for computations involving the floor operation.

AB - Given an integer k, and an arbitrary integer greater than {Mathematical expression}, we prove a tight bound of {Mathematical expression} on the time required to compute {Mathematical expression} with operations {+, -, *, /, ⌊·⌋, ≤}, and constants {0, 1}. In contrast, when the floor operation is not available this computation requires Ω(k) time. Using the upper bound, we give an {Mathematical expression} time algorithm for computing ⌊log log a⌋, for all n-bit integers a. This upper bound matches the lower bound for computing this function given by Mansour, Schieber, and Tiwari. To the best of our knowledge these are the first non-constant tight bounds for computations involving the floor operation.

KW - Subject classifications: 68Q40

UR - http://www.scopus.com/inward/record.url?scp=0009717068&partnerID=8YFLogxK

U2 - 10.1007/BF01272076

DO - 10.1007/BF01272076

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AN - SCOPUS:0009717068

SN - 1016-3328

VL - 2

SP - 244

EP - 255

JO - Computational Complexity

JF - Computational Complexity

IS - 3

ER -