A lower bound for integer greatest common divisor computations

Autor:	Baruch Schieber, Prasoon Tiwari, Yishay Mansour
Rok vydání:	1991
Předmět:	Upper and lower bounds Combinatorics Tree (descriptive set theory) Number theory Integer Artificial Intelligence Hardware and Architecture Control and Systems Engineering Greatest common divisor Computation tree Truncation (statistics) Software Multiple Information Systems Mathematics
Zdroj:	Journal of the ACM. 38:453-471
ISSN:	1557-735X 0004-5411
Popis:	It is proved that no finite computation tree with operations { +, -, *, /, mod, < } can decide whether the greatest common divisor (gcd) of a and b is one, for all pairs of integers a and b . This settles a problem posed by Gro¨tschel et al. Moreover, if the constants explicitly involved in any operation performed in the tree are restricted to be “0” and “1” (and any other constant must be computed), then we prove an Ω(log log n ) lower bound on the depth of any computation tree with operations { +, -, *, /, mod, < } that decides whether the gcd of a and b is one, for all pairs of n -bit integers a and b . A novel technique for handling the truncation operation is implicit in the proof of this lower bound. In a companion paper, other lower bounds for a large class of problems are proved using a similar technique.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::19e96682f9792112d4fd388f18a623e5 https://doi.org/10.1145/103516.103522 Zobrazit plný text záznamu