Name
Abstract | ||
|---|---|---|
It is proved that no finite computation tree with operations { +, -, *, /, mod, 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 &OHgr;(log log n) lower bound on the depth of any computation tree with operations { +, -, *, /, mod, 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. |
Year | DOI | Venue |
|---|---|---|
1991 | 10.1145/103516.103522 | SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science |
Keywords | Field | DocType |
floor operation,greatest common devisor,lower bound,mod operation,truncation | Integer,Discrete mathematics,Combinatorics,Upper and lower bounds,Omega,Greatest common divisor,Divisor,Computation tree,Mathematics,Computation,Theory of computation | Journal |
Volume | Issue | ISSN |
38 | 2 | 0004-5411 |
ISBN | Citations | PageRank |
0-8186-0877-3 | 16 | 2.45 |
References | Authors | |
14 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yishay Mansour | 1 | 6211 | 745.95 |
| Baruch Schieber | 2 | 2647 | 320.36 |
| Prasoon Tiwari | 3 | 592 | 96.81 |