A New Lower Bound Construction for Commutative Thue Systems, with Applications (1997)
| Citations: | 11 - 1 self |
BibTeX
@MISC{Yap97anew,
author = {Chee K. Yap},
title = {A New Lower Bound Construction for Commutative Thue Systems, with Applications},
year = {1997}
}
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Abstract
For n 1; d 2, we describe a commutative Thue system that has ¸ 2n variables and O(n) rules, each rule of size d + O(1) and that counts to d 2 n in a certain technical sense. This gives a more "efficient" alternative to a well-known construction of Mayr and Meyer. Using this construction, we sharpen the known double-exponential lower bounds for the maximum degrees D(n; d); I(n; d); S(n; d) associated (respectively) with Grobner bases, ideal membership problem and the syzygy basis problem: D(n; d) S(n; d) d 2 m ; I(n; d) d 2 m where m ¸ n=2, and n; d sufficiently large. For comparison, it was known that D(n; d) d 2 n and I(n; d) (2d) 2 n . Keywords: Lower bound, commutative Thue system, Grobner basis, ideal membership problem, syzygy basis problem This research is supported in part by NSF Grants DCR-84-01898, CCR-87-03458 and ONR Grant N00014-85-K-0046. The work was carried out while visiting the Research Institute for Symbolic Computation (RISC-LINZ), Johannes K...
Citations
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