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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:... (Update)
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BibTeX entry: (Update)
C.K. Yap. A New Lower Bound Construction for Commutative Thue Systems with Applications Journal of Symbolic Computation, 12:1--27, 1991. http://citeseer.ist.psu.edu/yap97new.html More
@article{ yap90new,
author = "Chee K. Yap",
title = "A new lower bound construction for commutative {Thue} systems with applications",
journal = "Journal of Symbolic Computation",
volume = "to appear",
year = "1990",
url = "citeseer.ist.psu.edu/yap97new.html" }
Citations (may not include all citations):77 The complexity of the word problems for commutative semigrou.. (context) - Mayr, Meyer - 1982
31 Recursive unsolvability of a problem of Thue (context) - Post - 1947
21 Die Frage der endlich vielen Schritte in der Theorie der Pol.. (context) - Hermann - 1926
15 the complexity of computing syzygies (context) - Bayer, Stillman - 1988
15 Constructions in Algebra (context) - Seidenberg - 1974
12 A superexponential lower bound for Grobner bases and ChurchR.. (context) - Huynh - 1986
11 Some effectivity problems in polynomial ideal theory (context) - Giusti - 1984
10 Upper and lower bounds for the degree of Grobner bases (context) - Moller, Mora
8 The structure of polynomial ideals and Grobner bases (context) - Dub'e - 1988
4 A double exponential lower bound for degree-compatible Grobn.. (context) - Yap - 1988
2 Fields of large transcendence degree generated by values of .. (context) - Masser, Wustholz - 1983
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