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» Ritt-Wu's Decomposition Algorithm and Geometry Theorem Provi...
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STOC
2007
ACM
108views Algorithms» more  STOC 2007»
14 years 7 months ago
Combinatorial complexity in O-minimal geometry
In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of n definable sets belonging to some fixed definable family of sets i...
Saugata Basu
MOC
1998
73views more  MOC 1998»
13 years 7 months ago
Detecting perfect powers in essentially linear time
This paper (1) gives complete details of an algorithm to compute approximate kth roots; (2) uses this in an algorithm that, given an integer n > 1, either writes n as a perfect ...
Daniel J. Bernstein
FCSC
2007
133views more  FCSC 2007»
13 years 7 months ago
Mathematics mechanization and applications after thirty years
The aim of mathematics mechanization is to develop symbolic algorithms for manipulating mathematical objects, proving and discovering theorems in a mechanical way. This paper gives...
Wenjun Wu, Xiaoshan Gao
JCT
2008
81views more  JCT 2008»
13 years 7 months ago
Algebraic characterization of uniquely vertex colorable graphs
Abstract. The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, it is known that k-color...
Christopher J. Hillar, Troels Windfeldt
COMPGEOM
2011
ACM
12 years 11 months ago
On the structure and composition of forbidden sequences, with geometric applications
Forbidden substructure theorems have proved to be among of the most versatile tools in bounding the complexity of geometric objects and the running time of geometric algorithms. T...
Seth Pettie