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» Bounding Degrees on RPL
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STOC
2003
ACM
110views Algorithms» more  STOC 2003»
15 years 10 months ago
New degree bounds for polynomial threshold functions
A real multivariate polynomial p(x1, . . . , xn) is said to sign-represent a Boolean function f : {0, 1}n {-1, 1} if the sign of p(x) equals f(x) for all inputs x {0, 1}n. We gi...
Ryan O'Donnell, Rocco A. Servedio
JCSS
1998
65views more  JCSS 1998»
14 years 9 months ago
Good Degree Bounds on Nullstellensatz Refutations of the Induction Principle
This paper gives nearly optimal, logarithmic upper and lower bounds on the minimum degree of Nullstellensatz refutations (i.e., polynomials) of the propositional induction princip...
Samuel R. Buss, Toniann Pitassi
CSL
2009
Springer
15 years 4 months ago
Automatic Structures of Bounded Degree Revisited
Abstract. It it shown that the first-order theory of an automatic structure, whose Gaifman graph has bounded degree, is decidable in doubly exponential space (for injective automa...
Dietrich Kuske, Markus Lohrey
ECCC
2006
123views more  ECCC 2006»
14 years 9 months ago
A Note on Adaptivity in Testing Properties of Bounded Degree Graphs
We show that in the bounded degree model for graph property testing, adaptivity is essential. An algorithm is non-adaptive if it makes all queries to the input before receiving an...
Sofya Raskhodnikova, Adam Smith
STOC
2007
ACM
239views Algorithms» more  STOC 2007»
15 years 10 months ago
Approximating minimum bounded degree spanning trees to within one of optimal
In the MINIMUM BOUNDED DEGREE SPANNING TREE problem, we are given an undirected graph with a degree upper bound Bv on each vertex v, and the task is to find a spanning tree of min...
Mohit Singh, Lap Chi Lau