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...
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...
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...
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...
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...