The problem of monotonicity testing of the boolean hypercube is a classic well-studied, yet unsolved question in property testing. We are given query access to f : {0, 1} 7→ R (for some ordered range R). The boolean hypercube B has a natural partial order, denoted by ≺ (defined by the product of coordinate-wise ordering). A function is monotone if all pairs x ≺ y in B, f(x) ≤ f(y). The distance...

In this paper we consider the problem of testing bipartiteness of general graphs. The problem has previously been studied in two models, one most suitable for dense graphs, and one most suitable for bounded-degree graphs. Roughly speaking, dense graphs can be tested for bipartiteness with constant complexity, while the complexity of testing bounded-degree graphs is ~ (pn), where n is the number...

The Euclidean Minimum Spanning Tree problem is to decide whether a given graph G = (P,E) on a set of points in the two dimensional plane is a minimum spanning tree with respect to the Euclidean distance. Czumaj, Sohler, and Ziegler [2] gave a 1-sided-error non-adaptive property-tester for this task of query complexity Õ( √ n). We show that every non-adaptive (not necessarily 1-sided-error) prop...

We consider the problem of testing whether a function f : {0, 1} → {0, 1} is computable by a read-once, width-2 ordered binary decision diagram (OBDD), also known as a branching program. This problem has two variants: one where the variables must occur in a fixed, known order, and one where the variables are allowed to occur in an arbitrary order. We show that for both variants, any nonadaptive...

of results Optimal concurrent-read concurrent-write parallel algorithms for two problems are presented: Finding all the periods of a string. The period of a string can be computed by previous eecient parallel algorithms only if it is shorter than half of the length of the string. Our new algorithm computes all the periods in optimal O(loglog n) time, even if they are longer. The algorithm can b...

In this thesis we survey the technique of analyzing the partial derivatives of a polynomial to prove lower bounds for restricted classes of arithmetic circuits. The technique is also useful in designing algorithms for learning arithmetic circuits and we study the application of the method of partial derivatives in this setting. We also look at polynomial identity testing and survey an e cient a...

in previous work a simple bound, ~ + 2 , on the aliasing probability in serial signature analysis for a random test pattern of length L was derived. This simple bound is sharpened here by almost a factor of two. For serial signature analysis, it is shown that the I+& 1 aliasing probability is bounded above by = L ( E L small for large L ) for test lengths L less than the period, Lc, of the sign...

Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits a number that is 0(log m). This has been generalized by Lagañas. Montgomery, and Odlyzko to give a similar bound for the least prime ideal that does not split completely in an abelian extension of n...

Several authors have theoretically determined distribution-free bounds on sample complexity. Formulas based on several learning paradigms have been presented. However, little is known on how these formulas perform and compare with each other in practice. To our knowledge, controlled experimental results using these formulas, and comparing of their behavior, have not so far been presented. The p...

We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function f : {0, 1}n →{0, 1} and sampling oracle access to an unknown distribution D over {0, 1}n, we present an Õ(n/ǫ)-query algorithm that tests whether f is a monotone conjunction versus ǫ-far from any monotone conjunction with respect to D. This improv...