On Rivest-Vuillemin Conjecture for Fourteen Variables

Rivest-Vuillemin conjecture is true for monotone boolean functions with twelve variables

Any Monotone Property of 3-Uniform Hypergraphs Is Weakly Evasive

For a Boolean function f, let D(f) denote its deterministic decision tree complexity, i.e., minimum number of (adaptive) queries required in worst case in order to determine f. In a classic paper, Rivest and Vuillemin [19] show that any non-constant monotone property P : {0, 1}( n 2) → {0, 1} of n-vertex graphs has D(P) = Ω(n). We extend their result to 3-uniform hypergraphs. In particular, we ...

On the Decision Tree Complexity of String Matching

String matching is one of the most fundamental problems in computer science. A natural problem is to find the number of characters that needs to be queried (i.e. the decision tree complexity) in a string in order to determine whether this string contains a certain pattern. Rivest [Riv77] showed that for every pattern p, in the worst case any deterministic algorithm needs to query at least n − |...

On Evasiveness , Permutation Embeddings , and Mappings on Sequences

In Chapter I, several results are obtained on the evasiveness of graph-theoretic properties extending the work of Vuillemin and Rivest. In particular, it is shown that any nontrivial vertex-independent monotone graph-theoretic property has minimal evasiveness n2 /9 . Particular stronger results are obtained for n values which are powers of primes less than (<) 13 . A new result allowing interpo...

Space - Time Tradeo s for Graph

We initiate a study of space-time tradeoos in the cell-probe model under restricted preprocessing power. Classically, space-time trade-oos have been studied in this model under the assumption that the pre-processing is unrestricted. In this setting, a large gap exists between the best known upper and lower bounds. Augmenting the model with a function family F that characterizes the preprocessin...