Complexity measures and decision tree complexity: a survey

Complexity measures and decision tree complexity: a survey

We discuss several complexity measures for Boolean functions: certiicate complexity, sensitivity , block sensitivity, and the degree of a representing or approximating polynomial. We survey the relations and biggest gaps known between these measures, and show how they give bounds for the decision tree complexity of Boolean functions on deterministic, randomized, and quantum computers.

Complexity Measures and De ision Tree Complexity: A Survey

Decision-tree Complexity

Two separate results related to decision-tree complexity are presented. The first uses a topological approach to generalize some theorems about the evasiveness of monotone boolean functions to other classes of functions. The second bounds the gap between the deterministic decision-tree complexity of functions on the permutation group Sn and their zero-error randomized decision-tree complexity.

A Survey on Complexity of Integrity Parameter

Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined t...

Lecture 17 : Decision Tree Complexity

A decision tree is a model of computation used to study the number of bits of an input that need to be examined in order to compute some function on this input. Consider a function f : {0, 1} → {0, 1}. A decision tree for f is a tree for which each node is labelled with some xi, and has two outgoing edges, labelled 0 and 1. Each tree leaf is labelled with an output value 0 or 1. The computation...