## Complexity Measures and Decision Tree Complexity: A Survey (2000)

Venue: | Theoretical Computer Science |

Citations: | 122 - 15 self |

### BibTeX

@ARTICLE{Buhrman00complexitymeasures,

author = {Harry Buhrman and Ronald De Wolf},

title = {Complexity Measures and Decision Tree Complexity: A Survey},

journal = {Theoretical Computer Science},

year = {2000},

volume = {288},

pages = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

We discuss several complexity measures for Boolean functions: certificate 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. 1 Introduction Computational Complexity is the subfield of Theoretical Computer Science that aims to understand "how much" computation is necessary and sufficient to perform certain computational tasks. For example, given a computational problem it tries to establish tight upper and lower bounds on the length of the computation (or on other resources, like space). Unfortunately, for many, practically relevant, computational problems no tight bounds are known. An illustrative example is the well known P versus NP problem: for all NP-complete problems the current upper and lower bounds lie exponentially ...