Decision Trees and Related Complexity Measures for Boolean Functions

Student: Shikhova Arseniya

Supervisor: Vladimir V. Podolskii

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2019

There are several ways to measure the complexity of a Boolean function. Some of them are determined by the properties of the function itself. Others characterize the complexity of the model computing this function. Such models can be Boolean formulas, Boolean schemes, decision trees, branching programs and so on. We see that for some functions different complexity measures are related. In particular, the class of monotone functions is well studied. In this paper, we investigate connections between different complexity measures for several classes of nonmonotonic Boolean functions. In particular, we focus on the class of functions with a single negation ——- these are functions that can be computed by a Boolean formula consisting of conjunctions, disjunctions, and one negation.

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