Boolean Function Complexity

Student: Filimonov Mikhail

Supervisor: Vladimir V. Podolskii

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Final Grade: 10

Year of Graduation: 2020

Boolean function complexity is an important aspect of computer science. Previous research in this area has developed methods for proving circuit lower bounds and established hierarchies of circuit classes defined using exact threshold gates and ordinary threshold gates. However, it remains major open problem to prove strong lower bounds for some circuit classes. Another problem is that provided hierarchies contain circuit classes for which no separations from other classes are known up to now. This study systematically reviews results obtained in recent research and provides generalization for some of them. More precisely, this work shows that some circuit classes can be rewritten by circuit classes of the same form without using negations.

Full text (added May 20, 2020)

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