What is abstract algebra? First note that mathematicians love abstractions, taking properties and generalizing them. Abstract algebra uses a generalization of the features of operations on numbers ...

Abstract: This paper extends Valiant's work on VP and VNP to the settings in which variables are not multiplicatively commutative and/or associative. Our main result is a theory of completeness for ...

Abstract: It is often convenient to consider the arguments of a switching function to be the components 0 or 1 of a vector. In order to investigate systematically the properties of switching functions ...