Abstract:
Proving lower bounds has been a notoriously hard problem for Theoretical Computer Scientists. The purpose of this thesis is to supplement the efforts in many theorems regarding lower bounds in restricted models of computation: namely, to point out some interesting new directions for lower bounds, and take some steps towards resolving these questions. *This thesis studies the question of proving lower bounds for constant-depth Boolean circuits with help functions and noncommutative Algebraic Branching Programs with help polynomials; of proving lower bounds for monotone arithmetic circuits of bounded width; and of proving lower bounds on the size of noncommutative arithmetic circuits computing the noncommutative determinant. These problems are introduced in greater detail and the corresponding results are stated.
