Abstract. In a general sequential model of computation, no restrictions are placed on theway in which the computation may proceed, except that parallel operations are not allowed. We show that in such an unrestricted environment TIME.SPACE fl(N2/logN) in order to sort N integers, each in the range [,N]. Key words, time-space tradeoffs, conputational complexity, sorting, time lower bounds, space lower bounds

This paper adopts the latter strategy in order to pursue the complexity of sorting

[15] N. Wirth, "Modula: A language for modular multiprogramming,"

Some Topics in Parallel Computation and Branching Programs by Rakesh Kumar Sinha Chairperson of the Supervisory Committee: Professor Paul Beame Department of Computer Science and Engineering There are two parts of this thesis: the first part gives two constructions of branching programs; the second part contains three results on models of parallel machines. The branching program model has turned out to be very useful for understanding the computational behavior of problems. In addition, several restrictions of branching programs, for example ordered binary decision diagrams, have proven to be successful data structures in several VLSI design and verification applications. We construct a branching program of o(n log 3 n) nodes for computing any threshold function on n variables and a branching program of o(n log 4 n) nodes for determining the sum of n variables modulo a fixed divisor. These are improvements over constructions of size 2(n 3=2 ) due to Lupanov [Lup65]. The second p...