%Nr: DS-93-06 %Author: John Tromp %Title: Aspects of Algorithms and Complexity Abstract: This thesis is a compilation of several studies within the area of theoretical computer science. Most deal with algorithms and their associated complexity measures like time and space, but there is also the odd measure like the use of energy in electronic circuits. Chapter 2 is concerned with the following problem. Given a finite set of strings, $w_1,w_2, \ldots, w_n$, find their shortest common superstring $w$. It is known' that no algorithm, given a set of words with total length $m$, can always find the shortest superstring within $m^{k}$ steps, for some constant $k$. Technically speaking, this problem is not solvable in polynomial time. There does exist an algorithm that finds a reasonable superstring in approximately $m^3$ steps, which is used in DNA sequencing, that is, determining the exact order of nucleotides in DNA molecules. In this chapter it is shown that the length of superstrings found with this algorithm is bound by four times the length of the shortest possile superstring. In Chapter 3 the central topic is the memory complexity of colouring a picture. An algorithm is derived that solves this problem with constant memory use, in contrast to current practice of using memory proportional to the size of the figure to be coloured. Using only a constant amount of memory, the problem appears like a gigantic Labyrinth, the part of which we find ourselves in must be completely walled in. Chapter 4 is concerned with upper bounds on the switching energy needed to compute treshold and counting functions with VLSI circuits. Through some redundancy in the number of switching elements, we show how to reduce the amount of wires switching on a change of inputs, by a factor which is the number of digits in the number of inputs to the curcuit. Chapter 5 introduces a new kind of computer, a parallel version of the storage modification machine'. The memory of this machine consists of cells, each pointing at several other cells. The machine has the ability to address a set of cells on which certain operations can be carried out, such as the creation of new cells or the redirecting of pointers. This turns out to be a very powerful computer, that could, for instance, solve chess in a relatively small number of steps (although the number of cells used would be as large as the number of possible chess games). The last four chapters are devoted to communication protocols that give different processes the idea that they are sharing a single memory: a process can read what other processes write. In the simplest case the memory consists of a single bit, written by one, and read by one other process. This building block serves as the basis for bigger and better memories: more values, more readers, more writers. A unique property of these protocols is that they are {\em wait-free\/}: one process does not have to wait for another process to complete its memory operation.