Sven Skyum

Fast Parallel Computation of Polynomials Using Few Processors

It is shown that any multivariate polynomial of degree d that can be computed sequentially in C steps can be computed in parallel in

A complexity theory based on Boolean algebra

O((\log d)(\log C + \log d))

A simple algorithm for computing the smallest enclosing circle

steps using only

Parallel context-free languages

(Cd)^{O(1)}

Complexity of some problems concerningL systems

processors.

Decomposition Theorems for Various Kinds of Languages Parallel in Nature

A projection of a Boolean function is a function obtained by substituting for each of its variables a variable, the negation of a variable, or a constant. Reducibilities among computational problems under this relation of projection are considered. It is shown that much of what is of everyday relevance in Turing-machine-based complexity theory can be replicated easily and naturally in this elementary framework. Finer distinctions about the computational relationships among natural problems can be made than in previous formulations and some negative results are proved.

A relationship between ET0L and EDT0L languages

Presented is a simple O(n log n) algorithm for computing the smallest enclosing circle of a convex polygon. It can be easily extended to algorithms that compute the farthest-and the closest-point Voronoi diagram of a convex polygon within the same time bound.

Recognition of deterministic ETOL languages in logarithmic space

The relation between the family of context-free languages and the family of parallel context-free languages is examined in this paper. It is proved that the families are incomparable. Finally we prove that the family of languages of finite index is contained in the family of parallel context-free languages.

k-visit attribute grammars

We determine the computational complexity of membership, emptiness and infiniteness for several types ofL systems. TheL systems we consider are ED0L, E0L, EDT0L, and ET0L, with and without empty productions. For each problem and each type of system we establish both upper and lower bounds on the time or memory required for solution by Turing machines.

Dynamic maintenance of majority information in constant time per update

In this paper we give a method for decomposing subclasses of different families of languages, parallel in nature, into other families. These decomposition theorems can be used to produce languages not it a family by using examples of languages not belonging to some “smaller” family.