The copying power of one-state tree transducers

One-state deterministic top-down tree transducers (or, tree homomorphisms) cannot handle "prime copying," i.e., their class of output (string) languages is not closed under the operation L → {$(w$)f(n) w ε L, f(n) ≥ 1}, where f is any integer function whose range contains numbers with arbitrarily large prime factors (such as a polynomial). The exact amount of nonclosure under these copying operations is established for several classes of input (tree) languages. These results are relevant to the extended definable (or, restricted parallel level) languages, to the syntax-directed translation of context-free languages, and to the tree transducer hierarchy.\ud \u

A Sweepline Algorithm for Generalized Delaunay Triangulations

We give a deterministic O(n log n) sweepline algorithm to construct the generalized Voronoi diagram for n points in the plane or rather its dual the generalized Delaunay triangulation. The algorithm uses no transformations and it is developed solely from the sweepline paradigm together with greediness. A generalized Delaunay triangulation can be based on an arbitrary strictly convex Minkowski distance function (including all L_p distance functions 1 < p < *) in contrast to ordinary Delaunay triangualations which are based on the Euclidean distance function

Confusion in the Garden of Eden

The publication contains an examination of the connection between unambiguity of cellular systems and the existence of Garden of Eden configurations in cellular automata. The examination includes both finite and infinite configurations. A rewritten and corrected version has been accepted for publication in Proc. of the Amer. Math. Soc

Garden of Eden-konfigurationer i cellulære automater

This publication is Sven Skyum's master's thesis. The first chapters contain some general results about cellular automata (the existence of a universal computerconstructor, self-reproducing automata etc.). In the last chapters the connection between unambiguity and the existence of Garden of Eden configurations in cellular automata is examined

Dynamic Maintenance of Majority Information in Constant Time per Update

We show how to maintain information about the existence of amajority colour in a set of elements under insertion and deletion ofsingle elements using O(1) time and at most 4 equality tests on coloursper update. No ordering information is used

The Complexity of Identifying Large Equivalence Classes

We prove that at least (3k−4) / k(2k−3) n(n-1)/2 − O(k) equivalence tests and nomore than 2/k n(n-1)/2 + O(n)equivalence tests are needed in the worst case to identify the equivalence classes with at least k members in set of n elements. The upper bound is an improvement by a factor 2 compared to known results. For k = 3 we give tighter bounds. Finally, for k > n/2 we prove that it is necessary and it suffices to make 2n − k − 1 equivalence tests which generalizes a known result for k = [(n+1)/2]

Searching Constant Width Mazes Captures the AC0 Hierarchy

We show that searching a width k maze is complete for Pi_k, i.e.,for the k'th level of the AC0 hierarchy. Equivalently, st-connectivityfor width k grid graphs is complete for Pi_k. As an application, weshow that there is a data structure solving dynamic st-connectivity for constant width grid graphs with time bound O(log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools