P. van Emde Boas

Preserving order in a forest in less than logarithmic time and linear space

By combination of ‘these basic instructions we obtain moreover the instructions Extractmin, Extractmax (remove the least resp. the largest element frem s) and the iterated instructions AlZmin(i) and Allmizx(i) (remove from S all elements 4 i resp. 2 i)* Traditionally a priority queue is a data structure supporting the instructions Insert, Delete, Member, Min and Extractmin, but in the present note we will use this term for structures supporting the complete repertoire given above. In [2] we introduced a data structure supporting all instructions with a worst-case processing time O(log log u) for each element processed, where we use the Uniform RAM time measure [ 11. The structure proposed in [2] has two important disadvantages. In the first place it cannot be used in situations where the priority quell? consists of real-valued items, like in the case of minimal path computations. Secondly the structure requires more than linear space. To be precise the storage needed is of order u l log log u; this space moreover must be initialized in time O(u l log log u) before the structure can be used. In this note we show that the second objection can be amended by combining some ideas used before in [2]. The present and previous results are expressed by the following lemma’s and theorem:

Preserving order in a forest in less than logarithmic time

We present a data structure, based upon a stratified binary tree, which enables us to manipulate on-line a priority queue whose priorities are selected from the interval 1...n, with an average and worst case processing time of O(log log n) per instruction. The structure is used to obtain a mergeable heap whose time requirements are about as good.

On tape versus core an application of space efficient perfect hash functions to the invariance of space

In Complexity Theory the use of informal estimates can be justified by appealing to the Invariance thesis which states that all standard models of computing devices are sufficiently equivalent. This thesis would require, among others, that a RAM can be simulated by a Turingmachine with constant factor overhead in space. Such a simulation is hard to obtain if the traditional spacemeasure for RAM-space is used. The simulation uses a new method for condensing space, based on perfect hashing.

The connection between modal logic and algorithmic logics

We investigate the connection between modal logic and the formal systems recently introduced for arguing about programs. The link is based on the common use of Kripke semantics. The bearing for semantics of some recent results in modal logic is explained. Finally we describe the possibilities to use intesional logic for the semantics of assignments.

Simplicity, immunity, relativizations and nondeterminism

A diagonalization method is discussed by which a recursive oracle A can be constructed such that NP(A) has a set L(A) which is both simple and P(A)-immune.

An appraisal of computational complexity for operations researchers

Abstract We review recent developments in the theory and practice of computational complexity, in order to highlight some of the basic concepts and ideas that have come out of this area. The discussion centers around the progress on twelve important open problems listed in 1979 by M.R. Garey and D.S. Johnson, the introduction of probabilistic elements in the analysis and design of algorithms, the problem classes around P and RP, and the P ≠ RP conjecture.

Symbolic computation in RL/1

This article discusses the use of RL/1 to build quantitative models and the application of these models to assist in decision making. A set of constraints constitutes a model. Constraint models can be extended and modified easily and the representation of model knowledge is separated from its use. The model knowledge is used by means of a constraint solver. This allows the application of the same knowledge for different purposes. In addition the knowledge representation allows the user to analyze relationships between variables ar’.d to infer new relationships that hold in special circumstances.

Some applications of the McCreight-Meyer algorithm in abstract complexity theory

Abstract The McCreight-Meyer algorithm is a priority-queue construction from abstract recursion theory which was designed for the proof of the so-called Naming or Honesty theorem. We explain the ideas behind the algorithm, pointing at its behaviour as a “closure operator” and obtaining various known and new results as corollaties of more general assertions.