Peter van Emde Boas

Machine models and simulations

Publisher Summary This chapter discusses machine models and simulations. The existence of many different machine models does not necessarily mean that there are no uniform underlying notions of computational complexity. In the theory of computation, a large variety of models and formal calculi has been proposed to capture the notion of effective computation. This has not lead to a proliferation of computation theories, because of the basic fact that the proposed formalisms have all been shown to be equivalent in the following sense—each computation in one formalism can be simulated by a computation in the other formalism. From the equivalence, it can be concluded that if a problem is unsolvable in one particular model, then it is also unsolvable for all other formalized computing devices to which this particular model is related by mutual simulation. Consequently the notion of solvability does not really depend on the model used. The basic models of computation themselves remain on the shelf, to be used if and when needed.

Compositionality and Concurrent Networks: Soundness and Completeness of a Proofsystem

Specification, construction and verification of programs should be done in a compositional way. This means that for each syntactic programming construct it should be possible to infer a specification for the whole construct from specifications of the constituent syntactic components of that construct. A compositional proofsystem is presented for a language that includes parallel executing networks and recursive creation of subnetworks. This system is then shown to be arithmetically complete.

Storing and evaluating Horn-clause rules in a relational database

This paper describes a practical approach to storing and evaluating Horn-clause rules in a relational database system. The intention is to give a complete outline of what needs to be added to an existing relational database system to allow it to support full logic programming functions. Implementation issues for each new function are discussed. We show how Horn-clause rules can be translated into database commands without recourse to semantics and how their evaluation can be performed in the database itself. This brings the complete logic programming environment within reach of the database management system, allowing data and rule sharing, concurrency control, recovery procedures, etc., to be used. New is that the complete logic programming environment is incorporated into the database system. IBM Business System 12, extended in this way, may be a suitable vehicle for expert system applications. Copying in printed form for private use is permitted without payment of royalty provided that (1) each reproduction is done without alteration and (2) the Journal reference and IBM copyright notice are included on the first page. The title and abstract, but no other portions, of this paper may be copied or distributed royalty free without further permission by computer-based and other information-service systems. Permission to republish any other portion of this paper must be obtained from the Editor.

The problem of space invariance for sequential machines

In complexity theory the use of informal estimates can be justified by appealing to the Invariance Thesis which states that all standard models of sequential computing devices are equivalent in the sense that the fundamental complexity classes do not depend on the precise model chosen for their definition. This thesis would require, among others, that a RAM can be simulated by a Turing machine with constant factor overhead in space. We argue that the definition of RAM space, at least in the manner it is traditionally given in the literature, is inadequate for this purpose. The invariance thesis can be validated only in a weak interpretation. The rather complicated simulation which achieves the constant factor space overhead is based on a new method for condensing space and uses perfect hash functions with minimal program size.

Space measures for storage modification machines

Abstract In the theory of Machine Models in Complexity Theory much attention has been given to establishing polynomial time overhead simulations between the various sequential models. It has been taken for granted that these models simulate each other with constant factor overhead in space. We show in this note that such constant factor space overhead simulations do not exist for pointer based models like the Storage Modification Machine and the Kolmogorov-Uspenskii Machine under the uniform space measure. On these devices one can simulate S · log ( S ) squares of Turing Machine space in O ( S ) nodes. As a consequence one faces the choice of either using a less evident logarithmic space measure for pointer machines, or giving up the fundamental notion of invariance of space for sequential devices.

Twenty questions to a p-selector

Abstract We show in this note that any set that is positive Turing reducible to a p-selective set is in fact many–one reducible to this set. Therefore such a set is itself p-selective.

On the Proper Treatment or Referencing, Dereferencing and Assignment

A Floyd-like semantics is presented for the assignment statement in a fragment of ALGOL 68. The fragment considered contains array identifiers, referencing, dereferencing and conditionals. The semantics is based upon an interpretation in a model of intensional logic, without use of addresses or stores. In doing so, several ideas developed by R. Montague concerning the treatment of semantics for natural languages are applied for the first time in the area of semantics of programming languages. We also consider an operational semantics, based on the same model and prove that the Floyd-like semantics is valid with respect to the operational one and always yields the strongest postcondition.

Diagonalisation methods in a polynomial setting

In the present paper an overview is presented of diagonalisation methods which have been used for the construction of oracle sets relative to which complexity classes in the P-Time Hierarchy are separated structurally. A comparison of the methods is made on the basis of inherent properties. A characterisation of these properties leads to a first attempt for a taxonomy for these diagonalisation methods.

The rule language RL/1

In this paper we introduce and illustrate the rule language RL/1. This language was designed as an intermediate step towards implementing the more extensive rule language RL intended to become a tool for integrating logical and functional programming and constraint solving with relational databases into a relational framework.

A Semantical Model for Integration and Modularization of Rules

We have presented the outlines of a system which integrates three rather distinct modern technologies for intelligent systems which share the property of having a relational model, but which otherwise have very little in common. Due to lack of space I cannot include a convincing example which will show that the RL language will be a convenient tool for expressing real life rules, but my experience is positive. Also the modularization feature turned out to be useful in the examples tried.