30 Result(s)

Chapter

Generalizing Computability Theory to Abstract Algebras

We present a survey of our work over the last four decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of c...

J. V. Tucker, J. I. Zucker in Turing’s Revolution (2015)

Chapter and Conference Paper

Programming Experimental Procedures for Newtonian Kinematic Machines

By experimental computation we mean the idea of computing a function by experimenting with some physical equipment. To analyse the functions computable by experiment, we are develo** a methodology that chooses ...

E. J. Beggs, J. V. Tucker in Logic and Theory of Algorithms (2008)

Chapter

Hierarchies of Spatially Extended Systems and Synchronous Concurrent Algorithms

First, we study the general idea of a spatially extended system (SES) and argue that many mathematical models of systems in computing and natural science are examples of SESs. We examine the computability and the...

M. J. Poole, J. V. Tucker, A. V. Holden in Prospects for Hardware Foundations (1998)

Article

Algebraic models of microprocessors architecture and organisation

We present an algebraic method for modeling microprocessors at different levels of abstraction, and for expressing the relationships between each level. We consider microprocessors at levels of abstraction det...

N. A. Harman, J. V. Tucker in Acta Informatica (1996)

Chapter and Conference Paper

Computable Functions on Stream Algebras

Let A be a many-sorted algebra. A stream over A is an infinite sequence of data from A. We study classes of computable functions on streams over A. We show how models of deterministic parallel computation on A ca...

J. V. Tucker, J. I. Zucker in Proof and Computation (1995)

Chapter and Conference Paper

Infinite Synchronous Concurrent Algorithms The Algebraic Specification and Verification of a Hardware Stack

An infinite synchronous concurrent algorithm (isca) is an algorithm composed of infinitely many modules and channels, computing and communicating in parallel, and synchronised by a global clock. A theory of su...

B. McConnell, J. V. Tucker in Logic and Algebra of Specification (1993)

Chapter and Conference Paper

Infinite systems of equations over inverse limits and infinite synchronous concurrent algorithms

We consider the existence, uniqueness and effectiveness of solutions to infinite systems of equations in certain inverse limits of algebras. The notion of a guarded infinite system of equations is defined and ...

V. Stoltenberg-Hansen, J. V. Tucker in Semantics: Foundations and Applications (1993)

Chapter and Conference Paper

Theoretical framework for analysing the behaviour of real and simulated neural networks

We outline the theory of synchronous concurrent algorithms, as it may be applied to models of neurobiological networks; and illustrate its application by an example of the behaviour of a neural network model (...

A. V. Holden, J. V. Tucker, B. C. Thompson, D. Withington… in Neural Network Dynamics (1992)

Chapter and Conference Paper

Examples of semicomputable sets of real and complex numbers

We investigate the concept of semicomputability of relations on abstract structures. We consider three possible definitions of this concept, which all reduce to the classical notion of recursive enumerability ...

J. V. Tucker, J. I. Zucker in Constructivity in Computer Science (1992)

Chapter and Conference Paper

Theory of computation over stream algebras, and its applications

The theory of computable functions on abstract data types is outlined. Methods for extending the theory to establish the scope and limits of computation on streams over abstract data types arc described. Appli...

J. V. Tucker, J. I. Zucker in Mathematical Foundations of Computer Science 1992 (1992)

Chapter

Excitable Media as Computational Systems

A number of mathematical approaches may be used to model a given excitable system. For an excitable system that is not spatially extensive a map, or a system of nonlinear ordinary differential equations may be ap...

A. V. Holden, J. V. Tucker, B. C. Thompson in Nonlinear Wave Processes in Excitable Media (1991)

Chapter and Conference Paper

Theory of Computation and Specification over Abstract Data Types, and its Applications

The theory of computable functions on abstract data types is outlined. The problems of extending the theory to establish the scope and limits of the specification and verification of functions are described. A...

J. V. Tucker in Logic, Algebra, and Computation (1991)

Chapter and Conference Paper

Verification of Synchronous Concurrent Algorithms Using OBJ3: A Case Study of the Pixel-Planes Architecture

This paper is concerned with the mechanical verification of synchronous concurrent algorithms using OBJ3. Our case study is a graphics engine, the Pixel Planes archi¬tecture which has been previously specified...

S. M. Eker, V. Stavridou, J. V. Tucker in Designing Correct Circuits (1991)

Chapter and Conference Paper

Theoretical Considerations in Algorithm Design

What is an algorithm and how do we design an algorithm to accomplish a given task?

B. C. Thompson, J. V. Tucker in Fundamental Algorithms for Computer Graphics (1991)

Chapter and Conference Paper

Provable computable functions on abstract data types

We work in the context of abstract data types, modelled as classes of many-sorted algebras. We develop notions of computability over such data types, in particular notions of primitive recursiveness and μ-recu...

J. V. Tucker, S. S. Wainer, J. I. Zucker in Automata, Languages and Programming (1990)

Chapter and Conference Paper

Toward a general theory of computation and specification over abstract data types

We describe an ongoing project, to develop a general theory of computation and specification over classes of structures, modelling abstract data types. Applications include logic programming module development...

J. V. Tucker, J. I. Zucker in Advances in Computing and Information — ICCI '90 (1990)

Chapter and Conference Paper

Tools for the Formal Development of Rasterisation Algorithms

We consider the mathematical foundations of the stepwise refinement of rasterisation algorithms. We describe tools taken from the theory of abstract data types and apply them to the formal derivation of line d...

S. M. Eker, J. V. Tucker in New Advances in Computer Graphics (1989)

Chapter and Conference Paper

Horn programs and semicomputable relations on abstract structures

J. V. Tucker, J. I. Zucker in Automata, Languages and Programming (1989)