Limits to measurement in experiments governed by algorithms (2009)
Beggs, E. J., Costa, J. F., Tucker, J. V.
We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the...
Bergstra, J. A., Hirshfeld, Y., Tucker, J. V.
A skew meadow is a non-commutative ring with an inverse operator satisfying two special equations and in which the inverse of zero is zero. All skew fields and products of skew fields can be viewed...
Meadows and the equational specification of division (2009)
Bergstra, J. A., Hirshfeld, Y., Tucker, J. V.
The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be...
J A Bergstra, Y Hirschfeld, J V Tucker
A meadow is a commutative ring with an inverse operator satisfying two equations and in which 0 −1 = 0. All fields and products of fields can be viewed as meadows. After reviewing alternate axioms...
J A Bergstra, J V Tucker, J A Bergstra, Singleton Park
A 0-totalised field is a field in which division is a total operation with 0 −1 = 0. Equational reasoning in such fields is greatly simplified but in deriving a term one still wishes to know...
Tabular Documentation of Interactive Deterministic Systems derived from Algebraic Models (2008)
A. J. Wilder, J. V. Tucker, Singleton Park
Many reactive deterministic systems have a simple algebraic model consisting of a set S of states, a set C of commands the system may receive and a state transition function n: S C! S that can be...
University of Wales Swansea, (2008)
E. J. Beggs, J. V. Tucker, Singleton Park
In the theoretical analysis of the physical basis of computation there is a great deal of confusion and controversy, especially on the issue of the existence of hypercomputers. First, we present some...
With gratitude, admiration and affection In 1979 the authors (hereafter JVT and JIZ) began our work together on developing a theory of computation that works for any data. We were members of Jaco de...
Division safe calculation in totalised fields (2008)
A 0-totalised field is a field in which division is a total operation with 0(−1)=0. Equational reasoning in such fields is greatly simplified but in deriving a term one still wishes to know whether...
The Algebraic Structure of Interface Definition Languages and Architectures (2007)
In this paper we examine formally a notion of architecture for the design of systems. The basic idea is that: System Architecture = Structured set of (sub)-system interfaces. Thus, the architecture...
Papers on Domain Theory (2007)
Logic Group, Spaces Domains, I. Lindstrom, V. Stoltenberg-hansen, V. Stoltenberg-hansen, J. V. Tucker
References
Infinitary Algebraic Specifications for Stream Algebras (2007)
. A stream is an infinite sequence of data from a set A. A wide variety of algorithms and architectures operate continuously in time, producing streams of data, for example: systolic arrays,...
Hierarchical Reconstructions of Cardiac Tissue (2007)
We consider the general problem of comparing and integrating computational models of cardiac tissue at different levels of physiological detail. We use a general theory of synchronous concurrent...
Interface = Name + Imports + Body. (2007)
D Ll, L Rees, K Stephenson, J V Tucker
In this paper we examine formally a notion of architecture for the design of systems, based on the idea that the architecture of a system can be modelled by the structure of its interface expressed...
Computational Biology of cardiac arrhythmias: from basic science to application (2007)
O. V. Aslanidi, V. N. Biktashev, M. Chen, R. H. Clayton, A. V. Holden, J. V. Tucker, ...
Cardiac virtual tissues are biophysically, histologically and anatomically detailed computational models that are sufficiently well validated to be used as a predictive tool, are currently used in...
The Rational Numbers as an Abstract Data Type (2007)
We give an equational specification of the field operations on the rational numbers under initial algebra semantics using just total field operations and 12 equations. A consequence of this...
J A Bergstra, Y Hirschfeld, J V Tucker
A meadow is a commutative ring with an inverse operator satisfying two equations and in which 0 −1 = 0. All fields and products of fields can be viewed as meadows. After reviewing alternate axioms...
A network model of analogue computation over metric algebras (2005)
Abstract. We define a general concept of a network of analogue modules connected by channels, processing data from a metric space A, and operating with respect to a global continuous clock T. The...
Computations via experiments with kinematic systems (2004)
E. J. Beggs, J. V. Tucker, Singleton Park
Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2-dimensional kinematic system BA with a single...
Abstract versus concrete computation on metric partial algebras (2004)
In the theory of computation on topological algebras there is a considerable gap between so-called abstract and concrete models of computation. In concrete models, unlike abstract models, the...
Abstract Computability, Algebraic Specification and Initiality (2001)
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to...
Abstract versus Concrete Computation on Metric Partial Algebras (2001)
A model of computation is abstract if, when applied to any algebra, the resulting programs for computable functions and sets on that algebra are invariant under isomorphisms, and hence do not depend...
Computation by `While' Programs on Topological Partial Algebras (1999)
The language of while programs is a fundamental model for imperative programming on any data type. It leads to a generalisation of the theory of computable functions on the natural numbers to the...
Kazuhiro Saitou: Self-Assembling Automata: A Model of (1998)
on the occasion of his 70th birthday Abstract. A stream is an innite sequence of data from a set A. A wide variety of algorithms and architectures operate continuously in time, processing streams of...
Hierarchies of Spatially Extended Systems and Synchronous Concurrent Algorithms (1998)
M.J. Poole, J.V. Tucker, A.V. Holden
. 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...
Hierarchical Reconstructions of Cardiac Tissue (1998)
A V Holden, M J Poole, J V Tucker
We consider the general problem of comparing and integrating computational models of cardiac tissue at different levels of physiological detail. We use a general theory of synchronous concurrent...
The data type variety of stack algebras (1995)
We define and study the class of all stack algebras as the class of all minimal algebras in a variety defined by an infinite recursively enumerable set of equations. Among a number of results, we...
We classify the computable and semicomputable algebras in terms of finite equational initial algebra specifications and their properties as term term rewriting systems, such as completeness. Further...
Algebraic Models Of Microprocessors: The Correctness And Verification Of A Simple Computer. (1995)
CIRCUIT DESIGN We now consider the abstract circuit representation of Gordon's Computer. A diagram of the basic implementation is shown in Figure 3. From the implementation representation in...
The Data Type Variety of Stack Algebras (1995)
We define and study the class of all stack algebras as the class of all minimal algberas in a variety defined by an infinite recursively enumerable set of equations. Among a number of results, we...
System Documentation Using Tables - A short course (1995)
ION IMPLEMENTATION DESIGN Figure 2.1: A simple process model. CHAPTER 2. SOFTWARE DESIGN PROCESS 51 2.2.2 Model Hierarchy Of importance in the early stages of all projects is the tendency to inflate...
System Documentation Using Tables - A short course (1995)
ION IMPLEMENTATION DESIGN Figure 2.1: A simple process model. CHAPTER 2. SOFTWARE DESIGN PROCESS 25 2.2.2 Model Hierarchy Of importance in the early stages of all projects is the tendency to inflate...
Computable Functions on Stream Algebras (1994)
. 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...
Projections Of Semicomputable Relations On Abstract Data Types (1991)
DATA TYPES J.V. TUCKER Department of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, Wales and J.I. ZUCKER Department of Computer Science and Systems, McMaster...
Toward a General Theory of Computation and Specification over Abstract Data Types (1990)
Data Types J.V. Tucker 1 Department of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, Wales csjvt@pyr.swan.ac.uk J.I. Zucker 2 Department of Computer Science and...
Algebraic specifications of computable and semi-computable data structures (1987)
An extensive survey is given of the properties of various specification mechanisms based on initial algebra semantics
Hoare's logic for programming languages with two datatypes (1984)
We consider the completeness of Hoare’s logic with a first-order assertion language applied to while-programs containing variables of two (or more) distinct types. Whilst Cook’s completeness...
Top-down design and the algebra of communicating processes (1984)
We develop an algebraic theory for the top-down design of communicating systems in which levels of abstraction are represented by algebras, and their stepwise refinements are represented by...
Floyd's principle, correctness theories and program equivalence (1982)
Bergstra, J.A., Tiuryn, J., Tucker, J.V.
A programming system is a language made from a fixed class of data abstractions and a selection of familiar deterministic control and assignment constructs. It is shown that the sets of all...
Expressiveness and the completeness of Hoare's logic (1982)
Three theorems are proven which reconsider the completeness of Hoare's logic for the partial correctness of while-programs equipped with a first-order assertion language. The results are about the...
Complexity Theory and the Operational Structure of Algebraic Programming Systems (1982)
An algebraic programming system is a language built from a fixed algebraic data abstraction and a selection of deterministic, and non-deterministic, assignment and control constructs. First, we give...
On the power of algebraic specifications (1981)
Bergstra, J.A., Broy, M., Tucker, J.V., Wirsing, M.
We study the expressive power of different algebraic specification methods. In contrast to (nonhierarchical) initial and terminal algebra specifications which correspond to semicomputable and...
Computing roots of unity in fields (1980)
V. Stoltenberg-hansen, J. V. Tucker
Here we consider some simple decision problems to do with fields and abelian groups and show that they are algorithmically insoluble and, indeed, that they can occur with arbitrary complexity....
On the Operational Structure of Algebraic Programming Systems (1980)
An algebraic programming system is a language built from a fixed algebraic data abstraction and a selection of deterministic, and non-deterministic, assignment and control constructs. First, we give...