Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Formal derivation of finite state machines for class testing

Previous work on generating state machines for the purpose of class testing has not been formally based. There has also been work on deriving state machines from formal specifications for testing non-object-oriented software. We build on this work by presenting a method for deriving a state machine for testing purposes from a formal specification of the class under test. We also show how the resulting state machine can be used as the basis for a test suite developed and executed using an existing framework for class testing. To derive the state machine, we identify the states and possible interactions of the operations of the class under test. The Test Template Framework is used to formally derive the states from the Object-Z specification of the class under test. The transitions of the finite state machine are calculated from the derived states and the class's operations. The formally derived finite state machine is transformed to a ClassBench testgraph, which is used as input to the ClassBench framework to test a C++ implementation of the class. The method is illustrated using a simple bounded queue example.

CXTANNEAL: an improved program for estimating solute transport parameters

CXTANNEAL is a program for analysing contaminant transport in soils. The code, written in Fortran 77, is a modified version of CXTFIT, a commonly used package for estimating solute transport parameters in soils. The improvement of the present code is that it includes simulated annealing as the optimization technique for curve fitting. Tests with hypothetical data show that CXTANNEAL performs better than the original code in searching for optimal parameter estimates. To reduce the computational time, a parallel version of CXTANNEAL (CXTANNEAL_P) was also developed. (C) 1999 Elsevier Science Ltd. All rights reserved.

A model of specification-based testing of interactive systems

In this paper we present a model of specification-based testing of interactive systems. This model provides the basis for a framework to guide such testing. Interactive systems are traditionally decomposed into a functionality component and a user interface component; this distinction is termed dialogue separation and is the underlying basis for conceptual and architectural models of such systems. Correctness involves both proper behaviour of the user interface and proper computation by the underlying functionality. Specification-based testing is one method used to increase confidence in correctness, but it has had limited application to interactive system development to date.

Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

Structuring real-time Object-Z specifications

This paper presents a means of structuring specifications in real-time Object-Z: an integration of Object-Z with the timed refinement calculus. Incremental modification of classes using inheritance and composition of classes to form multi-component systems are examined. Two approaches to the latter are considered: using Object-Z's notion of object instantiation and introducing a parallel composition operator similar to those found in process algebras. The parallel composition operator approach is both more concise and allows more general modelling of concurrency. Its incorporation into the existing semantics of real-time Object-Z is presented.