A new algorithm and refined bounds for extended gcd computation

Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipliers obtained.

The Qu-Prolog unification algorithm: Formalisation and correctness

Qu-Prolog is an extension of Prolog which performs meta-level computations over object languages, such as predicate calculi and lambda-calculi, which have object-level variables, and quantifier or binding symbols creating local scopes for those variables. As in Prolog, the instantiable (meta-level) variables of Qu-Prolog range over object-level terms, and in addition other Qu-Prolog syntax denotes the various components of the object-level syntax, including object-level variables. Further, the meta-level operation of substitution into object-level terms is directly represented by appropriate Qu-Prolog syntax. Again as in Prolog, the driving mechanism in Qu-Prolog computation is a form of unification, but this is substantially more complex than for Prolog because of Qu-Prolog's greater generality, and especially because substitution operations are evaluated during unification. In this paper, the Qu-Prolog unification algorithm is specified, formalised and proved correct. Further, the analysis of the algorithm is carried out in a frame-work which straightforwardly allows the 'completeness' of the algorithm to be proved: though fully explicit answers to unification problems are not always provided, no information is lost in the unification process.

Refining specifications to logic programs

The refinement calculus provides a framework for the stepwise development of imperative programs from specifications. In this paper we study a refinement calculus for deriving logic programs. Dealing with logic programs rather than imperative programs has the dual advantages that, due to the expressive power of logic programs, the final program is closer to the original specification, and each refinement step can achieve more. Together these reduce the overall number of derivation steps. We present a logic programming language extended with specification constructs (including general predicates, assertions, and types and invariants) to form a wide-spectrum language. General predicates allow non-executable properties to be included in specifications. Assertions, types and invariants make assumptions about the intended inputs of a procedure explicit, and can be used during refinement to optimize the constructed logic program. We provide a semantics for the extended logic programming language and derive a set of refinement laws. Finally we apply these to an example derivation.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.

Behavioral Types for Embedded Software - A Survey

At present, there is a variety of formalisms for modeling and analyzing the communication behavior of components. Due to a tremendous increase in size and complexity of embedded systems accompanied by shorter time to market cycles and cost reduction, so called behavioral type systems become more and more important. This chapter presents an overview and a taxonomy of behavioral types. The intentions of this taxonomy are to provide a guidance for software engineers and to form the basis for future research.

Ethical considerations for drug abuse epidemiological research

The mortality and morbidity caused by alcohol, tobacco and illicit drug misuse represents a significant public health burden (Ezzati et al., 2002). A key part of the public health response is the collection of epidemiological and social science data to define at-risk populations to identify opportunities for intervention and to evaluate the effectiveness of policies in preventing or treating drug misuse and drug-related harm. The systematic use of epidemiological and social science research methods to study illicit drug use is barely 40 years old in the United States and United Kingdom, which have pioneered this approach. Because of the sensitive nature of epidemiological research on illicit drug use a unique set of ethical challenges need to be explicitly addressed by the field. Although ethics guidelines have been proposed (Council for International Organizations of Medical Sciences, 1991), scholarship on the ethics of epidemiology is scant, and consensus on core values not yet achieved (Coughlin, 2000).

Proving Temporal Properties of Z Specifications Using Abstraction

This paper presents a systematic approach to proving temporal properties of arbitrary Z specifications. The approach involves (i) transforming the Z specification to an abstract temporal structure (or state transition system), (ii) applying a model checker to the temporal structure, (iii) determining whether the temporal structure is too abstract based on the model checking result and (iv) refining the temporal structure where necessary. The approach is based on existing work from the model checking literature, adapting it to Z.

A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

Specification, refinement and verification of concurrent systems - An integration of Object-Z and CSP

This paper presents a method of formally specifying, refining and verifying concurrent systems which uses the object-oriented state-based specification language Object-Z together with the process algebra CSP. Object-Z provides a convenient way of modelling complex data structures needed to define the component processes of such systems, and CSP enables the concise specification of process interactions. The basis of the integration is a semantics of Object-Z classes identical to that of CSP processes. This allows classes specified in Object-Z to he used directly within the CSP part of the specification. In addition to specification, we also discuss refinement and verification in this model. The common semantic basis enables a unified method of refinement to be used, based upon CSP refinement. To enable state-based techniques to be used fur the Object-Z components of a specification we develop state-based refinement relations which are sound and complete with respect to CSP refinement. In addition, a verification method for static and dynamic properties is presented. The method allows us to verify properties of the CSP system specification in terms of its component Object-Z classes by using the laws of the the CSP operators together with the logic for Object-Z.

Multi-threading and message communication in Qu-Prolog

This paper presents the multi-threading and internet message communication capabilities of Qu-Prolog. Message addresses are symbolic and the communications package provides high-level support that completely hides details of IP addresses and port numbers as well as the underlying TCP/IP transport layer. The combination of the multi-threads and the high level inter-thread message communications provide simple, powerful support for implementing internet distributed intelligent applications.

Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.