A backtracking algorithm with element order selection is presented, and its efficiency discussed in relation both to standard examples and to examples concerning relation-preserving maps which the algorithm was derived to solve. 1 Introduction Backtracking has long been used as a strategy for solving combinatorial problems and has been extensively studied (Gerhart & Yelowitz (1976), Roever (1978), Walker (1960), Wells (1971)). In worst case situations it may be highly inefficient, and a systematic analysis of efficiency is very difficult. Thus backtracking has sometimes been regarded as a method of last resort. Nevertheless, backtracking algorithms are widely used, especially on NP-complete problems. In order to make these algorithms computationally feasible on a range of large problems, they are usually tailored to particular applications (see, for example, Butler and Lam's approach to isomorphism-testing in Butler & Lam (1985) and Knuth and Szwarcfiter's approach to topological sort...

In this paper we address two problems concerned with the maintenance of safety-critical software. Firstly, we analyse the new issues required for the re-verse engineering of real-time existing code to extract high level designs. Secondly, we present a possible de-sign, abstraction mechanism that can be used for safety-critical software. We use formal transformations both in the reuerse engineering of systems involving tem-representation. We present a design framework and the results of initial experiments. The contributions are: (I) the requirements analysis for reverse engi-neering safety-critical systems, (2) the use of very-high-level domain languages, and (3) formal transfor-mations QS the unifying technology.

The weakest precondition semantics of recursive procedures with local variables are developed for an imperative language with demonic and angelic operators for unbounded nondeterminate choice. This does not require stacking of local variables. The formalism serves as a foundation for a proof rule for total correctness of (mutually) recursive procedures with local variables. This rule is illustrated by a simple example. Its soundness is proved for arbitrary well-founded variant functions. Keywords: predicate transformers, frames, recursive procedures, proof rule 1 Introduction Formalisms for weakest preconditions for imperative programs usually treat predicates as boolean functions on a single state space, cf. [BvW90, DiS90, Hes92, Nel89]. It follows that procedures cannot have local variables. For nonrecursive procedures, local variables can be made global by careful renaming. Actually, this is also possible for recursive procedures by means of methods analogous to those developed be...

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Successful evolution of software systems / Hongji Yang, Martin Ward. p. cm.—(Artech House computing library) Includes bibliographical references and index. ISBN 1-58053-349-3 (alk. paper) 1. Software reengineering. 2. Software maintenance.