A recent interesting paper by Melton et al. [1] discussed finding measures which preserve intuitive orderings on software documents. Informally, if less-than-or-equal-to is such an ordering, then they argue that a mea...
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A recent interesting paper by Melton et al. [1] discussed finding measures which preserve intuitive orderings on software documents. Informally, if less-than-or-equal-to is such an ordering, then they argue that a measure M is a real-valued function defined on documents such that M(F) less-than-or-equal-to M(F) whenever F less-than-or-equal-to F'. However, in measurement theory, this is only a necessary condition for a measure M. The representation condition for measurement additionally requires the converse;that F less-than-or-equal-to F' whenever M(F) less-than-or-equal-to M(F). Using the measurement theory definition of a measure, we show that Melton et al.'s examples, like McCabe's cyclomatic complexity [2], are not measures of the proposed intuitive document ordering after all. However, by dropping the restriction to real-valued functions, we show that it is possible to define a measure which characterises Melton et al.'s order relation;this provides a considerable strengthening of the results in Reference 1. More generally, we show that there is no single real-valued measure which can characterise any intuitive notion of 'complexity' of programs. The power of measurement theory is further illustrated in a critical analysis of some recent work by Weyuker 131 et al. on axioms for software complexity measures.
A method of making the intuitive notion of “complexity” more precise is exemplified by means of snowflakes. It utilizes the length of the shortest possible description of a structure in an appropriately defined lang...
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A method of making the intuitive notion of “complexity” more precise is exemplified by means of snowflakes. It utilizes the length of the shortest possible description of a structure in an appropriately defined language. Structures necessitating longer minimal descriptions are defined as more complex. This measure of complexity is compared with the intuitive, subjective notion of complexity.
Various intuitive notions of justice are characterized in terms of geometry. Three approaches to justice (Utilitaran, Rawlsian and Nash) are considered. A set of qualities which we might want a justice approach to hav...
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Various intuitive notions of justice are characterized in terms of geometry. Three approaches to justice (Utilitaran, Rawlsian and Nash) are considered. A set of qualities which we might want a justice approach to have is presented. Three different subsets of these qualities are shown to be uniquely satisfied (out of all possible approaches) by a different one of the three approaches considered.
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