Writing for Computer Science by Justin Zobel

Author:Justin Zobel
Language: eng
Format: epub, pdf
Publisher: Springer London, London

In the first version, the author has had to struggle to avoid ambiguity.

Many terms have well-defined mathematical meanings and are confusing if used in another way.

Normal, usual, typical. The word “normal” has several mathematical meanings; it is often best to use, say, “usual” or “typical” if a non-mathematical meaning is intended.

Definite, strict, proper, all, some. Avoid “definite”, “strict”, and “proper” in their non-mathematical meanings, and be careful with “all” and “some”.

Any. Avoid the word “any” in mathematical writing: sometimes it means “all” and sometimes it means “some”.

Intractable, infeasible. An algorithm or problem is “intractable” only if it is NP-hard, that is, the asymptotic cost (or computational complexity) is believed to be worse than polynomial. In the context of asymptotic cost, “infeasible” sometimes has the same meaning as “intractable”; in the context of an optimization problem, it might mean that the problem has no (feasible) solution.

In general writing, either “infeasible” and “intractable” is sometimes used to mean hard to do, which is acceptable if there is no possibility of confusion.

Formula, expression, equation. A “formula”, or an “expression” is not necessarily an “equation”; the latter involves an equality.

Equivalent, similar. Two things are “equivalent” if they are indistinguishable with regard to some criteria. If they are not indistinguishable, they are at best “similar”.

Element, partition. An “element” is a member of a set (or list or array) and should not be used to refer to a subpart of an expression. If a set is “partitioned” into subsets, the subsets are disjoint and form the original set under union.

Average, mean. “Average” is used loosely to mean typical. Only use it in the formal sense—of mean, that is, the arithmetic mean—if it is clear to the reader that the formal sense is intended. Otherwise use “mean” or even “arithmetic mean”.

Subset, proper subset, strict subset. “Subset” should not be used to mean subproblem. Orderings (or partial orderings) specified in writing are assumed to be non-strict. For example, “A is a subset of B” means that ; confusingly, this is sometimes written . To specify use “A is a proper (or strict) subset of B”.

Similar rules apply to “less than”, “greater than”, and “monotonic”.

Metric, measure. “Metric” is sometimes used informally to mean measure, but both have specific meanings in mathematics. In particular, when used in a formal context a metric is expected to satisfy conditions such as the triangle inequality. While “measure” also has a formal meaning, it is usually the less confusing of the two words, as it also has an appropriate informal usage. In mathematical contexts, use “measure” unless metric is intended.

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