By David F. Rico

This ebook masterfully illuminates very simple, yet overwhelmingly strong metrics, versions, and strategies for designing expert enterprise instances whereas the writer demystifies esoteric innovations in ROI.

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**Extra resources for ROI of Software Process Improvement: Metrics for Project Managers and Software Engineers**

**Example text**

Write w = t j t , where j ≥ 1 and t is a nonempty prefix of t (possibly equal to t). Then w begins and ends with t . Now we turn to a famous equation in words, which might be considered as the noncommutative version of Fermat’s last theorem. 5. 1) holds for strings x, y, z ∈ + and i, j, k ≥ 2 if and only if there exist a word w ∈ + and integers l, m, n ≥ 1 such that x = wl , y = w m , z = w n, with li = mj + nk. Proof. Suppose x = wl , y = w m , and z = wn and li = mj + nk. Then x i = w li = w mj +nk = w mj w nk = y j zk .

The English word antsy has the property that every nontrivial prefix is a valid English word. Can you find a longer English word with this property? 5. What is the smallest class of languages over containing each singleton {a} for a ∈ and closed under the operations of union, intersection, and complement? 6. Give regular expressions for each of the following languages: (a) The set of strings over {a, b, c} in which all the a’s precede all the b’s, which in turn precede all the c’s. (b) The complement of the language in (a).

Thus our original assumption that there is no w ∈ + with x, y, z ∈ w+ is false, and such a w must exist. 5 Repetitions in strings A square is a string of the form xx, such as the English word hotshots. If w is a (finite or infinite) string containing no nonempty subword of this form, then it is said to be squarefree. Note that the string square is squarefree, while the string squarefree is not. It is easy to verify (see Exercise 3) that there are no squarefree strings of length >3 over a two-letter alphabet.