" Book " — 2006/2/21 — Page 250 — #2

(in this model) is considered as a system of deterministic algorithms A1, . . . , An and a stochastic process (probability distribution) that switches performance from one algorithm from the list to another according to a given schema. This is, for example, how the operating system of a computer functions. An interesting property of randomized algorithms is that it is possible to consider them as parts of deterministic superrecursive algorithms [8]. This gives one more example how randomness can be reduced to determinism, although the price of such reduction can be too high and non-realistic. Chapter 2 of the book provides the reader with a very solid grounding in the basics of randomized algorithms. One more advantage of the book is its transparency. However, in some cases, the author skips essential particulars. For instance, in the Introduction the author gives a well-composed proof that communication complexity of randomized algorithms can be much less than communication complexity of deterministic algorithms when information of two databases is compared. To make his proof complete and correct, it is necessary to assume that organization of data in both databases is the same. Without this assumption the described algorithm does not work. To conclude, it is necessary to state that the book is undoubtedly written with deep knowledge of the subject, is well composed, and organized.