Algorithmic Information Theory - ISBN:0263210487

Algorithmic Information Theory

Date: 21 April 2011, 15:26

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(a) The mass of text required to describe an object;
(b) The volume of intermediate data which a computational process
would need to generate;
(c) The time for which such a process will need to execute, either on a standard "serial" computer or on computational structures unrestricted in the degree of parallelism which they can employ.
Of these three resource classes, the first is relatively static, and pertains to the fundamental question of object describability; the others are dynamic since they relate to the resources required for a computation to execute. It is with the first kind of resource that this book is concerned. The crucial fact here is that there exist symbolic objects (i.e., texts) which are algorithmically inexplicable," i.e., cannot be specified by any text shorter than themselves. Since texts of this sort have the properties associated with the random sequences of classical probability theory, the theory of describability developed in Part II of the present work yields a very interesting new view of the notion of randomness.

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