The following brief overview is intended to give a flavor of the questions addressed by Complexity Theory. It includes a brief review of the contents of the current book, as well as a brief overview of several more advanced topics. The latter overview is quite vague, and is merely meant as a teaser toward further study (cf., e.g., [13]).

Absolute Goals and Relative Results

Complexity Theory is concerned with the study of the intrinsic complexity of computational tasks. Its “final” goals include the determination of the complexity of any well-defined task. Additional goals include obtaining an understanding of the relations between various computational phenomena (e.g., relating one fact regarding Computational Complexity to another). Indeed, we may say that the former type of goals is concerned with absolute answers regarding specific computational phenomena, whereas the latter type is concerned with questions regarding the relation between computational phenomena.

Interestingly, so far Complexity Theory has been more successful in coping with goals of the latter (“relative”) type. In fact, the failure to resolve questions of the “absolute” type led to the flourishing of methods for coping with questions of the “relative” type. Musing for a moment, let us say that, in general, the difficulty of obtaining absolute answers may naturally lead to a search for conditional answers, which may in turn reveal interesting relations between phenomena. Furthermore, the lack of absolute understanding of individual phenomena seems to facilitate the development of methods for relating different phenomena. Anyhow, this is what happened in Complexity Theory.