Preface

Summary

The intuitive notion of complexity is well expressed by the usual dictionary definition: “a complex object is an arrangement of parts, so intricate as to be hard to understand or deal with” (Webster, 1986). A scientist, when confronted with a complex problem, feels a sensation of distress that is often not attributable to a definite cause: it is commonly associated with the inability to discriminate the fundamental constituents of the system or to describe their interrelations in a concise way. The behaviour is so involved that any specifically designed finite model eventually departs from the observation, either when time proceeds or when the spatial resolution is sharpened. This elusiveness is the main hindrance to the formulation of a “theory of complexity”, in spite of the generality of the phenomenon.

The problem of characterizing complexity in a quantitative way is a vast and rapidly developing subject. Although various interpretations of the term have been advanced in different disciplines, no comprehensive discussion has yet been attempted. The fields in which most efforts have been originally concentrated are automata and information theories and computer science. More recently, research in this topic has received considerable impulse in the physics community, especially in connection with the study of phase transitions and chaotic dynamics.