A mathematical structure for emergent computation
The monograph is the result of longterm research on optimization and computation. The main achievement of this work is the discovery of a new mathematical structure, called web of relations, whose elements are relations between integers organized in a certain manner, which is possibly capable to capture the world in mathematical terms as a whole. The main instrument is a theorem that gives an interesting representation of definite integrals of piecewise constant functions by integer code series. The web of relations is presented in algebraic and geometric form. It is also proposed as an universal scale to measure the complexity of things, called structural complexity, defined as the maximum level of elements that the hierarchical formation produces. A principle, that figuratively says that ''nature realizes structures with maximum complexity'' is stated and approved on a model of emergent computation. The book is suitable for students as well as research workers and practitioners in computer science, information technology, mathematics and physics. Only a basic knowledge of calculus is required.
scientific article; zbMATH DE number 1380563