Theories of Computational Complexity

Primitive Recursive Hierarchies. Examples. Ackermann-Peter's Hierarchy. Primitive Recursive Functions. Primitive Recursive Invariants. Primitive Recursive Enumerations. Sudan's Hierarchy. Universal Sequences of Primitive Recursive Functions. Primitive Recursive String-Functions. History. Exercises and Problems.Recursive Functions. Examples. Arithmetization of Computation: An Example. Equational Characterization of Partial Recursive Functions. Godel Numberings. Recursively Enumerable Sets. Undecidability and Independence. Uniformity. Operators. Recursive Real Numbers. History. Exercises and Problems.Blum's Complexity Theory. Examples. Blum Spaces. Recursive Dependence of Complexity Measures. Complexity Classes. The Speed-Up Phenomenon. The Union Theorem. Hard Recursive Functions. Complexity Sequences. A Topological Analysis. History. Exercises and Problems.Kolmogorov and Martin-Lof's Complexity Theory. Examples. Kolmogorov's Complexity. Martin-Lof Tests. Undecidability Theorems. Representability Theorems. Recursive Martin-Lof Tests. Infinite Oscillations. Probabilistic Algorithms. History. Exercises and Problems.Subrecursive Programming Hierarchies. Examples. The LOOP Language. LOOP Hierarchies. A Universal Language. A Dynamic Characterization of LOOP Classes. Augmented LOOP Languages. Simple Functions. Program Size. History. Exercises and Problems. Bibliography. Indexes.