Boolean Functions and Computation Models

This advanced textbook surveys research on boolean functions, circuits, parallel computation models, function algebras, and proof systems, with an overriding focus on the structure of "fast" parallel computation.

A survey of the present state of the art by internationally well-known authors Focus on "fast" parallel computation Includes numerous exercises ranging in difficulty Includes supplementary material: sn.pub/extras

Texte du rabat
This textbook presents a survey of research on boolean functions, circuits, parallel computation models, function algebras, and proof systems. Its main aim is to elucidate the structure of "fast" parallel computation. The complexity of parallel computation is emphasized through a variety of techniques ranging from finite combinatorics, probability theory, and finite group theory to finite model theory and proof theory. Nonuniform computation models are studied in the form of boolean circuits, uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems.
The book will benefit advanced undergraduate and graduate students as well as researchers in the field of complexity theory.

Contenu

1. Boolean Functions and Circuits.- 2. Circuit Lower Bounds.- 3. Circuit Upper Bounds.- 4. Randomness and Satisfiability.- 5. Propositional Proof Systems.- 6. Machine Models and Function Algebras.- 7. Higher Types.- References.