Complexity

This book commemorates Eric Goles’s achievements in science and engineering. Eric Goles is one of the world leaders in the field of automata and complexity. His groundbreaking discoveries are in the theory and analysis of complex systems, particularly in the field of discrete systems dynamics such as neural networks, automata networks, majority networks, bootstrap percolation models, cellular automata, computational complexity theory, discrete mathematics, and theoretical computer science. Topics include cellular automata, complex networks, models of computation, expansive systems, sandpile automata, Penrose tilings, Boolean automata, models of infection, Fibonacci trees, dominos, reversible automata, and fungal automata.

This advanced textbook presents a broad and up-to-date view of the computational complexity theory of Boolean circuits. It combines the algorithmic and the computability-based approach, and includes extensive discussion of the literature to facilitate further study.

Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability.

The Complexity Theory Companion is an accessible, algorithmically oriented, research-centered, up-to-date guide to some of the most interesting techniques of complexity theory.

This book delivers stimulating input for a broad range of researchers, from geographers and ecologists to psychologists interested in spatial perception and physicists researching in complex systems.