Mathematical theory of automata

Mathematical Grounds of Automata Theory

1 1 Warning! These notes are just a draft. They contain errors, unproved statements and a large part of the material is still missing. Introduction This course is an introduction to the algebraic foundations of automata theory. They are built on semigroup theory, a part of algebra which is usually not part of the standard background of a student in mathematics or in computer science. For this r...

Mathematical Foundations of Automata Theory

Cellular Automata Methods in Mathematical Physics Cellular Automata Methods in Mathematical Physics

Cellular automata (CA) are fully discrete, spatially-distributed dynamical systems which can serve as an alternative framework for mathematical descriptions of physical systems. Furthermore, they constitute intrinsically parallel models of computation which can be e ciently realized with special-purpose cellular automata machines. The basic objective of this thesis is to determine techniques fo...

Elements of Automata Theory

Mathematical Theory of Flight

We show by computational solution of the incompressible Navier-Stokes equations with friction force boundary conditions, that the classical inviscid circulation theory by Kutta-Zhukovsky for lift of a wing and laminar viscous boundary layer theory by Prandtl for drag, which have dominated 20th century flight mechanics, do not correctly describe the real turbulent airflow around a wing. We show ...