Theory of Computation Alexandre Duret-Lutz
[email protected] September 10, 2010 ADL Theory of Computation 1 / 121 References Introduction to the Theory of Computation (Michael Sipser, 2005). Lecture notes from Pierre Wolper's course at http://www.montefiore.ulg.ac.be/~pw/cours/calc.html (The page is in French, but the lecture notes labelled chapitre 1 to chapitre 8 are in English). Elements of Automata Theory (Jacques Sakarovitch, 2009). Compilers: Principles, Techniques, and Tools (A. Aho, R. Sethi, J. Ullman, 2006). ADL Theory of Computation 2 / 121 Introduction What would be your reaction if someone came at you to explain he has invented a perpetual motion machine (i.e. a device that can sustain continuous motion without losing energy or matter)? You would probably laugh. Without looking at the machine, you know outright that such the device cannot sustain perpetual motion. Indeed the laws of thermodynamics demonstrate that perpetual motion devices cannot be created. We know beforehand, from scientic knowledge, that building such a machine is impossible. The ultimate goal of this course is to develop similar knowledge for computer programs. ADL Theory of Computation 3 / 121 Theory of Computation Theory of computation studies whether and how eciently problems can be solved using a program on a model of computation (abstractions of a computer). Computability theory deals with the whether, i.e., is a problem solvable for a given model. For instance a strong result we will learn is that the halting problem is not solvable by a Turing machine. Complexity theory deals with the how eciently.