Mathematics methods for computer science
Scientific Disciplinary Sector (SSD)
INF/01 - INFORMATICS
I semestre dal Oct 4, 2010 al Jan 31, 2011.
The course covers standard principles and methods in theoretical computer science, notably in automata theory and computability. The course is structured in two parts: in the first part we cover automata, regular languages, context-free grammars, normal forms and formal Chomsky's language hierarchy. In the second part we cover the notion of computable function, decidability, security and issues in the mathematical or recursion
The course requires the standard courses on Discrete mathematics and logic.
Automata and formal languages (20h): Formal languages and grammars, finite state automata, regular languages, context-free languages, normal forms, Push-down automata, Chomsky classification of formal languages. Computability (25h): intuitive notion of algorithm, Turing analysis of computable functions, Turing machines and WHILE-programs, Church thesis, Goedelization, universality, Theorem s-m-n, unsolvable problems and halting problem, metaprogramming, recursive and recursive enumerable sets, Recursion theorems, Rice Theorem, reducibility, complete, creative and productive sets. Computational virology.
Discussion of a cooperative project.