The course gives an introduction is an introduction to the theory of computation with emphasis on the relationships between formal languages, automata and abstract models of computation.
Automata theory and formal languages form the foundations of theoretical computer science, as they allow us to talk precisely about what is an algorithm or a computation.
An automaton is in fact a model of computation that can be defined mathematically. The simplest model that we will consider in this course is given by finite state automaton: a machine that is only able to keep track of its current state but it has no memory. Finite state automata specify an algorithmic procedure for recognizing whether a word is in a language. We will concentrate on the relationships between language recognized by a finite state automaton, language generated by a grammar and language described by a specification, and will obtain algorithms for translating one description of a language into another description of a different type.
Adding restricted form of memory to finite state automata increase their expressivity. We will study push-down automata, i.e. the class of automata with an auxiliary memory organized as a stack. In particular we will concentrate on the class of languages recognized by push-down automata, because of its major role in compiler design and parsing.
Foundation of Computer Science I
The following book is mandatory for the course:
John C. Martin, Introduction to Languages and the Theory of Computation, 3rd edition, McGraw Hill, 2003.
Table of Contents
- Introduction and motivation
- Formal languages
- Regular expressions
- Finite state automata
a. Distinguish one string from another
b. New automata from old
- Non-deterministic finite automata
a. The powerset construction
b. Automata with empty-transitions
- Kleene’s theorem
a. From finite automata to regular expressions
b. From regular expressions to finite automata
- Minimal finite state automata
- The pumping lemma for regular languages
- Decision problems for regular languages
- Context-free grammars
a. Regular grammars
b. Derivation trees and ambiguity
c. The pumping lemma for context-free languages
- Chomsky normal form
- Decision problem for context-free languages
- Pushdown automata
Solutions selected exercises will be provided to the students for download.
Students will be evaluated by means of a written examination.
Yes, a weekly practice class is a mandatory component of the course.