Formal Languages and Automata Theory

1.1. Why study Automata Theory. History and origins

1.2. Relationship with others areas of knowledge

1.3. Machines, Languages and Algorithms

2.1. Introduction and Definitions

2.2. Mathematical model of an automaton

2.3. Automata and algorithms

2.4. Discrete, continuous, and hybrid automata. Classes of automata

2.5. Formal Languages: Introduction and Definitions

2.6. Operations with words. Operations with languages

3.1. Definition and Representation of Deterministic Finite Automata (DFA)

3.2. DFA as recognition devices

3.3. Equivalence and minimization of DFAs

3.4. Theorems of DFAs

3.5. Definition and Representation of Nondeterministic Finite Automata (NFA)

3.6. The Language of a NFA

3.7. Equivalence of DFAs and NFAs

4.1. Operations with languages. Derivations

4.2. Concept of grammar. Formal grammar

4.3. Chomsky Hierarchy and equivalent grammars

4.4. Context-free grammars

4.5. Language of a context-free grammar. Parse Trees

4.6. Well-formed grammars

4.7. Chomsky Normal Form. Greibach Normal Form

5.1. Definition of regular languages

5.2. DFA for a regular grammar

5.3. Equivalence of regular expressions

5.4. Kleene's Theorem

5.5. Characteristic equations

5.6. Synthesis Problem: Recursive algorithm

5.7. Derivatives of regular expressions

6.1. Definition of Pushdown Automata (PDA)

6.2. Transitions, Movement and Instantaneous Description in PDA

6.3. Acceptance by Empty Stack. Acceptance by Final State

6.4. Language Accepted by a PDA

6.5. Equivalence of PDA by Empty Stack and PDA by Final State

6.6. From Context-Free Grammar to Push-Down Automata

6.7. From Pushdown Automata to Context-Free Grammar

7.1. Definition of a Turing Machine

7.2. Variations of Turing Machines

7.3. Universal Turing Machine

8.1. Complexity Theory

8.2. Complexity of algorithms

8.3. P versus NP problems

8.4. Defining complexity classes

8.5. Time complexity

8.6. Hierarchy theorems

8.7. Non-computational problems

8.8. Limits of Computability