ITEC 420: Exam 1 topics - Fall 2011

1. Coverage
1. Through GNFA and some Pumping Lemma
2. No coverage of Grammars and Context Free Languages
3. Primarily on lecture and notes, supplemented by chapter 1 of the text
4. Homeworks


2. Chapter 0: Preliminaries
1. Basic Math
• Cross product
• Sequence
• Power Set
• Function, Domain, Range, f: A → B


2. Languages
• Symbol
• Alphabet
• String
• Empty String
• Language
• Empty Language


3. Proofs
• Contradiction
• Induction
• A = B for sets A and B


3. Chapter 1: Regular Languages
1. Regular Language: Definition


2. FSM
1. States, State Diagram
2. Accepts a string
3. Recognizes a language
4. Formal definition
5. Computation


3. Regular Operations: what each operates on and what it does
1. Union
2. Concatenation
3. Star


4. Regular Operations - Closure: Definition


5. NFA:
1. Purpose
2. Formal and Informal Definition
3. Diagram (difference from FSM)
4. How an NFA accepts a string
5. What a computation looks like and differs from DFA
6. NFA to DFA algorithm
7. NFA and regular languages


6. Regular Operations - Prove closure with NFA


7. Regular Expressions
1. Definition: six kinds; recursive definition and base case
2. Shorthands and precedence: Concat, parens, L(R), Plus, Σ, Σ*
3. Types and context (eg does 0 represent a symbol, string, RE, or language?)
4. RE describe Regular languages - as in exercises
1. GNFA: Difference from NFA and convert NFA to GNFA
2. Convert(GNFA) returns RE


8. Pumping Lemma
1. Purpose
2. Definition