Exam 2 Topics - Fall 2010

1. 11/15/11 - 12:17: Removed strike-through from one topic in pumping lemma section

1. Material: Notes and Chapter 2 and Pumping Lemma from Chapter 1


2. Definitions: Define the following terms and/or expressions and use them appropriately
1. Context Free Grammar (CFG)
2. Language of a grammar
3. Context Free Language (CFL)
4. Derivation
5. Derive
6. Derive in 0 or more steps
7. Derive Ambiguously
8. Ambiguous CFG
9. Inherently Ambiguous Language
10. Chomsky Normal Form (CNF)
11. Power set
12. PDA M recognizes Language L


3. Symbols - Define the following symbols and use them appropriately:
• Single arrow (ie →)
• Double arrow (ie ⇒)
• Double arrow starred
• Γ_ε


4. Grammars
• Describe the parts in the formal definition of a CFG
• Identify the parts of a given grammar
• Create a grammar that generates a given language
• Analyze a given grammar to find the language it generates
• Find the derivation of a given string with a given grammar, if one exists
• Find the parse tree of a given string with a given grammar, if one exists
• Identify the correspondences among a grammar, derivation of a string, and the parse tree for that string
• Prove that a given grammar is ambiguous
• Convert a grammar to CNF


5. Pushdown Automata (PDA)
1. Describe the difference in components and operation between a PDA, a DFA, and/or a NFA
2. Describe the parts in the formal definition of a PDA


3. Convert between the formal and graphical representations of a given PDA
4. Identify the correspondences between the formal and graphical representations of a given PDA


5. Describe the difference between Γ and Γ_ε and explain the role played by Γ_ε
6. Explain the consequences of the transition function of a PDA having a power set as its range
7. Describe the need motivating the pushing of a special symbol (typically $) and explain how this action satisfied that need


8. Describe the basic operation of a PDA, including how a PDA recognizes a string
9. Trace the behavior of a given PDA on a given input string


10. Analyze a PDA to identify the language it recognizes
11. Create a PDA that recognizes a given language


12. Create a PDA that recognizes the language of a given CFG


6. Context Free Languages
1. State and explain the following listing of the language recognition/generation power of various machines:
   DFA = NFA < (D)PDA < (N)PDA = CFG


2. State and explain the following listing of languages:
   Regular Languages < Context Free Languages


7. Pumping Lemma
1. State the Pumping Lemma (PL) for Regular Languages [from chapter 1!]
2. State the Pumping Lemma (PL) for Context Free Languages
3. Describe the significance of the PL for CFL
4. Explain why the PL cannot be used to show that a language belongs to a given class of languages.
5. Use the PL for CFL to prove that a language is NOT a CFL