# Practice Exam for CFG's

```Name: ______________________________
COT 3210 Exam 2. Answer all questions. Each question worth 10 points.
1. Use the pumping lemma to prove that 0n1m, n  m, is not regular.
2. Prove that L = 0nww0n , n &gt; 0, not regular, where w is a string.
3. Give a context-free grammar to generate the language 0n1m, n  m.
4. Give a context-free grammar to generate the language (0+1)0*(11)+.
For the next two questions, consider the CFG (S is the start symbol):
S -&gt; SA | a
A -&gt; Aa | aB
B -&gt; bB | SB | b
5. Show how to derive the string aabab using this CFG using a left-most derivation.
6. Show a parse tree for the string aabb
7. Describe (at a very high level) a PDA to accept sets of “balanced” “{“ and “ }”
symbols from a “C” program. That is, the alphabet consists of the two symbols: “{“ and
“}” Strings are sequences of these symbols such that no prefix of the string has more “}”
than “{“. For example, the following is legal: {{}{}}, but the following string is not:
{}}{.
8. Suppose we have a finite automata with TWO stacks (instead of just one stack as with
a PDA). Describe at a very high level how we can accept 0n1n2n using this type of
machine.
```