q12-grammar - Consider the ±ve state machine de±ned by...

CSE 260
QUIZ-12– Grammars and FAs- ANSWERS
(20 minutes)
NAME:
1. (15 points) Consider the following grammar G = ( V, T, S, P ), where V = { S, a, b } ,
T = { a, b } and the set of productions P consists of
S → aS
S → b
(a) Give a derivation for the word aab.
S ⇒ aS ⇒ aaS ⇒ aab
(b) Give the derivation (parse) tree for the above word.
S
a
S
S
a
b
(c) Give the language generated by the above grammar.
In set notaion: { a
i
b | i = 0 , 1 , 2 , ... }
Regular expression: a * b
2. (20 points) Let V = { S, A, B, a, b } and T = { a, b } . Find the language generated by
the grammar ( V, T, S, P ) when the set of productions P consists of
(a) S → AB, A → ab, B → bb
{ abbb }
(b) S → AA, S → b, A → aaA, A → aa
L = { b, a
2 i +4
| i = 0 , 1 , 2 , ... }
3. (20 points) This exercise covers finite state machines with output. Consider the five