Q No. 3: Grammar G1 = (N = { E, T, F, I, D}, T = { +, *, (, ), 0-9}, S = {E} and P is the set of productions: E → E +T | T T T * F | F → (E) | I I → DI |D F D 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 For the string w = (9*(9+9)+999), find- 1. Leftmost derivation 2. Rightmost derivation 3. Parse Tree

7) Give context-free grammars that generate the following languages. i) { w € {0, 1}* | the length of w is odd and the middle symbol is 0 } ii) { a¹ b³ ck | i, j, k ≥ 0 and i + j = k } iii) { a¹ b³ ck | i, j, k ≥ 0, and i = j or i= k }

Language L S->A | AX X->ABY | AB Y->ABCY | ABC BA -> AB CA -> AC CB -> BC A->a B->b C->c   Draw a state diagram for a linear-bounded automata that accepts L.

Let L, and L2 be the languages defined as follows: L1 ={ xe{0,1}* | x has an odd number of Os}. L2 ={ 0"1m0" | n, m 20} Which of the following context-free grammars generates the language L1 U L2? (Here all uppercase letters are variables) O E- 1E| OF F- 1F| OE je A- OAO | B B - 1B|E OS-E|A E - OF | 1E F- OE | 1F|E A- OAO | 1A|E OS- S1 | S2 S1 → 00S | 15 | 01A| 10A | B A- 10S | 01S B-1|8 S2→ OS,0| A2 A2 - 1| S2|E S-E|A E- 1E| OF F- 1F| OE je A- OAO | B B- 1B|E

a. Convert G to Chomsky Normal Form. b. Convert the language of G to a PDA.

C++ Consider the language that the following grammar defines: <S> =  c | <W> | c<S> <W> = abb|a<W>bb Write all strings that are in this language and that contain seven or fewer characters. If the answer includes multiple strings, you must enter the answers in alphabetical order. A. In alphabetic order, what are the two strings in this language that are 3 characters in length? B. In alphabetic order, what are the two strings in this language that are 4 characters in length? C. In alphabetic order, what are the two strings in this language that are 5 characters in length?

3. ?. Complete parts a) and b). X y a) :) Convert the following NFA into a DFA: {p} {p.q} {t} {r,s} r {t} {p,r} *S Ø *t Ø Ø b) DI Describe the language accepted by the finite automata in 3.a).

Construct a FA(in TG)that accepts the language generated by the Regular Grammer: A →aB B →abA| b

This is an Automata and Computation question on Functions/Sets.

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