8/8/2019 r5310501 Formal Languages and Automata Theory

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Code No: R5310501 R5III B.Tech I Semester(R05) Supplementary Examinations, November 2010

FORMAL LANGUAGES AND AUTOMATA THEORY(Computer Science & Engineering)

Time: 3 hours Max Marks: 80Answer any FIVE Questions

All Questions carry equal marks

1. Construct DFA over { a, b } for the following: [28]

(a) On input w, produce output an, where n is the number of occurrences of the sub string ab in w.

(b) On input w, produce output an, where n is the number of occurrences of the sub string aba inw.

2. Construct a NFA, which accepts language L=set of strings with zero (or) more number of 0s followedby zero (or) more number of 1s followed by zero (or) more number of 2s And construct equivalentDFA. [16]

3. Consider the two regular expressionsr=0*+1*, s=01*10*+1*0+(0*1)*

(a) Find a string corresponding to r but not to s.

(b) Find a string corresponding to s but not to r. [8+8]

4. Construct Left Linear Grammar and Right Linear grammars for the languages shown below.

(a) (0+1)*00(0+1)*

(b) (((01+10)*11)*00)*. [28]

5. Eliminate useless symbols, useless productions, unit productions. And null productions from thefollowing grammars:

(a) S aS |A| cA aB aaC acb

(b) S aa |A| B| CA aB |B AaC aCDD ddd. [8+8]

6. (a) Construct the PDA corresponding to the grammar:SaABB/aAAAaBB/aBbBB/A.

(b) Construct a PDA that accepts the language

L = {wcwR/w {a, b}}. [8+8]

7. (a) Compare and contrast Finite automation, push down automaton and Turing machines.

(b) Design Turing Machine, which multiplies two integers. Give its state transition diagram. [8+8]

8. (a) Give the CSL for L={anbncn : n >= 1}

(b) Writes the properties of recursive and recursive enumerable languages.

(c) Mention the properties of DCFLs. [5+6+5]