**Important RGPV Question **

Table of Contents

Toggle**CS-501 Theory of Computation (TOC)**

**V Sem, CS**

**UNIT 1-Introduction of Automata Theory**

**Q.1) **Convert the following Moore machine to Mealy.

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**UNIT 2-Types of Finite Automata**

**Q.1) **For Ξ£ = {a, b}, construct DFA’s that accept the sets consisting of

i) All the strings with exactly one βa’.

ii) All the string with atleast one βa’.

iii) All strings with atleast one ‘a’ and followed by exactly two b’s

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**Q.2) **Explain Arden’s theorem and Pumping Lemma.

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**Q.3) **Design a Push down automata.

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**Q.4) **Draw a DFA to accept string of 0’s and 1’s not ending with the string 01.

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**Q.5) **Design a DFA to accept string of O’s and 1’s when interpreted as binary numbers would be multiple of 3.

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**Q.6) **Derive regular expression from this finite automata

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**Q.7) **Construct an equivalent FA for the given regular expression (0+1)*(00+11) (0+1)*

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**Q.8) **Compute the Regular Expression for the DFA as shown below.

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**Q.9) **Design DFA’s for detecting 1001 Sequence without Overlap over the alphabet 2 = {0,1}

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**Q.10) **Design a NFA that accepts the language over the alphabet, Ξ£= {0, 1,2} where the decimal equivalent of the language is divisible by 3.

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**Q.11) **Convert the following NFA to an equivalent DFA.

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**Q.12) **Construct Non-Deterministic Pushdown Automata (NPDA) to accept the language L= {0n+112n | n> = m} over the alphabet, Ξ£={0, 1}

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**UNIT 3- Grammars**

**Q.1) **What is Ambiguity? Explain taking any two examples.

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**Q.2) **Define a context free grammar with example.

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**Q.3) **Find the context free grammar with no useless symbols equivalent to

SβAB/Ca, BβBC/AB, Aβa, CβaB/b.

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**Q.4) **What is meant by ambiguous grammar? Test whether the grammar is ambiguous or not.

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**Q.5) **Construct the following CFG grammar

i) a^{n} b^{n} c^{n }where m, n β₯ 1

ii) Obtain a CFG to generate a integer

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**Q.6) **Let G be the grammar given by SβaABB/aAA, AβaBB/a, BβbBB/A construct the PDA that accepts the language generated by this grammar G.

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**Q.7) **Define the context free grammars in the 4 tuple from (V, T, P, S) for the given languages on β (a, b).

i) All strings having atleast two ‘a’s.

ii) All possible strings not containing triple ‘b’s.

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**Q.8) **Identify the language, L generated by the following grammar, G:

G=({S, A, B), {a, b}, {SβAa, Aβa|B, BβbB|b}, S).

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**Q.9) **Find a regular grammar that generates the language on {a,b} consisting of all strings with exactly one a’s and no more than two b’s.

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**Q.10) **Construct context free grammars to accept the language L = {a^{n+2}, b^{m+1} | n = m} over the alphabet, β ={a, b}

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**Q.11) **Show that the following language on β = {a, b, c} is not context-free.

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**UNIT 4-**Friction

**Q.1) **Design a CFG.

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**Q.2) **Explain DPDA and NPDA with taking a suitable example.

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**Q.3) **Construct the PDA accepting the language.

i) L= {(ab)n|n >= 1} by empty stack.

ii) L{ww^{R}|w is in (a+b)*} by empty stack.

iii) L= {a^{2n} b^{n }| n >= 1} by empty stack.

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**Q.4) **Construct corresponding CFG for the following NPDA.

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**Q.5) **Give a Deterministic PDA that accepts {a^{m} b^{n} c^{n} |m,n β₯0} over the alphabet, β ={a, b, c}.

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**Q.6) **Give an NPDA that simulates the following grammar (S is start symbol):

SβaBB |cDD

BβCD | aS

DβdD|d

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**UNIT 5-Turing Machine**

**Q.1) **Explain Recursively enumerable language and decidability.

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**Q.2) **What is the difference between a recursive and recursively enumerable languages?

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**Q.3) **What do you mean by saying that the halting problem of TM is undecidable?

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**Q.4) **Construct Turing Machine (TM) to accept the language L= {0^{n}| 1^{n} |2^{n} | n >= 0} over the alphabet, Ξ£ ={0, 1, 2}

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**Q.5) **Prove that a language L is recursive if and only if L and L are recursively enumerable.

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**Q.6) **Prove that there is no algorithm that determines whether an arbitrary Tuning Machine halts when run with the input string 101.

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**Q.7) **Prove that the problem of determining whether for a Turing machine M the language L(M) is regular is undecidable.

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## EXTRA QUESTIONS-

**Q.1) **Describe the following sets by regular expression.

i) Strings containing 1100 as substrings.

ii) The set of all strings of 0’s are 1’s ending with 00. ………}.

iii) {Ξ, a, aa, aaa, aaaa, ………………..

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**Q.2) **Write short notes on: (Any three)

i) Halting problem

ii) Turing machine

iii) Chomsky Normal form

iv) 2 way DFA

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**Q.3)** Write short notes on (Any three)

i) Post correspondence problem

ii) Halting problem

iii) Closure property of regular grammar

iv) Turing machine

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**— Best of Luck for Exam —**