2025 question paper

Formal Language & Automata Theory

28 questions

1. Q1a. Which of the following is the smallest unit in the definition of a language? (i) Grammar (ii) Alphabet (iii) String (iv) Production20252m

   Module 1: Introduction, Regular languages and finite automata

   Which of the following is the smallest unit in the definition of a language?

   (i) Grammar
   (ii) Alphabet
   (iii) String
   (iv) Production

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2. Q1b. A language is a (i) Set of alphabets (ii) Set of strings over an alphabet (iii) Set of grammars (iv) Set of automata20252m

   Module 1: Introduction, Regular languages and finite automata

   A language is a

   (i) Set of alphabets
   (ii) Set of strings over an alphabet
   (iii) Set of grammars
   (iv) Set of automata

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3. Q1c. Which grammar type is the most powerful? (i) Type-0 (ii) Type-1 (iii) Type-2 (iv) Type-320252m

   Module 1: Introduction, Regular languages and finite automata

   Which grammar type is the most powerful?

   (i) Type-0
   (ii) Type-1
   (iii) Type-2
   (iv) Type-3

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4. Q1d. Epsilon (\varepsilon) transitions are allowed in (i) DFA only (ii) Both DFA and NFA (iii) NFA only (iv) None20252m

   Module 1: Introduction, Regular languages and finite automata

   Epsilon ($\varepsilon$) transitions are allowed in

   (i) DFA only
   (ii) Both DFA and NFA
   (iii) NFA only
   (iv) None

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5. Q1e. Context-Free Grammars are equivalent to (i) Finite Automata (ii) Turing Machines (iii) Linear Bounded Automata (iv) Pushdown Automata20252m

   Module 2: Context-free languages and pushdown automata

   Context-Free Grammars are equivalent to

   (i) Finite Automata
   (ii) Turing Machines
   (iii) Linear Bounded Automata
   (iv) Pushdown Automata

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6. Q1f. Pumping Lemma for CFLs is used to prove a language is (i) Not Context-Free (ii) Regular (iii) Decidable (iv) Turing recognizable20252m

   Module 2: Context-free languages and pushdown automata

   Pumping Lemma for CFLs is used to prove a language is

   (i) Not Context-Free
   (ii) Regular
   (iii) Decidable
   (iv) Turing recognizable

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7. Q1g. Which of the following requires context sensitivity? (i) a^n b^n (ii) a^n b^n c^n (iii) (a+b)^* (iv) a^*20252m

   Module 3: Context sensitive langauges

   Which of the following requires context sensitivity?

   (i) $a^n b^n$
   (ii) $a^n b^n c^n$
   (iii) $(a+b)^*$
   (iv) $a^*$

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8. Q1h. Recursively Enumerable languages are also called (i) Turing Recognizable (ii) Turing Decidable (iii) Regular (iv) Context-Free20252m

   Module 4: Turing machines

   Recursively Enumerable languages are also called

   (i) Turing Recognizable
   (ii) Turing Decidable
   (iii) Regular
   (iv) Context-Free

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9. Q1i. The Halting Problem is (i) Decidable (ii) Undecidable (iii) Context-Free (iv) Regular20252m

   Module 5: Undecidability

   The Halting Problem is

   (i) Decidable
   (ii) Undecidable
   (iii) Context-Free
   (iv) Regular

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10. Q1j. Which of the following is used to prove many undecidability results? (i) Pumping Lemma (ii) Rice's Theorem (iii) Chomsky Normal Form (iv) Subset Construction20252m

    Module 5: Undecidability

    Which of the following is used to prove many undecidability results?

    (i) Pumping Lemma
    (ii) Rice's Theorem
    (iii) Chomsky Normal Form
    (iv) Subset Construction

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12. Q2a. Define the terms: Alphabet, Language, Grammar, and Derivation. Explain the relationship between them with suitable examples.20257m

    Module 1: Introduction, Regular languages and finite automata

    Define the terms: Alphabet, Language, Grammar, and Derivation. Explain the relationship between them with suitable examples.

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13. Q2b. Explain Chomsky Hierarchy of languages with examples of each type and their corresponding automata.20257m

    Module 1: Introduction, Regular languages and finite automata

    Explain Chomsky Hierarchy of languages with examples of each type and their corresponding automata.

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14. Q3a. Explain the concept of a Finite Automaton. List and describe its main components. Also, differentiate between Deterministic Finite Automaton and Non-deterministic Finite Automaton with suitable examples.20257m

    Module 1: Introduction, Regular languages and finite automata

    Explain the concept of a Finite Automaton. List and describe its main components. Also, differentiate between Deterministic Finite Automaton and Non-deterministic Finite Automaton with suitable examples.

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15. Q3b. Construct a DFA that accepts all strings over \{0,1\} containing an even number of 0s and an odd number of 1s. Also, write its formal 5-tuple definition.20257m

    Module 1: Introduction, Regular languages and finite automata

    Construct a DFA that accepts all strings over $\{0,1\}$ containing an even number of 0s and an odd number of 1s. Also, write its formal 5-tuple definition.

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16. Q4a. Convert the regular expression (a + b)abb(a + b) into an equivalent DFA. Show all steps.20257m

    Module 1: Introduction, Regular languages and finite automata

    Convert the regular expression $(a + b)abb(a + b)$ into an equivalent DFA. Show all steps.

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17. Q4b. Using Pumping Lemma, prove that the language L = \{0^{n}1^{n} \mid n \ge 0\} is not regular.20257m

    Module 1: Introduction, Regular languages and finite automata

    Using Pumping Lemma, prove that the language $L = \{0^{n}1^{n} \mid n \ge 0\}$ is not regular.

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18. Q5a. Explain how ambiguity arises in the grammar E \rightarrow E + E \mid E \times E \mid id \mid (E). Remove the ambiguity by rewriting the grammar.20257m

    Module 2: Context-free languages and pushdown automata

    Explain how ambiguity arises in the grammar $E \rightarrow E + E \mid E \times E \mid id \mid (E)$. Remove the ambiguity by rewriting the grammar.

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19. Q5b. Using Pumping Lemma for CFLs, prove that L = \{a^{n}b^{n}c^{n} \mid n \ge 0\} is not context-free.20257m

    Module 2: Context-free languages and pushdown automata

    Using Pumping Lemma for CFLs, prove that $L = \{a^{n}b^{n}c^{n} \mid n \ge 0\}$ is not context-free.

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20. Q6a. Explain Linear Bounded Automata and its relationship with Context-Sensitive Languages.20257m

    Module 3: Context sensitive langauges

    Explain Linear Bounded Automata and its relationship with Context-Sensitive Languages.

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21. Q6b. Explain the basic model of a Turing Machine with its formal 7-tuple definition.20257m

    Module 4: Turing machines

    Explain the basic model of a Turing Machine with its formal 7-tuple definition.

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23. Q7a. Design a Turing Machine that accepts the language L = \{a^{n}b^{n} \mid n \ge 0\}. Show the transition diagram/table and trace for input aabb.20257m

    Module 4: Turing machines

    Design a Turing Machine that accepts the language $L = \{a^{n}b^{n} \mid n \ge 0\}$. Show the transition diagram/table and trace for input aabb.

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24. Q7b. State and explain the Church-Turing Thesis.20257m

    Module 4: Turing machines

    State and explain the Church-Turing Thesis.

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25. Q8a. Explain the concept of Universal Turing Machine. How does it help in proving undecidability?20257m

    Module 5: Undecidability

    Explain the concept of Universal Turing Machine. How does it help in proving undecidability?

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26. Q8b. Discuss the power and limitations of Turing Machines. Compare Turing Machines with Pushdown Automata.20257m

    Module 4: Turing machines

    Discuss the power and limitations of Turing Machines. Compare Turing Machines with Pushdown Automata.

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27. Q9a. Write a short note on: Pushdown Automata20257m

    Module 2: Context-free languages and pushdown automata

    Write a short note on:

    Pushdown Automata

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28. Q9b. Write a short note on: Rice's theorem20257m

    Module 5: Undecidability

    Write a short note on:

    Rice's theorem

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29. Q9c. Write a short note on: Minimization of finite automata20257m

    Module 1: Introduction, Regular languages and finite automata

    Write a short note on:

    Minimization of finite automata

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30. Q9d. Write a short note on: Closure properties of CFLs20257m

    Module 2: Context-free languages and pushdown automata

    Write a short note on:

    Closure properties of CFLs

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