(SEM IV) THEORY EXAMINATION 2024-25 THEORY OF AUTOMATA AND FORMAL LANGUAGES

This document contains the complete B.Tech (Semester IV) Theory Examination 2024–25 question paper for Theory of Automata and Formal Languages (BCS402). The paper spans four printed pages, carries 70 marks, and evaluates a student’s understanding of automata theory, formal grammars, Turing machines, PDA design, regular expressions, NFA–DFA conversion, and decidability concepts.
 

Section A – Short Conceptual Questions (14 Marks)

Section A contains seven 2-mark questions, each testing basic theoretical concepts:

Definition of Alphabet in automata (Page 1)

Difference between DFA and NFA

Writing a regular expression for strings ending with 01

Understanding ambiguity in CFGs

Constructing a CFG for L = {aⁿbⁿ}

Checking whether grammar S → S*S | S+S | a is ambiguous

Designing a Turing Machine for language L = {aⁿbⁿ | n ≥ 1}

These questions evaluate foundational knowledge of formal languages, grammars, and computation.
 

Section B – Medium-Length Analytical Questions (21 Marks)

Students must attempt any three out of five questions, covering NFA → DFA conversion, Arden’s theorem, grammar-to-FA conversion, PDA design, and unary Turing machine arithmetic:

Includes (Page 2):

Proving equivalence of NFA and DFA using subset construction

Finding regular expression using Arden’s Theorem for a given transition diagram

Converting a regular grammar into a finite automaton

Designing a PDA for L = {wwᴿ}, i.e., palindrome recognition

Designing a Turing Machine to compute f(n) = n + 1 for unary inputs

This section checks analytical thinking and construction-based problem-solving.
 

Section C – Long, Advanced Construction & Proof Questions (35 Marks)

Q3 – NFA to DFA / DFA Minimization (Page 3)

Construction of a DFA corresponding to the given NFA (figure shown)

OR finding the minimum state automaton equivalent to a given DFA (diagram on page)

Q4 – Pumping Lemma / Arden’s Theorem

Proving L = {aⁿbⁿcⁿ} is not regular

OR proving (a + b)* a (a + b)* is regular using Arden’s theorem

Q5 – CNF Conversion / Ambiguity Testing

Converting CFG S → aSB | ε to Chomsky Normal Form

OR checking ambiguity of grammar S → aSb | ε using derivation trees

Q6 – CFG Simplification / PDA for Palindromes

Simplifying CFG S → AbaC … (Page 3)

OR designing a PDA for palindromes over {a, b}*

Q7 – Universal Turing Machine / PCP

Explaining Universal Turing Machine and designing TM for f(n) = 2n

OR discussing Post’s Correspondence Problem and its undecidability

These questions evaluate deep understanding of computation theory, decidability, automata construction, and formal grammar transformations.
 

Summary

The Theory of Automata and Formal Languages (BCS402) exam paper comprehensively covers:

Deterministic & Non-Deterministic Automata

Regular Expressions & Regular Grammars

Context-Free Grammars & Ambiguity

PDA construction & palindrome recognition

Turing Machines, unary arithmetic, Universal TM

NFA–DFA conversion & DFA minimization

Arden’s theorem & pumping lemma

CNF conversion & CFG simplification

PCP and undecidability concepts

It serves as an excellent academic resource for students studying the foundations of computation and formal language theory.