Theory of Computation (CS-4005) - B.E RGPV CBCS & CBGS Scheme Notes -->

## Objective:

The purpose of this subject is to cover the underlying concepts and techniques used in Theory of Computation. In this syllabus we cover finite automata, pushdown automata, Context free grammars and Turing machines.

## Syllabus

UNIT 1:
Automata: Basic machine, FSM , Transition graph, Transition matrix, Deterministic and nondeterministic FSM’S, Equivalence of DFA and NDFA, Mealy & Moore machines, minimization of finite automata, Two-way finite automata. Regular Sets and Regular Grammars: Alphabet, words, Operations, Regular sets, Finite automata and regular expression, Myhill- Nerode theorem Pumping lemma and regular sets, Application of pumping lemma, closure properties of regular sets.

UNIT 2:
Context –Free Grammars: Introduction to CFG, Regular Grammars, Derivation trees and Ambiguity, Simplification of Context free grammars, Normal Forms (Chomsky Normal Form and Greibach Normal forms).

UNIT 3:
Pushdown Automata: Definition of PDA, Deterministic Pushdown Automata, PDA corresponding to given CFG, CFG corresponding to a given PDA. Context Free Languages: The pumping lemma for CFL’s, Closure properties of CFL’s, Decision problems involving CFL’s.

UNIT 4:
Pushdown Automata: Definition of PDA, Deterministic Pushdown Automata, PDA corresponding to given CFG, CFG corresponding to a given PDA. Context Free Languages: The pumping lemma for CFL’s, Closure properties of CFL’s, Decision problems involving CFL’s.

UNIT 5:
Tractable and Untractable Problems: P, NP, NP complete and NP hard problems, examples of these problems like satisfy ability problems, vertex cover problem, Hamiltonian path problem, traveling sales man problem, Partition problem etc.

• Unit 1
• Unit 2
• Unit 3
• Unit 4
• Unit 5

## Books Recommended

1. John E. Hopcroft, Jeffery Ullman,”Introduction to Automata theory, Langauges & computation” , Narosa Publishers.
2. K.L.P Mishra & N.Chandrasekaran,“Theory of Computer Science”, PHI Learning
3. Daniel I.A. Cohen,“Introduction to Computer Theory”,Wiley India.
4. John C Martin, “Introdution to languages and theory of computation”, McGraw Hill
5. Anami & Aribasappa , “ Formal Languages and Automata Theory”,Wiley India

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