Syllabus - Theory of Computation (IT-503 (A))

Information Technology

Theory of Computation (IT-503 (A))

V-Semester

UNIT I

Introduction of the theory of computation, Finite state automata – description of finite automata, properties of transition functions, Transition graph, designing finite automata, FSM, DFA, NFA, 2-way finite automata, equivalence of NFA and DFA, Mealy and Moore machines.

UNIT II

Regular grammars, regular expressions, regular sets, closure properties of regular grammars, Arden’s theorem, Myhill-Nerode theorem, pumping lemma for regular languages, Application of pumping lemma, applications of finite automata, minimization of FSA.

UNIT III

Introduction of Context-Free Grammar - derivation trees, ambiguity, simplification of CFGs, normal forms of CFGs- Chomsky Normal Form and Greibach Normal forms, pumping lemma for CFLs, decision algorithms for CFGs, designing CFGs, Closure properties of CFL’s.

UNIT IV

Introduction of PDA, formal definition, closure property of PDA, examples of PDA, Deterministic Pushdown Automata, NPDA, conversion PDA to CFG, conversion CFG to PDA.

UNIT V

Turing machines - basics and formal definition, language acceptability by TM, examples of TM, variants of TMs – multitape TM, NDTM, Universal Turing Machine, offline TMs, equivalence of single tape and multitape TMs. Recursive and recursively enumerable languages, decidable and undecidable problems – examples, halting problem, reducibility. Introduction of P, NP, NP complete, NP hard problems and Examples of these problems.

Course Objective

Student learns some fundamental concepts in automata theory and designing of Finite Automata, conversion NFA to DFA. Application of Finite Automata in computer science and real world. Obtain minimized DFA and Application of regular expression and conversion from RE to Finite Automata and Finite Automata to Regular Expression and Proving language are not regular. Designing of CFG’s , Construction of parse trees, finding and removing ambiguity in grammars, simplification of CFG, Conversion of grammar to Chomsky Normal Form ,Greibach normal form. Designing problems on Pushdown Automata and conversion of grammar to PDA, PDA to Grammar. Designing Turing machines, understanding the working of various types of Turing machines and study P and NP type problem.

Course Outcome

Convert between finite automata, regular grammars, and regular expression representations of regular languages. Apply the pumping lemma for regular languages to determine if a language is regular. Convert between grammars and push-down automata for context-free languages. Determine if a language is regular or context-free. Demonstrate that a grammar is ambiguous. Translate a context-free grammar from one form to another. Produce simple programs for a Turing Machine. Explain the concept of undecidability. List examples of undecidable problems.

Practicals

Reference Books

  • Daniel I.A. Cohen,“Introduction to Computer Theory”,Wiley India.

  • John E Hopcroft, Jeffrey D. Ullman and Rajeev Motwani, “Introduction to Automata Theory, Languages and Computation”, Pearson Education.

  • K.L.P Mishra & N.Chandrasekaran,“Theory of Computer Science”, PHI Learning.

  • Peter Linz, “Introduction to Automata Theory and Formal Languages”, Narosa Publishing.

  • John C Martin, “Introduction to languages and the theory of computation”, TATA McGraw Hill.