COURSE DELIVERY PLAN - THEORY Page 1 of 6 Department of Computer Science and Engineering B.E/B.Tech/M.E/M.Tech : B.E. Regulation: 2013 PG Specialisation : - Sub. Code / Sub. Name : CS6503 / THEORY OF COMPUTATION Unit : I Unit Syllabus: FINITE AUTOMATA LP: CS6503 Rev. No: 00 Date: 28-06-2017 Introduction- Basic Mathematical Notation and techniques- Finite State systems Basic Definitions Finite Automaton DFA & NDFA Finite Automaton with - moves Regular Languages- Regular Expression Equivalence of NFA and DFA Equivalence of NDFA s with and without -moves Equivalence of finite Automaton and regular expressions Minimization of DFA- - Pumping Lemma for Regular sets Problems based on Pumping Lemma. Objective: To introduce Finite state systems, to explain different types of Finite Automata like DFA, NDFA with and without -moves. To introduce Regular languages and expressions proofs to prove the equivalence of different automata and regular expressions, to explain how to minimize the given DFA and Pumping Lemma to prove that the given language is not regular. 1 Introduction to Automata Theory 1-Ch. 1;Pg:1-5, 3-Ch. 1;Pg:36-61, 4-Ch. 1;Pg:5-51, 5-Ch. 1;Pg:15-28, 2 Mathematical Notations and techniques 5-Ch. 1;Pg:1-14, 6-Ch. 1;Pg: 1-13, 3 Finite Automaton DFA & NDFA Definitions, Notations, Extended Transition Functions, Languages 4 Finite Automaton Problems 1-Ch. 1;Pg:28-33, 1-Ch. 2;Pg:37-60, 3-Ch. 3;Pg:71-79, 4-Ch. 2;Pg:55-73, 5-Ch. 2;Pg:35-55, 6-Ch. 3;Pg:60-68, 1-Ch. 2;Pg:47-59,Pg:66-68,72, 5-Ch. 1;Pg:37,39,41,43-47,49-50,52-54, 5 Finite Automaton with ε- moves 1-Ch. 2;Pg:72-80, 2-Ch. 4;Pg:133-143, 6 Finite Automaton with ε- moves-problems 1-Ch. 2;Pg:73-78,80, 2-Ch. 9;Pg:143-145 7 8 9 10 11 Regular Languages- Regular Expression Definitions, Notations, Operators, Problems Introduction to Formal proofs, Equivalence of NFA and DFA Equivalence of NDFA s with and without - moves Theorem and Problems Equivalence of finite Automaton and regular expressions, Algebraic laws Minimization of DFA - Table Filling Algorithm 12 Pumping Lemma for Regular sets - Theorem 1-Ch. 3;Pg:83-90, 3-Ch. 5;Pg:136-139, 4-Ch. 2;Pg:75-83, 5-Ch. 3;Pg:71-86, 6-Ch. 3;Pg:68-75, 1-Ch. 1;Pg:5-28, Pg:60-64, 3-Ch. 3;Pg:80-83, 5-Ch. 2;Pg:55-61, 6-Ch. 3;Pg:75-80, 7-Ch. 2;Pg:26-27, 1-Ch. 3;Pg:90-122, 3-Ch. 5;Pg:152-161, 1-Ch. 4;Pg:154-165, 3-Ch. 3;Pg:91-96, 4-Ch. 2;Pg:92-98, 1-Ch. 4;Pg:125-127, 3-Ch. 5;Pg:162-163, 5-Ch. 4;Pg:115-117, 6-Ch. 4;Pg:88-90, 13 Problems based on Pumping Lemma 1-Ch. 4;Pg:127-130, 3-Ch. 5;Pg:163-164, 5-Ch.4;Pg:117-121, Introduction to different types of formal proofs, Algebraic Laws Course Outcome 1: The student will be able to design Finite Automata and solve real world problems that can be represented in regular languages. * duration: 50 minutes
COURSE DELIVERY PLAN - THEORY Page 2 of 6 Unit : II Unit Syllabus: GRAMMARS Grammar Introduction Derivations and Languages Ambiguity- Types of Grammar - Context Free Grammars and Languages Relationship between derivation and derivation trees Simplification of CFG Elimination of Useless symbols - Unit productions - Null productions Greibach Normal form Chomsky normal form Problems related to CNF and GNF. Objective: To introduce Grammar and its types, to explain in detail about Context Free Grammars(CFG) and Languages, to introduce methods to identify ambiguous grammars, to simplify the given CFG and to find the normal forms of given CFG. 14 Grammar Introduction Types of Grammar, Derivations and Languages 3-Ch. 4;Pg:107-119, 4-Ch. 3;Pg:113-116, 5-Ch. 5;Pg:125-127, 6-Ch. 2;Pg:18-24, 15 Context Free Grammars and Languages Introduction and Problems 16 CFG problems,ambiguity 17 Relationship between derivation and derivation trees 1-Ch. 5;Pg:169-179, 3-Ch. 4;Pg:120-124, 5-Ch. 5;Pg:127-129, 6-Ch. 2;Pg:48-51, 1-Ch. 5;Pg:179-181, 3-Ch. 4;Pg:129-131, 4-Ch. 3;Pg:116-120, 5-Ch. 5;Pg:134-135, 6-Ch. 2;Pg:48-51, 1-Ch. 5;Pg:205-215, 3-Ch. 6;Pg:188-189, 4-Ch. 3;Pg:128-129, 5-Ch. 5;Pg:141-145, 6-Ch. 2;Pg:32-37, 1-Ch. 5;Pg:181-191, 3-Ch. 6;Pg:180-187, 4-Ch. 3;Pg:122-128, 5-Ch. 5;Pg:129-133, 18 Simplification of CFG Elimination of Useless symbols - Unit productions - Null productions - Chomsky normal form 1-Ch. 7;Pg:255-266, 3-Ch. 6;Pg:189-203, 5-Ch. 6;Pg:149-168, 6-Ch. 2;Pg:37-44, 19 Problems related to CNF 20 Greibach Normal form,problems 1-Ch. 7;Pg:266-273,3-Ch. 6;Pg:203-205, 5-Ch. 6;Pg:165-168,6-Ch. 2;Pg:42-44, 3-Ch. 6;Pg:206-212, 7-Ch. 4;Pg:94-97, 5-Ch. 6;Pg:168-170, 6-Ch. 2;Pg:44-46, 3-Ch. 6;Pg:207-213, 7-Ch. 4;Pg-97-99, 5-Ch. 6;Pg:165-170, 6-Ch. 2;Pg:46-48, Course Outcome 2: The student will be able to design Context Free Grammars, Derivation trees and Derive its Normal forms * duration: 50 mins
COURSE DELIVERY PLAN - THEORY Page 3 of 6 Unit : III Unit Syllabus: Pushdown Automata Pushdown Automata- Definitions Moves Instantaneous descriptions Deterministic pushdown automata Equivalence of Pushdown automata and CFL - pumping lemma for CFL problems based on pumping Lemma. Objective: To introduce Pushdown Automata, its Instantaneous descriptions and Deterministic Pushdown automata. To explain the Equivalence of Pushdown automata & Context free languages and to use pumping lemma to prove that the given language is not Context-free. 21 Pushdown Automata (PDA)- Introduction, Definitions, Language to PDA 1-Ch. 6;Pg:219-224, 3-Ch. 7;Pg:227-232, 4-Ch. 3;Pg:130-132, 5-Ch. 7;Pg:175-179, 6-Ch. 7;Pg:145-149, 22 Moves Instantaneous descriptions 1-Ch. 6;Pg:224-228, 3-Ch. 7;Pg:233-239, 6-Ch. 7;Pg:145-149, 23 Problems on designing Pushdown Automata 1-Ch. 6;Pg:228-231, 4-Ch. 3;Pg:132-136, 5-Ch. 7;Pg:179-184, 6-Ch. 7;Pg:148-149, 24 Equivalence of Pushdown automata and CFL - Context Free Grammar to PDA, PDA to Context Free Grammar Theorems 1-Ch. 6;Pg:237-241, 3-Ch. 7;Pg:240-250, 5-Ch. 7;Pg:184-189, 6-Ch. 7;Pg:151-159, 25 PDA to Context Free Grammar Problems 1-Ch. 6;Pg:241-245, 3-Ch. 7;Pg:240-250, 5-Ch. 7;Pg:189-193, 6-Ch. 7;Pg:151-159, 26 Context Free Grammar to PDA Problems 27 Deterministic Pushdown Automata 28 Pumping lemma for CFL Theorem & Problems 1-Ch. 6;Pg:245-246, 5-Ch. 7;Pg:193-194, 6-Ch. 7;Pg:159-162, 1-Ch. 6;Pg:246-251, 3-Ch. 7;Pg: 256-258, 5-Ch. 7;Pg: 195-198, 1-Ch. 7;Pg:274-277, 3-Ch. 6;Pg: 213-216, 4-Ch. 3;Pg:136-143, 5-Ch. 8;Pg: 206-207, 6-Ch. 8;Pg:165-167, Course Outcome 3: The student will be able to design Pushdown Automata and identify whether the given language is context free or not using pumping lemma * duration: 50 mins
COURSE DELIVERY PLAN - THEORY Page 4 of 6 Unit : IV Unit Syllabus: TURING MACHINES Definitions of Turing machines Models Computable languages and functions Techniques for Turing machine construction Multi head and Multi tape Turing Machines - The Halting problem Partial Solvability Problems about Turing machine- Chomskian hierarchy of languages. Objective: To understand a Turing Machine and its variants, to construct Turing Machine for problems that are computable, to introduce to halting problem and partial solvability. Teachin g 29 Definitions of Turing machines Models 1-Ch. 8;Pg:316-329, 2-Ch. 9;Pg:319-323, 3-Ch. 9;Pg:278-282, 4-Ch. 4;Pg:179-194, 5-Ch. 9;Pg:222-229, 6-Ch. 9;Pg:193-222, 30 Computable languages and functions 31 Techniques for Turing machine construction Proper Subtraction, subroutines, Storage in state, Multiple Track 32 Multi head and Multi tape Turing Machines 33 The Halting problem 2-Ch. 09;Pg:352-354, 3-Ch. 9;Pg:283, 6-Ch. 11;Pg:267-271, 1-Ch. 8;Pg:329-336, 3-Ch. 9;Pg:289-291, 6-Ch. 9;Pg:212-218, 1-Ch. 08;Pg:336-337, 2-Ch. 08;Pg:316-329, 3-Ch. 09;Pg:292-294, 4-Ch. 04;Pg: 201-209, 5-Ch. 10;Pg:258-262, 6-Ch. 10;Pg: 227-232, 5-Ch. 12;Pg:301-304, 3-Ch. 10;Pg:314, 4-Ch. 05;Pg:251-253, 5-Ch. 12;Pg:301-304, 6-Ch. 11;Pg:253-255, 34 Partial Solvability 2-Ch. 09;Pg:328-332, 3-Ch. 11;Pg:332-340, 35 Problems about Turing machine 36 Problems about Turing machine 37 Chomskian hierarchy of languages 2-Ch. 9;Pg:323-327, 4-Ch. 4;Pg:210-226, 6-Ch. 9;Pg:193-222, 2-Ch. 9;Pg:323-327, 4-Ch. 4;Pg:210-226, 6-Ch. 9;Pg:193-222, 2-Ch. 10;Pg:380-387, 5-Ch. 11;Pg:295-297, 6-Ch. 13;Pg:320-324, Course Outcome 4: The student will be able to design Turing Machine using different techniques for any computable problem * duration: 50 mins
COURSE DELIVERY PLAN - THEORY Page 5 of 6 Unit : V Unit Syllabus: UNSOLVABLE PROBLEMS AND COMPUTABLE FUNCTIONS Unsolvable Problems and Computable Functions Primitive recursive functions Recursive and recursively enumerable languages Universal Turing machine. MEASURING AND CLASSIFYING COMPLEXITY: Tractable and Intractable problems- Tractable and possibly intractable problems P and NP completeness - Polynomial time reductions. Objective: To introduce solvable and unsolvable problems, primitive recursive functions, Recursive and recursively enumerable languages, to explain Universal Turing machine, to introduce Tractable and Intractable problems- Tractable and possibly intractable problems P and NP completeness - Polynomial time reductions. 38 Unsolvable Problems Introduction & Examples 2-Ch. 11;Pg:407-439, 4-Ch. 5;Pg: 254-267, 5-Ch. 12;Pg:299-321, 39 Computable Functions - functions Primitive recursive 2-Ch. 12;Pg:442-451, 3-Ch. 11;Pg:323-328, 4-Ch. 05;Pg:267-271, 5-Ch. 13;Pg:326-329, 6-Ch. 11;Pg:267-273, 40 Recursive and recursively enumerable languages 41 Universal Turing machine 42 Measuring And Classifying Complexity 2-Ch. 10;Pg:365-401, 3-Ch. 11;Pg:329-331, 4-Ch. 04;Pg:196-200, 5-Ch. 11;Pg:276-282, 6-Ch. 11;Pg:248-250,Pg:255-259, 1-Ch. 09;Pg:377-379, 4-Ch. 05;Pg:247-250, 5-Ch. 10;Pg:266-270, 6-Ch. 11;Pg:251-255, 2-Ch. 13;Pg:481-499, 3-Ch. 12;Pg:346-371, 5-Ch. 14;Pg:343-353, 6-Ch. 12;Pg:280-283, 43 Tractable and Intractable problems - Tractable and possibly intractable problems 2-Ch. 14;Pg:500-505, 5-Ch. 14;Pg:353-354, 6-Ch. 12;Pg:284-286, 44 P and NP completeness Problems 45 P and NP completeness Problems 46 Polynomial time reductions 2-Ch. 14;Pg:506-510, 3-Ch. 12;Pg:346-371, 4-Ch. 05;Pg:275-277,Pg:301-349, 5-Ch. 14;Pg:353-356, 6-Ch. 12;Pg:286-300, 1-Ch. 10;Pg:427-434, 3-Ch. 12;Pg: 346-371, 4-Ch. 05;Pg:275-277,Pg:301-349, 5-Ch. 14;Pg:353-356, 6-Ch. 12;Pg:286-300, 1-Ch. 10;Pg:435-448, 3-Ch. 12;Pg:351, 4-Ch. 05;Pg:301-309, 5-Ch. 14;Pg:355-356, 6-Ch. 12;Pg:286-287, Course Outcome 5: The student will be able to explain and demonstrate the decidability and undecidability of various problems * duration: 50 mins
COURSE DELIVERY PLAN - THEORY Page 6 of 6 Sub Code / Sub Name: CS6503 / THEORY OF COMPUTATION REFERENCES: TEXT BOOKS: 1. Hopcroft J.E., Motwani R. and Ullman J.D, Introduction to Automata Theory, Languages and Computations, Second Edition, Pearson Education, 2008. (UNIT 1,2,3) 2. John C Martin, Introduction to Languages and the Theory of Computation, Third Edition, Tata McGraw Hill Publishing Company, New Delhi, 2007. (UNIT 4,5) REFERENCES: 3. Mishra K L P and Chandrasekaran N, Theory of Computer Science - Automata, Languages and Computation, Third Edition, Prentice Hall of India, 2004. 4. Harry R Lewis and Christos H Papadimitriou, Elements of the Theory of Computation, Second Edition, Prentice Hall of India, Pearson Education, New Delhi, 2003. 5. Peter Linz, An Introduction to Formal Language and Automata, Third Edition, Narosa Publishers, New Delhi, 2002. 6. Kamala Krithivasan and Rama. R, Introduction to Formal Languages, Automata Theory and Computation, Pearson Education 2009. 7. Hopcroft J.E., and Ullman J.D, Introduction to Automata Theory, Languages and Computations, First Edition, Pearson Education, 2008.