DURGAPUR INSTITUTE OF ADVANCED TECHNOLOGY AND MANAGEMENT DEPARTMENT OF INFORMATION TECHNOLOGY Subject Code: CS 402 Subject Name: Formal Language & Automata Theory Semester : IV Year: 2 ND Session : 2019 Branch Name: Information Technology Faculty Name: Amit Kumar Datta Assistant Professor IT Department Syllabus Prerequisites of Formal Language & Automata Theory: Elementary discrete mathematics including the notion of set,function,relation,product,partial order,equivalence relation,graph& tree. They should have a thorough understanding of the principle of mathematical induction. Module-1: [13 L] Fundamentals: Basic definition of sequential circuit, block diagram, mathematical representation, concept of transition table and transition diagram (Relating of Automata concept to sequential circuit concept) Design of sequence detector, Introduction to finite state model.finite state machine: Definitions, capability & state equivalent, kth- equivalent concept. Merger graph, Merger table, Compatibility graph.finite memory definiteness, testing table & testing graph. Deterministic finite automaton and non deterministic finite automaton. Transition diagrams and Language recognizers. Finite Automata: NFA with Î transitions - Significance, acceptance of languages. Conversions and Equivalence: Equivalence between NFA with and without Î transitions. NFA to DFA conversion. Minimization of FSM, Equivalence between two FSM s, Limitations of FSM. Application of finite automata, Finite Automata with output- Moore & Melay machine. Module-2: [8 L] Regular Languages : Regular sets. Regular expressions, identity rules. Arden s theorem state and prove. Constructing finite Automata for a given regular expressions, Regular string accepted by NFA/DFA. Pumping lemma of regular sets. Closure properties of regular sets (proofs not required). Grammar Formalism: Regular grammars-right linear and left linear grammars. Equivalence between regular linear grammar and FA. Inter conversion, Context free grammar. Derivation trees, sentential forms. Right most and leftmost derivation of strings. (Concept only). Module-3: [9L] Context Free Grammars, Ambiguity in context free grammars. Minimization of Context Free Grammars. Chomsky normal form and Greibach normal form. Pumping Lemma for Context Free Languages. Enumeration of properties of CFL (proofs omitted). Closure property of CFL, Ogden s lemma & its applications. Push Down Automata: Push down automata, definition. Acceptance of CFL, Acceptance by final state and acceptance by empty state and its equivalence. Equivalence of CFL and PDA, interconversion. (Proofs not required). Introduction to DCFL and DPDA. Module-4: [6L] Turing Machine : Turing Machine, definition, model. Design of TM, Computable functions. Church s hypothesis, counter machine.types of Turing machines (proofs not required). Universal Turing Machine, Halting problem. TEXT BOOK: 1. Introduction to Automata Theory Language and Computation, Hopcroft H.E. and Ullman J. D., Pearson education. 2. Theory of Computer Science, Automata Languages and computation, Mishra and Chandrashekaran, 2nd edition, PHI. 3. Formal Languages and Automata Theory, C.K.Nagpal, Oxford REFERENCE BOOK: 1. Switching & Finite Automata, ZVI Kohavi, 2nd Edn., Tata McGraw Hill 2. Introduction to Computer Theory, Daniel I.A. Cohen, John Wiley 3. Introduction to languages and the Theory of Computation, John C Martin, TMH 4. Elements of Theory of Computation, Lewis H.P. & Papadimitrou C.H. Pearson, PHI.
Course Outcomes: 1. The student will be able to define a system and recognize the behavior of a system. They will be able to minimize a system and compare different systems. 2. Student will convert Finite Automata to regular expression. 3. Students will be able to check equivalence between regular linear grammar and FA. 4. Students will be able to minimize context free grammar. 5. Student will be able to check equivalence of CFL and PDA. 6. They will be able to design Turing Machine. LESSION PLAN Sr. No. Day Reference of the Syllabus Remarks 1 Lecture 1 Fundamentals: Basic definition of sequential circuit, block diagram, mathematical representation, concept of transition tableand transition diagram 2 Lecture 2 Design of sequence detector, Introduction to finite state model 3 Lecture 3 Finite state machine: Definitions, capability & state equivalent, kth- equivalent concept 4 Lecture 4 Merger graph, Merger table, Compatibility graph 5 Lecture 5 Finite memory definiteness, testing table & testing graph. 6 Lecture 6 Deterministic finite automaton and non deterministic finite automaton. 7 Lecture 7 Transition diagrams and Language recognizers. 8 Lecture 8 Finite Automata: NFA with Î transitions - Significance, acceptance of languages. 9 Lecture 9 Conversions and Equivalence: Equivalence between NFA with and without Î transitions. NFA to DFA conversion 10 Lecture 10 Conversions and Equivalence: Equivalence between NFA with and without Î transitions. NFA to DFA conversion. 11 Lecture 11 Minimization of FSM, Equivalence between two FSM s, Limitations of FSM 12 Lecture 12 Application of finite automata, Finite Automata with output- Moore & Melay machine. 13 Lecture 13 Regular Languages: Regular sets. 14 Lecture 14 Regular expressions, identity rules. Arden s theorem state and prove 15 Lecture 15 Constructing finite Automata for a given regular expressions, Regular string accepted by NFA/DFA 16 Lecture 16 Pumping lemma of regular sets. Closure properties of regular sets 17 Lecture 17 Grammar Formalism: Regular grammars-right linear and left linear grammars.
18 Lecture 18 Equivalence between regular linear grammar and FA. 19 Lecture 19 Inter conversion, Context free grammar. 20 Lecture 20 Derivation trees, sentential forms. Right most and leftmost derivation of strings. 21 Lecture21 Context Free Grammars, Ambiguity in context free grammars. 22 Lecture 22 Minimization of Context Free Grammars. 23 Lecture 23 Chomsky normal form 24 Lecture 24 Greibach normal form 25 Lecture 25 Pumping Lemma for Context Free Languages. 26 Lecture 26 Enumeration of properties of CFL. Closure property of CFL, Ogden s lemma & its application 27 Lecture 27 Push Down Automata: Push down automata, definition. 28 Lecture 28 Acceptance of CFL, Acceptance by final state and acceptance by empty state and its equivalence. 29 Lecture 29 Equivalence of CFL and PDA, inter conversion. 30 Lecture 30 Introduction to DCFL and DPDA. 31 Lecture 31 Turing Machine : Turing Machine, definition, model 32 Lecture 32 Design of TM, Computable functions 33 Lecture 33 Church s hypothesis, counter machine 34 Lecture 34 Types of Turing machines 35 Lecture 35 Universal Turing Machine 36 Lecture 36 Halting problem ----------------------------- ------------------------------------ Signature of HOD Signature of the faculty
DURGAPUR INSTITUTE OF ADVANCED TECHNOLOGY AND MANAGEMENT DEPARTMENT OF INFORMATION TECHNOLOGY Name of the Faculty: Mr. Amit Kumar Datta Subject: Introduction to Computing Paper Code: CS 402 Semester/Branch: 2 nd Semester/ IT Lesson Plan Lecture No. Reference of the Topic(s) to be covered Syllabus 1 History of Computer, Generation of Computer, Classification of Computers, Basic Anatomy of Computer System 2 Primary & Secondary Memory, Processing Unit, Input & Output devices 3 Binary & Allied number systems
representation of signed and unsigned numbers. BCD, ASII. Binary Arithmetic 4 logic gates 5 Assembly language, high level language, compiler and assembler 6 Basic concepts of operating systems like MS DOS, MS WINDOW, UNIX, Algorithm & flow chart 7 The C character set identifiers and keywords, data type & sizes 8-10 variable names, declaration, statements, Arithmetic operators, relational and logical operators, type 11 conversion, increment and decrement operators, bit wise operators, assignment operators and expressions 12-13 precedence and order of evaluation. Input and Output: Standard input and output, formatted output -- printf, formatted input scanf 14 Statement and blocks, if - else, switch 15-16 loops - while, for do while, break and continue, go to and labels. 17-18 Basic of functions, function types, functions returning values 19-21 functions not returning values, auto, external 22 static and register variables, scope rules 23-24 recursion, function prototypes, C preprocessor, command line arguments 25-27 One dimensional arrays, pointers and functions 28 multidimensional arrays 29 Basic of structures, structures and functions 30 arrays of structures, bit fields 31 formatted and unformatted files Reference book: