Theory of Automata and Formal Languages Handwritten Notes


At the end of course , the student will be able to understand

CO 1 Analyse and design finite automata, pushdown automata, Turing machines, formal languages, and
CO 2 Analyse and design, Turing machines, formal languages, and grammars
CO 3 Demonstrate the understanding of key notions, such as algorithm, computability, decidability, and
complexity through problem solving
CO 4 Prove the basic results of the Theory of Computation.
CO 5 State and explain the relevance of the Church-Turing thesis.



Unit-I  Basic Concepts and Automata Theory: Introduction to Theory of Computation- Automata,
Computability and Complexity, Alphabet, Symbol, String, Formal Languages, Deterministic Finite
Automaton (DFA)- Definition, Representation, Acceptability of a String and Language, Non
Deterministic Finite Automaton (NFA), Equivalence of DFA and NFA, NFA with ε-Transition,
Equivalence of NFA’s with and without ε-Transition, Finite Automata with output- Moore
Machine, Mealy Machine, Equivalence of Moore and Mealy Machine, Minimization of Finite
Automata, Myhill-Nerode Theorem, Simulation of DFA and NFA

Unit-II  Regular Expressions and Languages: Regular Expressions, Transition Graph, Kleen’s Theorem,
Finite Automata and Regular Expression- Arden’s theorem, Algebraic Method Using Arden’s
Theorem, Regular and Non-Regular Languages- Closure properties of Regular Languages,
Pigeonhole Principle, Pumping Lemma, Application of Pumping Lemma, Decidability- Decision
properties, Finite Automata and Regular Languages, Regular Languages and Computers,
Simulation of Transition Graph and Regular language.

Unit-III  Regular and Non-Regular Grammars: Context Free Grammar(CFG)-Definition, Derivations,
Languages, Derivation Trees and Ambiguity, Regular Grammars-Right Linear and Left Linear
grammars, Conversion of FA into CFG and Regular grammar into FA, Simplification of CFG,
Normal Forms- Chomsky Normal Form(CNF), Greibach Normal Form (GNF), Chomsky
Hierarchy, Programming problems based on the properties of CFGs.

Unit-IV Push Down Automata and Properties of Context Free Languages: Nondeterministic Pushdown
Automata (NPDA)- Definition, Moves, A Language Accepted by NPDA, Deterministic Pushdown
Automata(DPDA) and Deterministic Context free Languages(DCFL), Pushdown Automata for
Context Free Languages, Context Free grammars for Pushdown Automata, Two stack Pushdown
Automata, Pumping Lemma for CFL, Closure properties of CFL, Decision Problems of CFL,
Programming problems based on the properties of CFLs.

Unit-V Turing Machines and Recursive Function Theory : Basic Turing Machine Model,
Representation of Turing Machines, Language Acceptability of Turing Machines, Techniques for
Turing Machine Construction, Modifications of Turing Machine, Turing Machine as Computer of
Integer Functions, Universal Turing machine, Linear Bounded Automata, Church’s Thesis,
Recursive and Recursively Enumerable language, Halting Problem, Post’s Correspondance
Problem, Introduction to Recursive Function Theory.


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