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CSE

Formal Languages and

Automation Theory

Lecture 0- 3

Course Details

• LTP – 3 0 0 [Three lectures/week]
• Text Book
  • Theory of Computer Science: Automata, Languages and Computation
    • Author: KLP Mishra and N. Chandrasekaran

Detail of Academic Tasks

• AT1: Test1 Lecture #11 (Before MTE)
• AT2: Test2 Lecture #19 (Before MTE)
• AT3: Test3 Lecture #33 (After MTE)

The course contents

• UNIT 1 - Finite automata
• UNIT 2 - Regular expressions and regular sets
• UNIT 3 - Formal languages and regular grammars
• UNIT 4 - Context- free languages and simplification of context-free grammar
• UNIT 5 - Pushdown automata and parsing
• UNIT 6 - Turing machines and complexity

COMPUTABILITY THEORY

What kind of problems it can compute

• COMPUTABLE Problems(Algorithms)
• UNCOMPUTABLE Problems(Procedure)

AUTOMATA THEORY +FORMAL LANGUAGES

• How problems can be solved?
• ABSTRACT MODELS<--->Formal languages →Turing Machine/UNRESTICTED GRAMMAR →Linear Bound Automata/CONTEXT SENSITIVE GRAMMAR →Pushdown Automata (PDA)/CONTEXT FREE GRAMMAR →Finite Automata(FA)/REGULAR GRAMMAR
• Hierarchy of grammar is given by CHOMSKY.

Theory of Computation

• Theory of Computation is a branch that deals with how efficiently problems can be solved in a model of computation using algorithms.
• Problems? 1)Difficult Problems that can’t be solved simply by computers or calculators 2)To solve difficult problems with an easiest way.
• Theory---->Implementation

• Study of Abstract machines
• ABSTRACT MACHINES—aka ---ABSTRACT COMPUTER Theoretical model of a computer hardware or software system used in automata theory. Automata is a Greek word which means “Self Acting” Machine input Rules Output 1 Output 2

Pillars of TOC

• Language(Alphabet+Rules)
• Automata
• Grammar

LANGUAGE

• Strings(w)or Sentence→[Def1]Combination of symbols from an alphabet or sigma. [Def2]Collection of alphabets.
• Alphabet→Finite,non-empty set of symbols
• Symbols→digits,letters,special symbols,operators.
• LANGUAGE→Def1[Collection or set of Strings]. Def2[Combination of Alphabet and rules]
• Word vs String?

Power of Sigma

• Kleene closure
• Kleene Plus or Positive Closure

Types of Language(Finite and Infinite)

• Finite Language L1=Create all the strings of length possible upto 3 with alphabet=(a,b). {e,a,b,ab,ba,ab,bb,aaa,aab,aba,abb,baa,bab,bba,bbb}
• Infinite Language L2=Create all the strings of all the length starting with ‘a’ and alphabet=(a,b). {a,aa,aaa,aaaa,……………………..ab,abb,abbb,…………..}

Grammar

• Defined by Quardruple. G={V,T,P,S} Where V=Variable T=Terminal P=Production Rule S=Starting point Eg:- This is Book. [correct] Book is this.[correct] Is Book this.[Incorrect because not well formed or grammatically fine]

Finite Automata

• Automata-To represent a language whether Finite or Infinite. It tells us that whether the string will be accepted by the language or not.
• Finite Automata-It is a standard way of representation of a language in a diagramatical or graphical form.
• Why named Finite Automata?

• Automata-Self Acting

• Finite-Finite no of states/letters/transitions