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Materials
Introduction
Basic knowledge of string
Power of Alphabet ( ∑ )
Languages
Language Definition and Concept
Interesting Question from Language
Some important points of languages
Grammars
Definition of Grammars
Identify Language from Grammar
Example1: S→aSb|λ
Example2: S→aSb|ab
Example 3: A→aSb|λ
Example 4: S→aS|λ
Example 5: S→aS|bS|λ
Few Important Grammars must remember
Example 6
Example 7
Types of Grammar
Power of Grammars
Grammar Identification
Concept of Grammar Identification
Example 1
Example 2
Example 3
Example 4
Example 5
Regular Grammar or type 3 grammar
Definition of Regular Grammar
Construction of Regular Grammar from Finite Automata
Automata
Introduction of Automata
Deterministic Finite Acceptor (DFA)
Definition of DFA
Example of DFA
Non Deterministic Finite Acceptor (NFA)
Definition of NFA
Example of NFA
Every DFA is NFA
How to Design DFA / NFA Machine
Design a DFA for Language: “Starting with ‘a’ "
Design a DFA for Language: “Ending with ‘a’ "
Design a DFA for Language: “Start with a and end with b”
Design a DFA for Language: “Not start with ‘a’ or not end with ‘b’ “
Design a DFA for L = “Start with ‘a’ and end with ‘a’”
Design a DFA for L = “Start with ‘001’ ”
Design a DFA for L = “Ending with ‘001’ ”.
Design a DFA for L = “At least one ‘a’”
Design a DFA for L = “At most one ‘a’ ”
Design a DFA for L = “At least two ‘a’ ”
Design a DFA for L = “Exactly one ‘a’ ”
Design a DFA for L = “At most two ‘a’ ”
Design a Machine for L = “Containing substring ‘ab’”.
Design a Machine for L = “Not containing substring ‘001’ ”
Difference between DFA and NFA: Minimum number of states
Design of DFA/NFA machine
Design a machine of L = Containing even a where ∑ = {a, b}
Design a machine of L = Containing odd b where ∑ = {a, b}
Machine with Unary Alphabet
Design a machine of L = Even number of a’s AND odd number of b’s
Design a machine of L = Even number of a’s OR odd number of b’s
Some exercise problems with same pattern
Q. UGCNET-July-2018-II-32
(Number of a) mod 2 = 0 and (Number of b) mod 3 =0
(Number of a) mod 2 =0 and (Number of b) mod 4 =0
Design a machine of L= (Number of a) mod 4 <= 2
Design a machine of L = { ω | |ω|=3}, ∑ = {a, b}
Solve the related Question
Design a machine L= {Every substrings of 001}
Design a machine of L = a* b* where ∑ = {a, b}
Set of all string no consecutive 1’s where ∑ = {0, 1}
Design a machine of L = Exactly two a’s where ∑ = {a,b}
Design a machine of L = At most two a’s where ∑ = {a, b}
Design a machine of L = Exactly two a’s and two b’s ∑ = {a, b}
At least two a’s and at least two b’s ∑ = {a, b}
Design a machine of L = (111)*+ (11111)* , ∑ = {1}
Design a machine of L = (111+ 11111)* , ∑ = {1}
NFA to DFA Conversion
Minimization of DFA
Null removal or λ move removed
Some more DFA machine design examples
Application of DFA and NFA
How to convert DFA/NFA to Higher Machine
Regular Language and Expressions
Definition Regular Language and Expression
Some rules for Regular Expression
Identities for Regular Expression
Closer property of Regular Language
Q. UGC NET 2016 (July)
Regular Language not closed under
Precedence order
Some important points
Find Regular Expression from language
DFA/NFA to Regular Expression
DFA/NFA to Regular Expression Calculation
Write a Regular Expression: Example1
Write Regular Expression: Example2
Write Regular Expression: Example3
Example1: find Regular Expression
Example2: find regular expression
Find Regular Expression of the given machine
Example3: Find Regular Expression
Example4: Find regular expression
Example5: Find regular expression
Example6: Find Regular Expression
Here we calculate Regular Expression
Q. Select the correct Regular Expression
All form of (a+b)*
All form of (a+b)*
Q UGC NET 2016
Simplification Regular Expressions
Arden’s Theorem
Arden’s Theorem and Procedure
Find Regular Expression by Arden’s Theorem
Important question from Arden's Theorem
Regular Expressions to Finite Automata
Procedure of Regular Expressions to Finite Automata
Regular Expression to Finite Automata: Example
Finite State Machine (Transducer)
Definition of Mealy and Moore
Example 1: Machine for Same Input
Example 2: Machine for 1’s complement
Example 3: Machine for 2’s complement
Example 4: Machine for change Sign Bit
Example 5: Machine for Increment by one
Example 6: Machine for Full adder
Example 7: Machine for Mod 3
How to find minimum no. of state in mod N
Mealy machine to Moore machine conversion
Moore machine to Mealy machine conversion
Identification of Language
Power of Language and Machine
How to identify language
Example 1: Identification of Language
Example 2: Identification of Language
Example 3: Identification of Language
Example 4: Identification of Language
Language Identification: Important points
Language Identify: Examples
Language Identify: Examples
Some Exercise and Solve
Some Exercise and Solve
Some Examples
Some More Examples
Important Exercise and Solutions
Special Cases: Examples
Special Cases: Examples
Special Cases: Examples
Special Cases: Examples
Special Cases: Examples
Special Cases: Examples
Special Cases: Examples
Special Cases of CSL: Example
Important Examples: Identification of language
Example CSL: Identification of language
Important Examples: Identification of language
Important Examples: Identification of language
Important Examples: Identification of language
Important Examples: Identification of language
Important Examples: Identification of language
Important Examples: Identification of language
Exercise: Identification of language
Exercise: Identification of language
Pumping Lemma
Introduction to Pumping Lemma
Pumping Lemma Theorem for Regular Language
Q .UGC-NET 2017
Example: L= a^n b^n
Example: L={a^i^2, i≥1}
Example: L={a^p, p is prime}
Example: L={a^p, p is not prime}
Example: L={ωω^R, ωϵ∑*}
Example: L= Balance parenthesis
Example: L={ωω, ωϵ∑*}
Example: L={0^n 1^n, n≥0}
Example: L={a^n ; n is perfect square}
Example: L={ω|n_a (ω) = n_b (ω)}, where ∑={a, b}, ω ϵ∑*}
Exercise
Shortcut Prove: One Language is Not Regular
Pumping Lemma Theorem for Context Free Language
Example: L={a^p ; p is prime}
Example: L={a^i^2, i≥1}
Example: L={ωω, ωϵ∑*}
Exercise
Ogden’s Lemma for CFL
Myhill-Nerode Theorem
Grammar Part- II
Examples: Grammar Construction from Language
Examples: Grammar Construction from Language
Reverse of Grammar
Reverse of Grammar and Machine
Example: Reverse of language
Context Free Grammar (CFG)
Introduction: Context Free Grammar
Simplification of Context Free Grammar
Type of simplification process
Procedure to remove Null Production
Removal of Unit Production
CFL and some examples
Constructing CFG from CFL
Constructing CFL from CFG
Different forms of Context Free Grammar
Introduction and Chomsky Normal Form
How to convert CFG to CNF
Greibach Normal Form
Simple Grammar
Linear Grammar
Backus Naur Form (BNF)
Partial Derivation Tree
Membership Algorithm and Parsing
Different Grammar example of CFG
Push Down Automata (PDA)
Introduction: Push Down Automata
DPDA and NPDA
How to design DPDA and NPDA
PDA Design Method
Design PDA of L = a^n b^n
Design PDA of L = a^m b^n, m<n
Design PDA of L = a^m b^n, m>n
Design PDA of L = a^m b^n, m ≤ n
Design PDA of L = a^m b^n, m ≥ n
Design PDA of L = a^m b^n, m ≠ n
Design PDA of L = a^n b^2n
Design PDA of L = a^2n b^n
Design PDA of L = n_a (ω) = n_b (ω)
Design PDA of L = ωω^R
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Subject Mock
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Previous Year
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Reference Book
Peter Linz
Identities for RE
Regular Expression
holds associative property
but
not holds communicative property
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