This document discusses the pumping lemma and its applications. It introduces the pumping lemma for regular languages and context-free languages. For regular languages, any string of length n or greater can be broken into five parts where the second and fourth parts can be repeated any number of times to create a new string that is still in the language. For context-free languages, any string of length n or greater can be broken into two parts that can be repeated to create a new string in the language. Examples are provided to demonstrate how the pumping lemma can be used to prove that a language is not regular or context-free. The pumping lemma has applications in areas like proving invalid moves in games and determining operating temperatures in power stations.

1. AUTOMATA
PUMPING-LEMMA

2. Name- Anshika Das
Roll no- 14400121029
Subject code-PEC-IT501A
Subject-Theory of Computation
Sem-5th
College-Neotia Institute of Technology
Management and Science

3. agenda
• Introduction
• Types
• Examples
• Advantages
• Applications

4. INTRODUCTION
• Pumping Lemma IsUsedTo ProveThat
a Language Is Not Regular .
• ItCan Not BeUse to ProveThat a
Language Is Regular.

5. TYPES OF PUMPING LEMMA
Context-free
languages
Regular
languages

6. For regular languages
• Pumping Lemma IsUsedTo ProveThat a Language
Is Not Regular
• ItCan Not BeUse to ProveThat a Language Is Regular
• n simple terms, this means that if a string v is ‘pumped’,
i.e., if v is inserted any number of times, the resultant
string still remains in L.
• Pumping Lemma is used as a proof for irregularity of a
language.Thus, if a language is regular, it always
satisfies pumping lemma. If there exists at least one
string made from pumping which is not in L, then L is
surely not regular.
The opposite of this may not always be true.That is, if
Pumping Lemma holds, it does not mean that the
language is regular

7. P.L For Regular Language Rules

8. Example

9. Pumping Lemma of Context Free Language
• Pumping Lemma isUsed to Prove that a
Language Is NotContext Free.
• Pumping Lemma forCFL states that for any
Context Free Language L, it is possible to
find two substrings that can be ‘pumped’
any number of times and still be in the
same language. For any language L, we
break its strings into five parts and pump
second and fourth substring.
Pumping Lemma, here also, is used as a
tool to prove that a language is notCFL.
Because, if any one string does not satisfy
its conditions, then the language is notCFL.

10. P.L For CFG Rules
• Let L(G) IsCFGThen FollowingCondition Must BeSatisfied.
• Steps
n is natural Number AndZ=uvwxy For
1. EveryZ ∈ L(G) With |Z|>=n
String Divide Into Five Parts.
2. |vx|>=1
3. |uwx|<=n
4. u v^k w x^k y ∈ L forAll K>=0

11. Example
• Prove L={a^i,b^i,c^I / i>=1} is NotCFG.
n=10
1. Assume L Is CFG & n is Natural Number
2. L={abc,aabbcc,aaabbbccc,aaaabbbbcccc….}
3. Z=aaaabbbbcccc |z|>=n
4. v & x Contain Some Symbols
5. u=aa, v=aa, w=bbbb, x=c, y=ccc
6. u v^i w x^i y ∈ L K>=0
7. K=1 aaaabbbbcccc ∈L
8. K=2 aaaaaabbbbccccc ! ∈ L

12. ADVANTAGES OF PUMPING-LEMMA
• Pumping lemma for regular languages, the fact that all
sufficiently long strings in such a language have a substring
that can be repeated arbitrarily many times, usually used to
prove that certain languages are not regular.
• Pumping lemma for context-free languages, the fact that all
sufficiently long strings in such a language have a pair of
substrings that can be repeated arbitrarily many times,
usually used to prove that certain languages are not context-
free
• Pumping lemma for indexed languages

13. Applications of Pumping Lemma
• Pumping lemma is a negative test. It can be used in
applications like Showing an invalid move in game of chess.As
the move may not obey rules of game.

14. Applications of Pumping Lemma
• pumping lemma can be applied to prove
that the inputted move is invalid.
Moreover, some Power stations also use
this lemma for determining the cut off
temperatures to be kept in furnaces.
• For an example, say pumping lemma can
answer to why the temperature shouldn’t
go beyond 250 Degrees, etc.Thus, in a
nutshell, pumping lemma has variety of
applications in practical engineering.

15. REFRENCES
https://en.wikipedia.org/wiki/Pumping_lemma
https://www.geeksforgeeks.org/theory-of-computation-pumping-lemma/
https://www.sanfoundry.com/automata-theory-pumping-lemma-regular-languages