Arden’s Theorem

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TOC: Arden’s Theorem

This lecture shows the proof of Arden’s Theorem which states that: If P and Q are two Regular Expressions over Σ and if P does not contain Є, then the equation given by R=Q+RP has a unique solution i.e. R=QP*

Music:
Axol x Alex Skrindo - You [NCS Release]

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inception movie is over rated in front of arden's theorem's proof

justanaverageguy

I used the stones to destroy the stones😂

tusharupadhyay

Correct is
R = Q + RP … (1)
R = Q + (Q+RP)P …(2) from 1
R = Q + QP + RP^2
Again keep substituting n times
R = Q + QP + QP^2 + QP^3….
R = Q( E + P + P^2 + P^3..)
R = QP*
Proved

riturajnavindgikar

Mindblowing Explain ability of Nesco academy.Thank you sir. ❤

sknasimhossen

Normally in regular algebra or, trigonometry n, when in an equal its given an equation- x=y+x+1
And if we say we put x= -y we put LHS x, and RHS x both as -y and get answer like y=1 but here in ardens theorem we, did not substitute value for LHS, R

zackcarl

Sometimes sir's Genius… It's Almost Frightening.

SumitKumar-fjsy

05:50
R = Q + QP + QP^2 + ... + Q^n + {some strings with length > n unless trivial case P empty}, for all n \in N
Then
R = Q + QP + QP^2 + ...
= Q P*

lamaspacos

Thank you very much sir
Good explanation

nagapushpa

Statement −

Let P and Q be two regular expressions.

If P does not contain null string, then R = Q + RP has a unique solution that is R = QP*

Proof −

R = Q + (Q + RP)P [After putting the value R = Q + RP]

= Q + QP + RPP

When we put the value of R recursively again and again, we get the following equation −

R = Q + QP + QP2 + QP3…..

R = Q (ε + P + P2 + P3 + …. )

R = QP* [As P* represents (ε + P + P2 + P3 + ….) ]

Hence, proved

abdulhaseeb

I can see in the comment section about the nature of people. When sir did one single mistake everyone is putting laughing emojis . I don't know why. Didn't he help us through tough times ? No we just need to bash when someone makes mistake.

saibunny

0:42 I think the following statement is a bit more accurate to the one in the video the set P* does not contain the empty word, then this solution is unique'' versus video's sentence which says: ''...has a unique solution...''

myonlynick

Thank you sir.and sir please post some problem on Arden theorem and how to convert a regular expression into finite automata.please sir .

learnwithmanu

Great sir thnk u so much its was look like very simple theorem in the way you explain it ...

nigamkumar

How to fire a fire take out the fire from fire😂😂😂

abhayrajlodhi

what was that you used the same expression which we wanted to prove ... rip to this proof

AlinaMirzaCS-

how you can say, that you prooved it ??

h.raouzi

We basically say ok, that's my question that my solution, use them both to prove they are made for each other, you can use one to prove other 😆.

zackcarl

interstellar's final scene is overrated in front of this

_jain_darsh

can we write Arden's equation directly if regular grammar is given in question

divyanshudwivedi

I don't understand how can say p doesn't contain €(epsilon)

lone_wolf

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