Identities of Regular Expression

[@ugcnet8015]

Eminent channel and Eminent Teacher. Hats off to you Sir.

[@LALANKumar-en5rv]

00:01 The identity Phi plus R equals R represents the union of an empty set and any regular expression R, resulting in R. 00:50 Different properties of regular expressions explained. 01:36 Epsilon Closure 02:28 Concatenating the closure of two regular expressions gives the total of that SS patient as the result. 03:21 The closure of a regular expression when performed again gives the closure of the same expression. 04:10 The closure of R plus excluding the epsilon symbol gives the closure of R 05:01 Concatenation and closure properties of regular expressions 05:57 Important identities of regular expressions

[@flakeyguy000]

Thanks for this!

[@ZinxM8]

is there a difference between closure properties and identities?

[@aryanv1406]

Let R be {a,b} and R* would be {epsilon, a, b, aa , bb , ab , ba ...}, now let's take one symbol from R and one Symbol from R* and we will never be able to have only epsilon. There will be always epsilon and a or epsilon and b. As we know (epslion and a = a). Thats why it is R+.

[@vasireddyganesh]

thank you so much

[@Yuki-wn9kj]

thats correct

[@MM-vc5ic]

thank you

[@Lian-np5xm]

Thank u so much

[@leanroorael]

But what if R includes epsilon? Since epsilon is also a regular expression. Then epsilon from R and epsilon from R* would result in epsilon. Why is it that R*R*=R* but RR*=R+?

[@unknownlifeform4077]

Is RR* = R+ ?

[@ayankumarpahari83]

Zhechun zhou yes

[@ProfessionalTycoons]

This is such good comment.

[@ChristianBurnsShafer]

You can figure this out if you look at identity (9). Observe, Epsilon + RR* = R*. If we subtract Epsilon from both sides we obtain, RR* = R+

[@javaexpertsa8947]

Let R be {a,b} and R* would be {epsilon, a, b, aa , bb , ab , ba ...}, now let's take one symbol from R and one Symbol from R* and we will never be able to have only epsilon. There will be always epsilon and a or epsilon and b. As we know (epslion and a = a). Thats why it is R+.

[@kushwanthkapa2041]

yes

[@sirisha.vamisetti]

Thanks for giving the video but I need example also

[@karanvenkateshupamanyuise-9407]

How is RR* = R+ as said in example 9?

[@aakashp]

According to definition of + there should be at least 1 R. There fore first R for atleast one R , And after that any number of R can come (R*)

[@aryankhanna8295]

R*={€ , R , RR , RRR ,..........} R.R*=R.{€ , R , RR , RRR ,..........} ={R.€ , R.R , R.RR , R.RRR ,.....} ={R , RR , RRR , RRRR ,.........} =R+

[@pozlong8614]

@@shahrak6306 THANK YOU.

[@mohammadzaid9189]

With that logic, ^ also get included in that set, and if empty symbol included then how it is referred to as R+ not R*. ?

[@rajatmishra9676]

r+ = r.r* = r*r, as r* = ∈ + r + rr+ rrr …. and r.r* = r+ rr + rrr …… and rE=Er=r

[@sandipdas5684]

Thank you so much sir 🙏

[@talhamalik3tm]

Point 9: R* already includes the epsilon symbol within itself. Hence the concatenation of R* with R yields R* regardless if you add epsilon to it or not.

[@krishnakrmahto97]

second identity should be: (phi)R = R(phi) = phi

[@aydict]

you sure? I was so confused because of that

[@backslash8874]

@@aydict Yes, it should be (Phi)R=R(Phi)=Phi...

[@Farahat1234]

@@backslash8874 to vhi to h!

[@athukutti]

It may can be also like that , bcoz when R is multiply with phi the result will be phi , the phi is like zero then when two zeros are added then result will be phi

[@venkatarohitpotnuru38]

@@backslash8874 yaa

[@BigyanChap]

I was expecting that you would explain with examples.

[@ruhanmuzaffar2012]

me too .....or else why would someone come here

[@sanchitbhalla1176]

Watch knowledge gate Sanchit sir is best

[@Shivam-wg6eq]

@@sanchitbhalla1176 tum bhi binod nikle 🙄🤔

[@arjunmalli50]

I have one doubt sir. In previous video you told instead of or (a, b) we used in RE + (a+b) in this video we used + for union?

[@mnaresh3382]

technically they are the same, we can represent Union of a and b as (a, b) or a+b, both means the same, for concatenation we can write either a . b or (ab)

[@arjunmalli50]

@@mnaresh3382 thank you

[@arjunmalli50]

​@@mnaresh3382thank you sir...

[@AL-go2mv]

Can you tell me what all the symbols mean?? *, epsilon, +, concat

[@varunkamani2528]

Aaron Loomis In video above this all this symbol are described. € means null * Means occurance of element 0 or more time which includes ^ too + Is same as * but it doesn't include ^

[@nabhavlogs371]

But in the previous video ^ was shown as null symbol

[@Farahat1234]

@@varunkamani2528 now where are you after 2years?

[@amanlrwtfsm1323]

@@Farahat1234 where u are after 1 year ??

[@Farahat1234]

@@amanlrwtfsm1323 😅😅😅at home but why did you asked😄

[@gouravvishak6046]

what will be R + R* ? if there any identity?

[@raghavmanish24]

R*

[@ahmednabil5119]

Thanks alot for you clear explanation.

[@kainaatmakhani6550]

good job

[@phralma1000BC]

what is the difference between € and phi?

[@simran4930]

epsilon means that a set contains a value called null value but phi means that a set doesn't contain any value.

[@ProfessionalTycoons]

I was asking the same thing

[@vasudevp1703]

If you have the idea of Finite State Machines or any mathematical model machine then PHI means NO INPUT STRING SET, ie. MACHINE IS NOT EVEN IN THE START STATE. Whereas the € means Machine has a input string set, but no elements in it. MACHINE IS NOW IN START STATE. Major difference is where the control lies whether in START STATE or machine didn't even need to start.

[@abhijeetsharma5715]

​@@simran4930​ i think epsilon is a word and not a set.( math.stackexchange.com/questions/1116218/difference-between-phi-anf-epsilon-in-regular-language )

[@akashkaaa7193]

What is the result of fi . {a} = ? fi concatenation of {a} = ?

[@rajatmishra9676]

fi

[@rahulbhoir3498]

you have changed the 2nd equation in another video(regular languages and finite automata problem 2) so which is correct

[@HosRo4161]

Agree: The second identity should read: 0R = R0 = 0

[@surbhiyadav4461]

what is the difference between fii ,null and epsilon??

[@vishaliguru3630]

@surbhi yadav Null and epsilon means the same....it's a string of length zero.phi is a null set symbol.

[@kamalpatel5262]

∅ is the empty set. ϵ is the empty string.

[@prohightension2000]

@@kamalpatel5262 Thanks you!! I was wondering about this too

[@u_ziben]

I apologize but can you give me a link to the track you play at the end of the video? It sounds really cool

[@dhairyasharma6243]

still finding the link huh?

[@vybhavchaturvedi8348]

Description man, its not that tough

[@youssef_uchiha]

Axol x Alex Skrindo - You [NCS Release]

[@scottzeta3067]

I don't understand the second one.

[@mohamadtabbakh9887]

I wish you demonstrated the laws using an aribitrary set of symbols. That would have made this into 100/100 instead of a 80/100

[@doudou7074]

abstract. I can't understand. I don't know why. But I find the comments are very useful. Thanks.

[@vasireddyganesh]

Yeah

[@vatsalgp]

The second identity is wrong. It should be either : phiR + Rphi = R or phiR = Rphi = R

[@amanagarwal9700]

(a*ab+ba)*a*=(a+ab+ba)* how to prove this?

[@LetTheWritersWrite]

What exactly does epsilon mean?

[@abhinav9058]

LetTheWritersWrite its a constant of physics

[@abhinav9058]

Also it means null here

[@yassinerh7709]

empty string

[@jeneyify]

It's like space in a sentence, nothing.

[@yassinerh7709]

Its not even a space :) actually its something like char c=''; in this case c equal to epsilon

[@MagaTecnologica]

I missed some examples... It was just too abstract

[@ozanercan2052]

where is the proof of this identities ?

[@surbhiyadav4461]

there is no need to prove these identities

[@Karansingh-gh4oy]

thankyou sir

[@asanitian6218]

Epsilon+regular expression=??

[@jethanpaul818]

it is regular expression because epsilon represent an empty string and not set as phi, if it was phi it would have meant an empty set and the outcome could be empty set

[@blahblahbla710]

Why is 10 true

[@oshoconner4003]

Sir operating system memory management dal do...please🇮🇳🇮🇳

[@marcaironcantal515]

🤔

[@marxman1010]

Why ∅ star becomes epsilon? ∅ means nothing inside and not contain empty string.

[@therealkon_]

I guess with an empty set you can't create any strings. That is why it is the empty string

[@neiljohn2637]

47

[@mohssinmanj3874]

Its help us a looot

[@GagandeepSingh-b9k]

2nd identity is wrong

[@LadderVictims]

it is indeed correct

[@arpitsaxena5972]

Sirf padh kr ni sunana tha chacha....

[@vimalsheoran8040]

I believe it should be called intersection and not concatenation.

[@6066Y]

Brother where is explaination Ur just reading 😂

[@dhairyasharma6243]

are sir, kya hi bol gaye ;_;

[@kasozivincent107]

what u are doing is what any book will do. i wish u could really explain

[@solarchat9413]

You are just reading what is written. That's not teaching

[@probot_x_falcon9054]

i think the second identity is wrong because i checked it on geeks for geeks theres it is ∅.r= r.∅ = ∅ instead of +

[@yitzchakmeltz1309]

Why is ∅ ∗ = ε ? If you repeat the empty set {} many times, isn't it still the empty set {}?

[@mypowerlevelisover9000]

Repeat empty set 0 times you get ε

[@SaatvikPandey-t2y]

what is the difference between epsilon and phi?