closure properties of non regular languages

Are languages regular or nonregular?
To review what we now know: There are languages that are regular, and there are languages that are nonregular. Regular languages can be represented in any of several interchangeable ways. Some nonregular languages can be proved such using tools like the Pumping Lemma, and closure properties. These facts should lead us to ask some broader questions.
Do closure properties only apply when both languages are regular?
My understanding is that the closure properties only apply when both languages are regular. So, I'm not sure what such a proof would look like and I'm looking for an outline of what the proof would look like. The class of regular languages is closed under intersection.
Why are non regular languages closed under reverse?
The question to the description is different and more easy to answer. Non regular languages are closed under reverse, because L = ( L R) R. Same is true for complement. Non regular languages are not closed under most other basic operations though. Consider, for example, that L ∪ L ¯ = Σ ⋆.
How do you prove a non-regular language is closed under concatenation?
You can't prove it because it isn't true: the class of non-regular languages isn't closed under concatenation. Let X ⊆ N be any undecidable set containing 1 and every even number. For example, take your favourite undecidable set S and let X = { 0, 2, 4, … } ∪ { 1 } ∪ { 2 i + 1 ∣ i ∈ S }.

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PDF	Lecture 9: Proving non-regularity 17 Feb 2009 From these seed languages we can show that many similar languages are also not regular

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PDF	Talen en Automaten 1 Non-regular languages via closure properties on Fri 30th Nov 2018. 1 Non-regular languages via closure properties. Show that L = 1wv ∈ 1a

PDF	Non-regular Languages or a (non-)deterministic automaton (with λ-steps). •. To show closure properties of the class of regular languages we can use regular expressions

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PDF	Regular and Nonregular Languages is finite. 5. Exhibit a regular grammar for L. 6. Exploit the closure theorems. Page 5. Closure Properties of Regular. Languages. ○ Union. ○ Concatenation.

PDF	Non-regular languages Closure properties. Languages are closed under: Union Concatenation

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PDF	CS411-2015S-07 Non-Regular Languages Closure Properties of 07-10: Using the Pumping Lemma You have an adversary who thinks L is regular You need to prove that your adversary is wrong you Language L is not regular! adv

PDF	Proving a Language is Not Regular A second method (which also doesn't always work) is by using closure properties of regular languages and relying on the fact that we already know that

PDF	Languages That Are and Are Not Regular - UT Computer Science Once we have some languages that we can prove are not regular such as anbn we can use the closure properties of regular languages to show that other languages

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PDF	Regular and Nonregular Languages Closure Properties of Regular Languages ? Union ? Concatenation ? Kleene star ? Complement ? Intersection ? Difference ? Reverse

PDF	1 Closure Properties i e the universe of regular languages is closed under these operations Then M = (Q? ? q0Q \ F) (i e switch accept and non-accept states)

PDF	Lecture 9: Proving non-regularity 17 fév 2009 · From these seed languages we can show that many similar languages are also not regular using closure properties 1 State and regularity

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PDF	Closure Properties of Regular Languages - Stanford InfoLab Closure Properties of Regular Languages Union Intersection Difference Concatenation Kleene Closure Reversal Homomorphism Inverse Homomorphism

PDF	Regular and Non regular Languages nonempty alphabet So there are many more nonregular languages than there are reg- ular ones 8 3 Some Important Closure Properties of Regular Languages

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Languages That Are and Are Not Regular - UT Computer Science

Using Closure Properties Once we have some languages that we can prove are not regular, such as anbn, we can use the closure properties of regular languages to show that other languages are also not regular L = {w : w contains an equal number of a's and b's } a*b* is regular

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PDF	Lecture 9: Proving non-regularity 17 fév 2009 · In this lecture, we will see how to prove that a language is not regular many similar languages are also not regular, using closure properties

PDF	Closure Properties of Regular Languages - CS 373: Theory of guaranteed to preserve interesting properties of the language Agha- Viswanathan CS373 Regular Languages are closed under an operation op on languages if L1,L2, Applying a homomorphism can “simplify” a non-regular language