[PDF] CS 301 - Lecture 07 – Closure properties of regular languages

1. For each of the following statements indicate whether it is true or

For the false ones (if any) provide a counter example. For the true ones (if any) give a proof outline. (a) Union of two non-regular languages cannot be 

Regular and Non regular Languages

positive integer n then it is defined by the regular expression: So it too is regular. EXAMPLE 8.1 The Intersection of Two Infinite Languages.

CS 341 Homework 9 Languages That Are and Are Not Regular

Two numbers p and q are a pair of twin primes iff q = p + 2 and both p and (j) If L1 and L2 are nonregular languages then L1 ? L2 is also not regular.

CS411-2015S-07 Non-Regular Languages Closure Properties of

Closure Properties of Regular Languages Is LREG closed under union? ... E(0)[i j]=1 if qi and qj are both accept states

CS 301 - Lecture 07 – Closure properties of regular languages

To show that A is not pumpable play as Player Two Does this mean the union of any two nonregular languages is regular?

Regular and Nonregular Languages

Closure Properties of Regular. Languages. ? Union. ? Concatenation. ? Kleene star which is non-prime if both factors are greater than 1:.

Properties of Regular Languages

A non-regular language can be shown that it is not regular using the pumping As an example the intersection of two regular languages is also regular.

assessment id-70

1. Union of two non-regular languages is non-regular. 2. Intersection of a non-regular language and a regular language is 

Examples from Elements of Theory of Computation

(both regular and non-regular) and elementary number theory. L are two regular languages

DECISION PROBLEMS FOR NON-REGULAR LANGUAGES This

This part of the lecture is an introduction to techniques both for devising deci- homomorphisms and intersection with regular languages.

pumping lemma - Union of two non-regular languages - Mathematics

To prove that a language L is not regular using the Myhill-Nerode theorem do the following: Find an infinite set of strings Prove that any two distinct strings in that set are distinguishable relative to L The tricky part is picking the right strings but these proofs can be very short

Chapter 10: Nonregular Languages - UC Santa Barbara

What is the Union of two non-regular languages?

the first s = a^p b^p-1. second s = a^pb^p+1 is the correct. Union of two non-regular languages may or may not be non-regular. It may be regular. Let us assume two Non-regular languages L 1 = { a i b j | i >= j } and L 2 = { a i b j | i < j } where i, j ? 0. But their union is L = L 1 ? L 2 = { a ? b ?}, which is regular.

Are L 1 l 2 always non-regular languages?

Are L 1 ? L 2, L 1 ? L 2 , L 1 L 2 and L 1 ? L 2 are always non-regular languages? We know that two regular languages always gives us a regular language under all of the above. I can't find anywhere any proof that combination of two languages, one regular and one non-regular results always in a regular or a non-regular language.

Does the Union of two always result in context-free language?

But it is always good to understand with the help of an example. L = {0*1*} which is regular language but since every regular language is context-free. So, we can say the union of two always results in context-free language.

What is the Union of L 1 and L 2?

The union of L 1 and L 2 is the set of strings a i b j where i < j or i > j. This is equivalent to saying that i ? j by trichotomy. Therefore, L 1 ? L 2 = {a i b j : i ? j}. It's worth adding that Q2 is a union of non-regular languages where the result is regular, and Q3 is a union of non-regular languages where the result is not regular.