# Why is DCFL not closed under intersection?

## Why is DCFL not closed under intersection?

However Labc is not a deterministic context free language, because DCFL is closed under complementation. It follows that DCFL is not closed under union. But then DCFL is not closed under intersection, since otherwise by De Morgan’s laws, it would be closed under union.

Which language are not closed under intersection?

Context-free languages
Context-free languages are not closed under intersection or complement.

### Is DCFL closed under difference?

DCFL is closed under complement (If we complement the accept states of DPDA for L we get DPDA for the complement of L, but this is not true for a general PDA.)

Is DCFL closed under Homomorphism?

Note : DCFL are closed only under complementation and Inverse Homomorphism.

## Are CFLs closed under intersection?

Theorem: CFLs are not closed under intersection If L1 and L2 are CFLs, then L1 ∩ L2 may not be a CFL. 3. L1 ∩ L2 = {anbnan | n ≥ 0}, which is known not to be a CFL (pumping lemma). Theorem: CFLs are not closed under complement If L1 is a CFL, then L1 may not be a CFL.

Is regular language closed under infinite union?

Each one is regular because it only contains one string. But the infinite union is the set {0i1i | i>=0} which we know is not regular. So the infinite union cannot be closed for regular languages.

### What is closed under intersection?

elementary-set-theory. I read this definition: “A collection C of subsets of E is said to be closed under intersections if A ∩ B belongs to C whenever A and B belong to C.”

Is intersection the same as concatenation?

Concatenation is a union of two sets. intersection is a difference of two sets. Those sets may be ordered or unordered.

## Is Dcfl closed under concatenation?

As without non determinism, PDA cannot decide when to jump to the next one in case of concatenation and without epsilon moves Union is not possible. However, DCFL is a proper subset of CFL (unambiguous) and CFL is closed under union and concatenation.

Which of the following is are CFLs not closed under?

CFLs are not closed under Intersection , complement operation.

### How can we prove a language is regular?

To prove a language is regular: construct a DFA, NFA or RE that recognizes it. To prove a language is not regular: show that recognizing it requires keeping track of infinite state (hard to be completely convincing in most cases) or use the pumping lemma to get a contradiction.

Is regular language closed under?

A regular language is one which has an FA or an RE. Regular languages are closed under union, concatenation, star, and complementation.

## When is DCFL closed under complement and union with regular languages?

By he way, once we know that DCFL is closed under complement and closed under intersection with regular languages, closure under union with regular languages follows by De Morgan: L ∪ R = ( L c ∩ R c) c. Thanks for contributing an answer to Computer Science Stack Exchange!

When is the normal form of DCFL proved?

That normal form is usually proved when showing DCFL are closed under complement (and is non-trivial). By he way, once we know that DCFL is closed under complement and closed under intersection with regular languages, closure under union with regular languages follows by De Morgan: L∪R = (Lc∩Rc)c.

### When is a CF language closed under Union?

For the general term “closed under union” it is always important to state: closed for which set. A set X (having sets as elements) is closed under union if for every element A in X and for every B in X, A U B is also in X. So: Taking two languages L1, L2 from the set of all CF languages, the language L1 U L2 is ALSO CF language.

Why are context free languages closed under Union?

CFLs are closed under union which follows from a powerful result, called the substitution theorem, which, roughly speaking, says that given a context-free language L we can replace each symbol of the strings of L by an entire context-free language, and end up with a context-free languge.