Table of Contents

## Are DCFL closed under concatenation?

Since DCFL is closed under complementation and CFL is closed under union, it follows that Labc is a context-free language. However Labc is not a deterministic context free language, because DCFL is closed under complementation. It follows that DCFL is not closed under union.

**Is DCFL closed under prefix?**

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

### What is DCFL and CFL?

They are the context-free languages that can be accepted by a deterministic pushdown automaton. DCFLs are always unambiguous, meaning that they admit an unambiguous grammar. There are non-deterministic unambiguous CFLs, so DCFLs form a proper subset of unambiguous CFLs.

**What are CFLS closed under?**

CFL’s are closed under union, concatenation, and Kleene closure. Also, under reversal, homomorphisms and inverse homomorphisms. But not under intersection or difference.

#### Is every DCFL a CFL?

While remembering the fact that DCFL is a proper subset of CFL.

**What is CSL in TOC?**

Context-sensitive Language: The language that can be defined by context-sensitive grammar is called CSL. Properties of CSL are : Union, intersection and concatenation of two context-sensitive languages is context-sensitive. Complement of a context-sensitive language is context-sensitive.

## Under Which operation are deterministic context free languages closed?

Important Points:

Context free languages | Only Deterministic Context free languages |
---|---|

Not Closed under Complementation Intersection | Not Closed under Union Intersection Concatenation Kleene closure Homomorphism Reversal of language |

**What are CFLs closed under?**

### In which of the following CFL is not closed?

Explanation: CFL is closed under union, kleene and concatenation along with the properties reversal,homomorphism and inverse homomorphism but not difference and intersection. Explanation: Context free languages are not closed under difference, intersection and complement operations.

**Are Decidable languages closed under complement?**

– Decidable languages are closed under complementation. To design a machine for the complement of a language L, we can simulate the machine for L on an input. If it accepts then accept and vice versa. – Turing recognizable languages are not closed under complement.

#### Which of the following is are CFL not closed under?

Context-free language is closed under Union, Concatenation, and Kleen closure. But not closed under complementation and intersection.