Table of Contents

## What are recursively enumerable languages closed under?

Recursively enumerable languages are also closed under intersection, concatenation, and Kleene star. Suppose that M1 and M2 accept the recursively enumerable languages L1 and L2. We need to show that if w is in our new language, it will be accepted.

## Is recursively enumerable closed under complement?

Recursive enumerable languages are not closed under complementation.It signifies that Y′ may/may not be recursive enumerable. But the answer will be Y′ is not recursive Enumerable. Why? If a language and its complement are both recursively enumerable, then both are recursive.

**Is recursively enumerable language closed under intersection?**

Explanation: Recursive Enumerable Language are closed under Union, Intersection, Concatenation and Kleene Closure (but not Complementation).

### Are recursive languages closed under union?

a) Union Recursive and Recursively Enumerable languages are closes under union. Let’s built a Turing Machine M which is going to simulate M1 and M2 on the input it gets. M will accept if either accept.

### What are the properties of recursively enumerable languages?

A recursively enumerable language is a formal language for which there exists a Turing machine (or other computable function) that will halt and accept when presented with any string in the language as input but may either halt and reject or loop forever when presented with a string not in the language.

**What is a recursively enumerable set in computer science?**

A recursively enumerable set is a set where there is a partially computable algorithm for deciding if an element is contained in the set or not (it can be computed but it isn’t necessarily going to terminate)

#### Is the class of recursive languages closed under complement?

The class of recursive languages is closed under union, complementation, intersection, concatenation, and Kleene star.

#### Is Re closed under complementation?

R.E. languages are not closed under complementation. Proof. Atm is r.e. but Atm is not. A TM to recognize L1L2: On input x, do in parallel, for each of the |x| + 1 ways to divide x as yz: run M1 on y and M2 on z, and accept if both accept.

**Which language is closed under infinite union?**

The class of regular languages is closed under infinite union.

## What is recursively enumerable language explain?

## Are recursively enumerable languages countable?

Recursively enumerable languages are countable because TMs are countable. Therefore, recursively enumerable languages ⊂ all languages.

**Which is recursively enumerable?**

### How do you know if a set is recursively enumerable?

If A ≤ m B and B is recursively enumerable then A is recursively enumerable. If A ≤ m B and B is not recursively enumerable then A is not recursively enumerable.

### Are recursively enumerable sets closed under complementation?

If the recursively enumerable sets were closed under complementation, then this asymmetry would disappear via complement-union-complement – and in fact, for the recursive sets (which are closed under complementation), recursive intersection and recursive union have the same closure properties (the recursive sets are closed under neither; exercise).

**Are recursively enumerable languages closed under intersection or set difference?**

I read that recursively enumerable languages are closed under intersection but not under set difference. We know that, $A \\cap B = A – ( A – B)$. Now for LHS (left-hand side) to be closed under Stack Exchange Network

#### Is L’recursively enumerable if L’is also recursive?

If L is recursively enumerable, then L’ is recursively enumerable if and only if L is also recursive. Let L be a language and L’ be its complement. Which one of the following is NOT a viable possibility? Neither L nor L’ is recursively enumerable (r.e.). Both L and L’ are r.e. but not recursive. A) It is possible if L itself is NOT RE.