Is the complement of a Turing recognizable language?

– Turing recognizable languages are not closed under complement. If L is decidable then it is Turing recognizable. Moreover since decidable languages are closed under complement, L is also Turing recognizable. Suppose L is Turing recognizable via a TM M and L is Turing recognizable via a TM M/.

Is it possible for a language and its complement to both be unrecognizable?

If some other language S and its complement ¯S are both recognizable, then S and ¯S are decidable. If ¯S is unrecognizable, then then S is undecidable but still recognizable.

Can a language reduce to its complement?

(j) Every language reduces to its complement. False.

Can a language be both recognizable and Corecognizable?

You might want to add the significance of a language being both Turing-recognizable and Co-Turing-Recognizable since this implies decidability. It’s possible that a language is co-Turing recognizable and also recursively enumerable – that means that it’s decidable!

Is the complement of A_TM recognizable?

As Atm is recognizable, its complement cannot be recognizable, due to being so Atm would be decidable.

How do you show a language is Turing recognizable?

To prove that a given language is Turing-recognizable: Construct an algorithm that accepts exactly those strings that are in the language. It must either reject or loop on any string not in the language.

What makes a language Turing recognizable?

A language which is Turing Recognizable if there is a Machine that will halt and accept only the strings in that language and not in that language, then that TM either rejects, or does not halt at all. A Language is called Turing Recognizable if some Turing Machine recognizes it.

What is co Turing recognizable?

Intuitively, if a language is co-Turing-recognizable, it means that there is a computer program that, given a string not in the language, will eventually confirm that the string is not in the language. It might loop infinitely if the string is indeed within the language, though.

What is the complement of L?

Defination: The complement of a language is defined in terms of set difference from Σ* (sigma star). that is L’ = Σ* – L. And the complement language (L’) of L has all strings from Σ* (sigma star) except the strings in L. Σ* is all possible strings over the alphabet Σ.