What does it mean when we say that language A is co-Turing-recognizable?

What does it mean when we say that language A 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 language recognized by this Turing Machine?

Explanation: The language accepted by Turing machines are called recursively ennumerable (RE), and the subset of RE languages that are accepted by a turing machine that always halts are called recursive.

Can a language be co recognizable but not recognizable?

If M2 accepted then M rejects.” Notice that M terminates on any input x as either x ∈ L or x ∈ L. Corollary The language ATM is co-recognizable but not recognizable. Because we know that ATM is recognizable, our theorem implies that ATM and ATM are both decidable.

Are Turing recognizable languages closed under union?

Theorem 5: The set of Turing-recognizable languages is closed under set union and intersection.

What does it mean to be not Turing recognizable?

No. Turing Recognizable. Turing decidable. 1. 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.

Is ETM Turing recognizable?

ETM is not Turing-recognizable. Rice’s Theorem: Every nontrivial property of the Turing-recognizable languages is undecidable.

How do you prove a language is decidable?

To show that a language is decidable, we need to create a Turing machine which will halt on any input string from the language’s alphabet. Since M is a dfa, we already have the Turing Machine and just need to show that the dfa halts on every input.

Is the union of two recognizable languages recognizable?

The union of recognizable languages is recognizable The intent is that L(M)=L(M1)∪L(M2). The idea behind the construction is that if M processes x and ends in state (q1,q2) then M1 would be in state q1 and M2 would be in state q2.

How is a Turing machine defined?

• A Turing machine is a mathematical model of computation that defines an abstract machine that manipulates symbols on a strip of tape according to a table of rules.
• The machine operates on an infinite memory tape divided into discrete “cells”.

What makes a language Turing-decidable?

A language is Turing-decidable(or decidable) if some Turing machine decidesit Aka RecursiveLanguage Review: Turing Recognizable Language A language is Turing-recognizableif some Turing machine recognizesit Aka Recursively EnumerableLanguage

What is the difference between a decider and a Turing decider?

Language is Turing recognizableif some Turing machine recognizes it Also called “recursively enumerable” Machine that halts on all inputs is a decider. A decider that recognizes language L is said to decidelanguage L Language is Turing decidable,or just decidable, if some Turing machine decides it

Is it possible to prove a language is decidable?

You won’t be able, given a language, to just state if it’s decidable or not. There isn’t any algorithm that can do that, and proving a language isn’t decidable takes some thinking, and can require some knowledge on Turing Machines, Diagonal arguments, etc…

Is there an algorithm that can prove a language is decidable?

There isn’t any algorithm that can do that, and proving a language isn’t decidable takes some thinking, and can require some knowledge on Turing Machines, Diagonal arguments, etc… However, here is my personal way of handling this question.