How do you prove not Turing recognizable?

How do you prove not Turing recognizable?

(a) Set M1 := N1 and M2 := N2. (b) Construct a TM M3 that accepts the string ϵ only and rejects every other string. Therefore, L(N1) = L(N2) ⇐⇒ L(M1) = L(M2) · L(M3) and hence EQTM ≤m CONTM . This proves that CONTM is not Turing recognizable.

What is Turing Co 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.

How do you know if a language is recognizable?

Recognizable Language A Turing machine M recognizes language L if L = L(M). We say L is Turing-recognizable (or simply recognizable) if there is a TM M such that L = L(M). Decidable Language A Turing machine M decides language L if L = L(M) and M halts on all inputs.

Is ATM Turing recognizable?

Recall that a language L is Turing recognizable if there is a Turing machine that accepts exactly the words in L, but can either reject or loop indefinitely on an input that’s not in L. We will show that ATM , the complement of ATM , is not Turing-recognizable.

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 the complement of a Turing recognizable language Turing recognizable?

If it accepts then accept and vice versa. – Turing recognizable languages are not closed under complement. 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 L accept recognizable?

Thus, L is a Turing Recognizable Language (since the TM M recognizes it).

Is ETM Turing recognizable?

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

What is a Turing acceptable language?

A language is called Decidable or Recursive if there is a Turing machine which accepts and halts on every input string w. Every decidable language is Turing-Acceptable. A decision problem P is decidable if the language L of all yes instances to P is decidable.

Can a Turing machine decide a language?

A language is recursively enumerable (generated by Type-0 grammar) if it is accepted by a Turing machine. A TM decides a language if it accepts it and enters into a rejecting state for any input not in the language. A language is recursive if it is decided by a Turing machine.

Is L M infinite?

If M does not accept w, then M will accept every x, and so L(M )=Σ∗ is infinite.

Is the Turing recognizable language close under complementation?

– Turing recognizable languages are not closed under complement.

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 the collection of Turing-recognizable languages closed under the operation of Union?

Show that the collection of Turing-recognizable languages is closed under the operation of union. For any two Turing-Recognizable languages L 1 and L 2, let M 1 and M 2 be the TM s that recognize them. We construct a TM M ′ that recognize the union of L 1 and L 2:

What is the difference between a decider and a recognizer?

Recognizers and Deciders. A recognizer of a language is a machine that recognizes that language. A decider of a language is a machine that decides that language. Both types of machine halt in the Accept state on strings that are in the language. A Decider also halts if the string is not in the language.