Because we know that
ATM is recognizable
, our theorem implies that ATM and ATM are both decidable. But we know that ATM is not decidable. This is a contradiction, hence ATM cannot be recognizable. The language ATM and its undecidability
Is ATM co Turing?
We know that
ATM is Turing recognizable
, but not co-Turing recognizable. … If any string is accepted, accept” This Turing machine will accept any Turing machine whose language is non- empty. Now assume ATM is mapping reducible to ETM. Then ¬ATM is mapping reducible to ¬ETM.
Is ATM complement decidable?
Corollary 4.23: ATM is Turing-recognizable but
not decidable
, so its complement ATM is NOT Turing-recognizable.
Is ATM reducible to its complement?
ATM can not reduce to its complement
. … From the lecture, we know the complement of L1 is decidable, so does L1. (b) L2 = {〈N,w〉 : N is a NFA and w ∈ L(N)} Decidable.
How do you prove a problem is recognizable?
Prove that the language it recognizes is equal to the given language and that the algorithm halts on all inputs. 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 is ATM in theory of computation?
In computational complexity theory,
an alternating Turing machine
(ATM) is a non-deterministic Turing machine (NTM) with a rule for accepting computations that generalizes the rules used in the definition of the complexity classes NP and co-NP.
Is halt complement recognizable?
and HALT are undecidable
What language is ATM?
In the US, around 80 percent of in-person transactions and 95 percent of ATM swipes are based on programs written in
COBOL
.
What is Turing unrecognizable?
~
A
TM
is the canonical example of a Turing-unrecognizable language. This means there does not exist a Turing Machine which will accept the set of all machine-string pairs <M,w> such that M does NOT halt when run on w. The proof of this is very short: Lemma: A
TM
is Turing-recognizable.
How do you prove a language is undecidable?
How can you prove a language is undecidable? To prove a language is undecidable,
need to show there is no Turing Machine that can decide the language
.
Why ATM is 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.
Can a language be recognizable and decidable?
Note: Decidable languages are closed under complementation, but
recognizable languages are not
. – Write-only means (a) symbol on output tape does not affect transitions, and (b) tape head only moves right. Note M need not enumerate strings in order. It is also possible that M lists some strings many times!
What is a recognizable language?
A language is Recognizable iff there is a Turing Machine which will halt and accept only the strings in that language and for strings not in the language, the TM either rejects, or does not halt at all. Note: there is no requirement that the Turing Machine should halt for strings not in the language.
Is Eqcfg recognizable?
Otherwise, exactly one of the CFGs generates the string and the other CFG does not, so the CFGs are not equivalent, and the TM accepts. Thus, D
is Turing- recognizable
. We showed in a previous homework that the class of Turing-recognizable languages is closed under union, so EQCFG is Turing-recognizable.
Is every decidable language finite?
All finite languages are regular
. Some infinite languages are regular. Only infinite languages can be undecidable
What are the unsolvable problems?
Definition:
A computational problem
