However, ETM is Turing-recognizable (HW 8, problem 4) and ATM is not Turing- recognizable (Corollary 4 23), contradicting Theorem 5 22 3 Consider the
hwsoln
Consider the emptiness problem for Turing machines: ETM = { 〈M〉 M is a Turing machine with L(M) = ∅} Show that ETM is co-Turing-recognizable (A
hwsoln
If both L and L are recognizable then L is decidable As we know that ATM , HALTTM , ETM are recognizable, their complements cannot be rec- ognizable,
t sol
HALTTM is Turing-recognizable since it can be recognized by TM U ETM = {< M > M is a TM and L(M) = /0} is undecidable Proof: Reduce ATM to ETM
ln
But, ¬ETM is Turing recognizable and ¬ATM is not, which contradicts Theorem 5 22 This is a contradiction Therefore, ATM is not mapping reducible to ETM 5 7 A
SolnHW
ETM = {〈M〉 M is a TM such that L(M) = {}} is undecidable Let R be a TM that decides ETM If A ≤m B and B is recognizable, then A is recognizable
reducibility
ETM = { M is TM, L(M) is empty} A Decidable B Undecidable, recognizable, with recognizable complement C Undecidable, recognizable, with
Lect CSE Sp
28 nov 2006 · The emptiness problem, ETM = {(M )M is a TM and L(M) = ∅}, is undecidable How to prove a language is Turing-recognizable or
discussion
Skip ahead to section 2.2 or 2.3 and show that ETM is not recognizable. Then by the theorem that. “a language is decidable iff it is both recognizable and
This in turn implies that ETM is undecidable. At least one of them must be not recognizable. ETM is recognizable. ETM is not recognizable.
Consider the emptiness problem for Turing machines: ETM = { ?M?
However ETM is Turing-recognizable (HW 8
If both L and L are recognizable then L is decidable. As we know that ATM HALTTM
But ¬ETM is Turing recognizable and ¬ATM is not
HALTTM is Turing-recognizable since it can be recognized by TM U. HALTTM is not Turing-decidable. ETM = {< M >
Since ETM is undecidable (Theorem 5.2) EQTM must be undecidable. • We'll see later that EQTM is not Turing-recognizable not co-Turing-recognizable
Show that the language ETM = {?M?
4 Mar 2019 But ETM is Turing-recognizable (why?) which would mean ATM recognizable (false). ? Mapping reductions may not exist!
Skip ahead to section 2 2 or 2 3 and show that ETM is not recognizable Then by the theorem that “a language is decidable iff it is both recognizable and
However ETM is Turing-recognizable (HW 8 problem 4) and ATM is not Turing-recognizable (Corollary 4 23) contradicting Theorem 5 22 3 Consider the language
Rice's Theorem: any nontrivial property of the language of a TM is undecidable • ETM is not Turing-recognizable • EQTM is neither Turing-recognizable nor co-
Show that the language ETM = {?M?M is a Turing machines and L(M) = ? } is not Turing-recognizable Proof: We provide two different proofs Proof 1: We
As we know that ATM HALTTM ETM are recognizable their complements cannot be rec- ognizable because then the languages would be decidable and we know that
HALTTM is Turing-recognizable since it can be recognized by TM U HALTTM is not Turing-decidable Proof: We will reduce ATM to HALTTM Assume TM R decides
HALTTM = {?Mw? M is a TM that halts on input w} is undecidable If A ?m B and B is recognizable then A is recognizable Corollary 5 23
26 oct 2020 · Theorem: Every nontrivial property about recognizable languages (of Turing machines) is undecidable • The proof is a generalization of the
29 juil 2013 · We mentioned that ETM is co-TM recognizable We will prove next that ETM is undecidable Intuition: You cannot solve this problem UNLESS
HALTTM is undecidable since ATM is undecidable This in turn implies that ETM is undecidable At least one of them must be not recognizable
Skip ahead to section 2.2 or 2.3 and show that ETM is not recognizable. Then by the theorem that. “a language is decidable iff it is both recognizable and
Is ETM Turing-recognizable?
ETM is not Turing-recognizable. Rice's Theorem: Every nontrivial property of the Turing-recognizable languages is undecidable.Is ETM undecidable proof?
Note that ?M1? ? ETM ?? L(M1) = ? ?? M accepts w ?? ?M, w? ? ATM. But then TM S decides ATM, which is undecidable. Therefore, TM R cannot exist, so ETM is undecidable.Is EQTM Turing-recognizable?
EQTM is not recognizable.- ATM = {?M,w?M is a Turing machine and M accepts w} However, unlike ADFA and ACFG, ATM is not decidable. But ATM is Turing-recognizable.
Note on ETM