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Michael Sipser Edition 3 Exercise 5 Question 30 (Page No. 241)
Use Rice’s theorem, to prove the undecidability of each of the following languages. $INFINITE_{TM} = \{\langle M \rangle \mid \text{M is a TM and L(M) is an infinite language}\}$. $\{\langle M \rangle \mid \text{M is a TM and }\:1011 \in L(M)\}$. $ ALL_{TM} = \{\langle M \rangle \mid \text{ M is a TM and}\: L(M) = Σ^{\ast} \}$.
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Oct 20
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Lakshman Patel RJIT
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Michael Sipser Edition 3 Exercise 5 Question 29 (Page No. 241)
Rice's theorem. Let $P$ be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given Turing machine's language has property $P$ is undecidable. In more formal ... that $P$ is an undecidable language. Show that both conditions are necessary for proving that $P$ is undecidable.
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Oct 20
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Michael Sipser Edition 3 Exercise 5 Question 28 (Page No. 241)
Rice's theorem. Let $P$ be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given Turing machine's language has property $P$ is undecidable. In more formal terms, let $P$ be a language ... $M_{1}$ and $M_{2}$ are any $TMs$. Prove that $P$ is an undecidable language.
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Oct 20
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Lakshman Patel RJIT
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Ullman (TOC) Edition 3 Exercise 9.3 Question 4 (Page No. 400)
We know by Rice's theorem that none of the following problems are decidable. However are they recursively enumerable,or nonRE? Does $L(M)$ contain at least two strings? Is $L(M)$ infinite? Is $L(M)$ a contextfree language? Is $L(M) = (L(M))^{R}$?
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Jul 21
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Lakshman Patel RJIT
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SELF DOUBT_ RICE THEOREM
L = {<M1, M2>M1 and M2 are two TMs, and ε ∈ L(M1) \ L(M2) }. is it RECURSIVE OR RECURSIVE ENUMERABLE OR NOT EVEN RECURSIVE ENUM.
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Dec 29, 2018
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Rice theorem
1.{<M> M is a TM accepts any string starting with 1} 2.{<M> M is TM accept exactly 20 strings} Please guide I don’t know how to apply rice theorem. for 1. Is Tyes = { string starting with 1} Tno = { all strings – strings starting with 1} what is Tyes and Tno here? I only conclude by intution that when we provide strings as input some got into loop and some got accepts .
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Dec 17, 2018
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Learner_jai
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Halting problem of TM which recognize recursive languages is undecidable?
Halting problem of Turing machines which recognize recursive languages is undecidable. (True / False)
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Dec 10, 2018
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gmrishikumar
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TOCUndecidability
Here is my analysis. P1: When we bound the number of steps a turing machine can tape, the total number of input possible that can be taken by such turing machine becomes finite and by running TM in an interleaved mode I can decide whether TM M halts on x within k ... decide P3. Hence, P3 is decidable.>REC. So, I think here answer must be 1. Please let me know what's right.
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Nov 23, 2018
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Ayush Upadhyaya
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SELF DOUBT _ RICE THEOREM
L1 = { <M>  M is a TM and  L (M) <=1 } L2= { <M>  M is a TM and  L (M) >=1 } NOW QUESTION IS WHICH ARE RECURSIVE ENUMERABLE AND WHICH ARE NOT ???? I JUST READ BASICS OF rice theorem DONT PRACTICE MUCH QUESTIONS ON THIS I ... = 0...... and REL_yes as string length >= 1 . REL_YES is a proper subset of REL _NO . so we can say that it is also non re
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Nov 14, 2018
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Undecidability
L1:{<M>  there exist a Turing machine M' such that <M>$\neq$<M'> and L(M) = L(M')} How this problem becomes trivial? and if it nontrivial then please explain why is that so. According to my understanding, nontrivial properties ... it is then is it okay to say M1=M2 because they are kind of same machine but other one is just with some non deterministic nature.
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Oct 30, 2018
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Swapnil Naik
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undecidability
Writes Non Blank: Given a turing machine T, does it ever writes a nonblank symbol on its tape, when started with a blank tape. how the above problem is solvable? somewhere i got this explanation: Let the machine only writes blank symbol. Then ... is a nontrivial property of turing machine and every non trivial property of turing machine is undecidable, so this is also undecidable.
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Sep 21, 2018
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TOC Undecidability
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Sep 9, 2018
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Rice's Theorem
What is monotonic and nonmonotonic property. Please explain the second postulate of Rice's Theorem.
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Jan 23, 2018
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Sumaiya23
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14
Undecidability Confusion
I was Studying About Undecidability on GateCSE. I am facing a doubt that : L = {<M>  M accepts "1"} L is set of String & each String is an Encoding of TM & TM accepts 1 L = {<M>  L(M) = {1}} Given a Input Program ... really is difference between both of them ? Can you definition of 2 in words like " L is set of String ............"
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Jan 13, 2018
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yogi_p
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undecidability
Define languages L0 and L1 as follows : L0={⟨M,w,0⟩∣M halts on w} L1={⟨M,w,1⟩∣M does not halt on w} Here ⟨M,w,i⟩is a triplet, whose first component M is an encoding of a Turing Machine, second component w is a string, and the third component i is a ... an acceptor for L as even when L0 is RE L1 is not RE but can anyone explain me what about L COMPLEMENT what is the language ??
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Jan 9, 2018
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Venkat Sai
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Doubt in Rice's Theorem
I have a doubt while understanding step 2 in proof of Rice's Theorem According to my understanding,proof of Rice's theorem as follows ( Please suggest If something is wrong in my understanding) P is a property of languages of TM which is nontrivial ... Same problem as ATM). Can M' take decision in finite time. Please give me some insights to I can understand this point.
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Dec 15, 2017
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Durgesh Singh
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Rice theorem G is a CFG. Is L(G)= Σ ∗ L(G)=Σ∗ .What is it  Decidable / Undeciable .How?
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Dec 1, 2017
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hem chandra joshi
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Rice theorem problem
Problem : It is undecidable whether an arbitrary Turing Machines halt within 10 steps? Let consider Two Turing machine in which first one it is halt in 10 steps while in other it is not , so as it is undecidable. @arjun sir ,@bikram sir or @others
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Dec 1, 2017
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Can any one proof decidability/undecidability of following on Rice Theorem ?
Rice theorem : 1. Any nontrivial property of the LANGUAGE recognizable by a Turing machine is undecidable. 2. Any nonmonotonic property of the LANGUAGE recognizable by a Turing machine is unrecognizable While ... is regular. Whether a finite state automation halts on all inputs. Membership problem for type 00 languages.
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Dec 1, 2017
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Rice's Theorem
Example# 3 from Part1 Rice's Theorem from https://gatecse.in/ricestheorem/ states as follows (3) L(M) is recognized by a TM having even number of states Sol: This is a trivial property. This set equals the set of recursively enumerable languages. According to ... then? Can someone give me an example for which TYES and TNO cannot be found and let me know if my approach is correct ?
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Oct 28, 2017
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Salazar
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21
$\{\langle M \rangle \mid M$ is a TM and there exist an input whose length is less than 100, on which $M$ halts$\}$
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Sep 9, 2017
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sourav.
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Turing Machine Rice's Theorem
L = {MM is a TM that accepts all even numbers} For the above language i can have Tyes machine which has all even numbers.And Tno as machine whose language is empty.So i can say it is undecidable. But to show it is Not RE. What ... am assuming here that the property of the language as "Only all even numbers",i guess the same has been given in the question.
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Aug 5, 2017
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rahul sharma 5
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23
Rice theorem Example from (https://www.cs.rice.edu/~nakhleh/COMP481/final_review_sp06_sol.pdf)
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Jul 18, 2017
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24
http://www.cs.rice.edu/~nakhleh/COMP481/
Can anybody please explain this reduction and rice theorem. http://www.cs.rice.edu/~nakhleh/COMP481/ Thanks
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May 24, 2017
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Arpit Dhuriya
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rice theorem problem
L(M) has at most 10 strings We can have Tyes for ϕ and Tno for Σ∗. Hence, L={M∣L(M) has at most 10 strings} is not Turing decidable (not recursive). problem : It should not b Tyes Σ∗ and Tno for ϕ
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Jan 24, 2017
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Wanted
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General Doubt In rice theorem
If we are not able to apply nonmonote property ,then is it always true that it is RE but not REC,are there any scenarios where we can't apply nonmonotone property but still language is NOT RE. Say,L={TM L(TM) has atleast one string}, Now it is ... theat RE but not REC. P.S: By (i) and (ii) ,i mean the definitions mentioned here.(http://gatecse.in/ricestheorem/)
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Jan 22, 2017
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rahul sharma 5
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Rice theorem Clarification
I need to understand when to apply RICE's theorem and when to not. Questions like: Turing machine makes at least five moves,It accepts a string input of length atleast five ,TM halts for every input on length <50 are all decidable. But these are ... some TM will say yes and some will say NO.Then why can't we use same concept on above metioned questions? Please help
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Jan 13, 2017
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rahul sharma 5
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28
Rice's Theorem
I am unable to understand when to apply Rice's theorem and when to not. How L2 is decidable.
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Jan 3, 2017
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Lucky sunda
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29
Rices theorem
I mean how it is a trivial property, we can write Tyes ( TM having even states) and Tno ( TM having odd states) for it.Can Turing machine can never have odd number of states?
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Jan 2, 2017
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L1 = {<M>  M is a TM and L(M) ⊆ {00, 11}}
L1 = {<M>  M is a TM and L(M) ⊆ {00, 11}} R.E or not RE..??
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Dec 27, 2016
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