Recent questions tagged rice-theorem - GATE Overflow

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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} \}$.

asked Oct 20, 2019 in Theory of Computation by Lakshman Patel RJIT Veteran (58.9k points) | 25 views

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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.

asked Oct 20, 2019 in Theory of Computation by Lakshman Patel RJIT Veteran (58.9k points) | 12 views

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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.

asked Oct 20, 2019 in Theory of Computation by Lakshman Patel RJIT Veteran (58.9k points) | 21 views

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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 non-RE? Does $L(M)$ contain at least two strings? Is $L(M)$ infinite? Is $L(M)$ a context-free language? Is $L(M) = (L(M))^{R}$?

asked Jul 21, 2019 in Theory of Computation by Lakshman Patel RJIT Veteran (58.9k points) | 17 views

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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.

asked Dec 29, 2018 in Theory of Computation by Deepanshu Loyal (7.8k points) | 120 views

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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 .

asked Dec 17, 2018 in Theory of Computation by Learner_jai Active (2.7k points) | 82 views

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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)

asked Dec 10, 2018 in Theory of Computation by gmrishikumar Active (2.1k points) | 209 views

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TOC-Undecidability
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.

asked Nov 23, 2018 in Theory of Computation by Ayush Upadhyaya Boss (29.1k points) | 156 views

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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

asked Nov 14, 2018 in Theory of Computation by Deepanshu Loyal (7.8k points) | 67 views

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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 non-trivial then please explain why is that so. According to my understanding, non-trivial 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.

asked Oct 30, 2018 in Theory of Computation by Swapnil Naik Active (3.2k points) | 69 views

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undecidability
Writes Non Blank: Given a turing machine T, does it ever writes a non-blank 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 non-trivial property of turing machine and every non trivial property of turing machine is undecidable, so this is also undecidable.

asked Sep 21, 2018 in Theory of Computation by aambazinga Active (3.4k points) | 67 views

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TOC- Undecidability

asked Sep 9, 2018 in Theory of Computation by sidlewis Junior (903 points) | 68 views

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Rice's Theorem
What is monotonic and non-monotonic property. Please explain the second postulate of Rice's Theorem.

asked Jan 23, 2018 in Theory of Computation by Sumaiya23 Active (1.7k points) | 113 views

+2 votes

2 answers

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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 ............"

asked Jan 13, 2018 in Theory of Computation by yogi_p Active (1.7k points) | 175 views

+2 votes

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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 ??

asked Jan 9, 2018 in Theory of Computation by Venkat Sai Active (3.8k points) | 133 views

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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 non-trivial ... Same problem as ATM). Can M' take decision in finite time. Please give me some insights to I can understand this point.

asked Dec 15, 2017 in Theory of Computation by Durgesh Singh Junior (755 points) | 142 views

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Rice theorem G is a CFG. Is L(G)= Σ ∗ L(G)=Σ∗ .What is it - Decidable / Undeciable .How?

asked Dec 1, 2017 in Theory of Computation by hem chandra joshi Active (4.1k points) | 74 views

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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

asked Dec 1, 2017 in Theory of Computation by hem chandra joshi Active (4.1k points) | 298 views

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Can any one proof decidability/undecidability of following on Rice Theorem ?
Rice theorem : 1. Any non-trivial property of the LANGUAGE recognizable by a Turing machine is undecidable. 2. Any non-monotonic 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.

asked Dec 1, 2017 in Theory of Computation by hem chandra joshi Active (4.1k points) | 102 views

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Rice's Theorem
Example# 3 from Part-1 Rice's Theorem from https://gatecse.in/rices-theorem/ 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 ?

asked Oct 28, 2017 in Theory of Computation by Salazar Active (1.1k points) | 190 views

+6 votes

2 answers

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$\{\langle M \rangle \mid M$ is a TM and there exist an input whose length is less than 100, on which $M$ halts$\}$

asked Sep 9, 2017 in Theory of Computation by sourav. Boss (16.2k points) | 1.3k views

+1 vote

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22

Turing Machine Rice's Theorem
L = {M|M 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.

asked Aug 5, 2017 in Theory of Computation by rahul sharma 5 Boss (25.6k points) | 202 views

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Rice theorem Example from (https://www.cs.rice.edu/~nakhleh/COMP481/final_review_sp06_sol.pdf)

asked Jul 18, 2017 in Theory of Computation by akb1115 Active (3.3k points) | 265 views

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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

asked May 24, 2017 in Theory of Computation by Arpit Dhuriya Active (3.8k points) | 148 views

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25

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

asked Jan 24, 2017 in Theory of Computation by Wanted Active (1.9k points) | 70 views

+2 votes

1 answer

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General Doubt In rice theorem
If we are not able to apply non-monote property ,then is it always true that it is RE but not REC,are there any scenarios where we can't apply non-monotone 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/rices-theorem/)

asked Jan 22, 2017 in Theory of Computation by rahul sharma 5 Boss (25.6k points) | 179 views

+1 vote

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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

asked Jan 13, 2017 in Theory of Computation by rahul sharma 5 Boss (25.6k points) | 187 views

+4 votes

1 answer

28

Rice's Theorem
I am unable to understand when to apply Rice's theorem and when to not. How L2 is decidable.

asked Jan 3, 2017 in Theory of Computation by Lucky sunda Active (4.5k points) | 331 views

+1 vote

1 answer

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?

asked Jan 2, 2017 in Theory of Computation by Lucky sunda Active (4.5k points) | 98 views

+2 votes

2 answers

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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..??

asked Dec 27, 2016 in Theory of Computation by Akriti sood Boss (12.2k points) | 395 views

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