4.30 Let A be a Turing-recognizable language consisting of descriptions of Turing ma-chines, ((M1), (M2), ...), where every M, is a decider. Prove that some decidablelanguage D is not decided by any decider M, whose description appears in A.(Hint: You may find it helpful to consider an enumerator for A.)

To prove that some decidable language D is not decided by any decider M₁ whose description appears…

Answered: 4.30 Let A be a Turing-recognizable…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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2. Let A be a Turing-recognizable language consisting of descriptions of Turing machines, i.e., A = {(M1), (M2),...}, where every M; is a decider. Prove that some decidable language D is not decided by any decider M, whose description appears in A.
Can you help me with this question? I'm struggling to grasp how to tackle it and come up with an answer. Could you simplify it into steps, guiding me towards the solution so I can understand the approach you used?
Prove that the language L over {a,b,c}",given by L= {wcv: |w\a = |vl6} is recursive. You must provide a Turing machine that decides this language. You may submit a state-transition diagram or the delta function definition.
Let A be a language such that A ≤m PCP and ETM ≤m A. What can you say about A? Briefly explain your answer.
1. The notion of a verifier is central to the definition of the complexity class NP. However, we can consider the idea of a verifier independent of ideas from complexity theory. Recall that a verifier for a language L is an TM V such that L = {w | V accepts <w, c> for some c}. Prove that ATM, the acceptance language for Turing machines, has a verifier even if we add the extra condition that the verifier is a decider. Note that the verifier need not run in polynomial time. We are not asking for a polynomial-time verifier. 2. Let L be a context-free language. Prove that L is NP-Complete if and only if P = NP. 3. For a string w, let w_rev be the string w reversed. For any language A, Let reverse(A) = { w_rev| w is in A}. For which of the following classes of languages is closed under the reverse operation. In other words, for which classes is it true that for every language A in the class, reverse(A) is also in the class. Context-Free languages(Closed or Not Closed) Nonregular…
Let Mx be a Turing machine that decides the language X and let My be a Turing machine that decides the language Y. Describe a Turing machine M that decides the language XYX. (You don't have to formally define the machine. Describe the behaviour of the machine in sentences.)
Could you assist me with this question? I'm having difficulty understanding how to approach it and formulate a response. Would you be able to break it down step by step, guiding me towards the solution so that I can comprehend the method you employed to solve it?
Problem 2. Let A be a TM-recognizable language consisting of TM descriptions of deciders. Prove that some decidable language D is not decided by any machine that appears in A.
2. Consider the language DOUBLE-SAT, all of the boolean expressions with at least two satisfying assignments. (a) What would a possible DOULBE-SAT solution look like for an expression? (b) Is DOUBLE-SAT in NP?
Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.
Develop a Turing machine for the language L={w∈{0,1}∗ ||w|isoddandwcontainsatleastone1}. This means that the Turing machine should accept all strings over {0, 1} of odd length that contain at least one 1. Show the state transition diagram in addition to your defi- nition of the Turing machine. Show the working of your Turing machine on the strings “0010”, “00101”, and “000”.
Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

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