Prove that the following language L is decidable:L = {(M) : 3x € {0,1}*, 1000 ≤ ReachCells(M, x)}. For a Turing machine M, (M) refers to the binary representation of M.For a Turing machine M, L(M) contains the set of all strings accepted by M.For a Turing machine M and an input x = {0,1}*, Steps(M, x) refers to the number of steps takenby M to execute on x before it halts. Here, one step of execution of M on x = one movement (left orright) of the tape head.For a Turing machine M and an input x = {0,1}*, we define the following:ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x}Informally, it contains all locations on the tape that are visited when M is ecuted on x. Theleftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and soon.A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, ifw₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elementssuch that π(w₁) = W2.

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Prove that the following language L is decidable: L = {(M) : 3x = {0,1}*, 1000 € ReachCells(M,x)}.

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

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Question

Prove that the following language L is decidable:
L = {(M) : 3x € {0,1}*, 1000 ≤ ReachCells(M, x)}.

For a Turing machine M, (M) refers to the binary representation of M.
For a Turing machine M, L(M) contains the set of all strings accepted by M.
For a Turing machine M and an input x = {0,1}*, Steps(M, x) refers to the number of steps taken
by M to execute on x before it halts. Here, one step of execution of M on x = one movement (left or
right) of the tape head.
For a Turing machine M and an input x = {0,1}*, we define the following:
ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x}
Informally, it contains all locations on the tape that are visited when M is ecuted on x. The
leftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and so
on.
A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, if
w₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elements
such that π(w₁) = W2.

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