Let T be the Turing machine defined by the following 5-tuples: (8o, 0, s1, 0, R) (8o,1, 81,0, L) (so, B, 81, 1, R) ($1, 0, s2, 1, R) (81, 1, 81, 1, R) ($1, B, 82,0, R) (82,0, s3, 0, R) (s83,0, s2, 1, R) For the following tape, determine the intermediate tapes, states, and head positions; and final tape, state, and head position when T halts. Assume T begins in the initial position. state |B|B|1|0|0|B |B|B| So

Let T be the Turing machine defined by the following 5-tuples: (8o, 0, s1, 0, R) (8o,1, 81,0, L) (so, B, 81, 1, R) ($1, 0, s2, 1, R) (81, 1, 81, 1, R) ($1, B, 82,0, R) (82,0, s3, 0, R) (s83,0, s2, 1, R) For the following tape, determine the intermediate tapes, states, and head positions; and final tape, state, and head position when T halts. Assume T begins in the initial position. state |B|B|1|0|0|B |B|B| So

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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Concept explainers

Problems on Turing Machines

In the computational world, the Turing machine is a powerful computation engine. The invention of the Turing Machine is done by Alan Turing in 1936. A Turing Machine (TM) is a diagrammatic model of a fictional computer. It determines an output from a set of input variables using a pre-defined set of rules. It is used to get around the limitations of finite automata and pushdown automata.

Question

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Let T be the Turing machine defined by the following 5-tuples:
(80, 0, 81,0, R) (8o,1, 81,0, L)
(8o, B, s1, 1, R)
,0, R)
(81,0, s2, 1, R)
(83,0, s2, 1, R)
(81, 1, s1, 1, R) ($1, B, s2,0, R) ($2,0, s3,
For the following tape, determine the intermediate tapes, states, and head positions; and final
tape, state, and head position when T halts. Assume T begins in the initial position.
state
| B |B|1|0|0|B|B|B ||

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1. Which of the following strings are accepted by the following Turing machine with q5 is the final state? aab, abb, aaabb, aaab, aaaaabbb δ (q0; a) = (q1; a; R); δ (q1; a) = (q2; a; R); δ (q2; a) = (q3; a; R); δ (q3; a) = (q3; a; R); δ (q3; b) = (q4; b; R); δ (q3; blank) = (q5; blank; L); δ (q4; b) = (q4; b; R); δ (q4; blank) = (q5; blank; L); 2. What language is accepted by the Turing machine in Q1?
2) Recall that a final state of a Turing machine T is a state that is not the first state in any of the 5-tuples that make up T. Construct a Turing machine that recognizes the set {0²n1n | n ≥ 0}. Write down 5- tuples for the Turing Machine. (You will not receive credit if you only draw an FSM.)
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Suppose that Turing machine M computes the unary number-theoretic function f defined by f(n) = n2 + 6n + 3 and suppose, further, that M is started scanning the leftmost 1 in an unbroken string of six 1s on an otherwise blank tape. Then M will halt scanning the leftmost 1 in an unbroken string of how many 1s?
1. Determine the Turing machine that computes the function: f(n) = 4n+3 The machine should therefore start with a natural number n on the tape and stop with the number 4n+3 on it the tape . (Hint: Think binary.) 2. Determine a Turing machine for creating palindromes. That is, if we start with w on the tape, then we should end with ww on the tape, where w is the reversed string of w. E.g. if we start with |-011 on the tape, then we should stop with |-011110 on the tape