1. Turing machines may also be used to compute functions. Give a state-transition diagram for a Turing machine that takes as input a binary string w, increments w, and enters the accepting state. For example, on input w = 100111, the Turing machine begins like this: 90 1|0|0|1|11|-|- The Turing machine should halt with 101000 on the tape: qaccept 101000-

1. Turing machines may also be used to compute functions. Give a state-transition diagram for a Turing machine that takes as input a binary string w, increments w, and enters the accepting state. For example, on input w = 100111, the Turing machine begins like this: 90 1|0|0|1|11|-|- The Turing machine should halt with 101000 on the tape: qaccept 101000-

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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Draw a state diangram for a Turing machine which, when given an input string 0", outputs 0"1". For example, if the tape contains 0000 at the beginning, then the tape should contain 00001111 when the TM halts. You may omit transitions that won't ever be taken. 4.
Explain a Turing Machine that accepts the following, and give examples of when the Turing Machine accepts/rejects the language . L = { ww : w ∈ {a,b}+}
Design a Turing machine M that decides the language L = {0n1n|n> 0}.
Let M be a Turing machine and w be a string in the input alphabet of M. Consider the problem A = {(M, w)|M moves left at some point during its computation on w} %3| Show that A is decidable.
Define a Turing machine that accepts an integer n as an input string in unary representation, w = { 1 } *, and calculates n mod 3. When the machine halts, the tape should contain only the unary representation of f(w) followed by a zero. For example, ƒ(1111) = 10 or f(11111) 11111) = 0.
Not so. The real question states that: Construct a turing machine that computes the function ?(?) = 2?, , i.e. if the input is 0^? then the output would be 0^2? e.g. if it says 000 on the tape before the machine is run it should read 000000 on the tape when it has stopped.
4. Give a formal state diagram of a Turing Machine which recognizes the language {#a" + am : n+m = a' : n, m E N}. (You can use the "#" symbol to recognize the beginning of the tape.) SOLUTION:
Imagine a Turing machine M' that works like a normal Turing machine except that whenever it moves to the left, it moves by two squares instead of one. Its movements to the right are by one square as usual. Show that M' can compute all functions that normal Turing machines can compute.
The reverse function maps a string w to wR. Draw a multi-tape Turing machine that computes the reverse of a binary string. That is, given a binary string w as input, your Turing machine should compute wR, write the result to tape 1, and halt.
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?
Explain a Turing Machine that accepts the following, and give examples of when the Turing Machine accepts/rejects the language . L = { ww : w ∈ {a,b}+}
Given: Turing Machine TM Transition Diagram O.L 1,R 1,L 0,R 1,R gou.L 1/UL U,R 9⁰ O,L go 0/u,R O.R 9⁰ OL qr Identify the string whether either ACCEPTED or NOT ACCEPTED by the given TM. NOTE: 0, R means read data (0) and write data (0), move right 1/u, L means read data (1) and write data (u), move left u - tape blank symbol UR ✓0000011 ✓ 0000001 ✓ 00001 0001 O,L U,R U,L A. NOT ACCEPTED B. ACCEPTED