Answered: Construct a Turing machine that…

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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Question

Construct a Turing machine that transforms an initial tape of the form 0m10n
(m and n
0’s with m, n > 0 separated by a 1) into 0m1_0n
(m and n 0’s with m, n > 0 separated by
a 1 followed by a blank). The tape head should be at the 1 before and after the
computation. Run your machine on the input 00100.

Expert Solution

Step 1: Turing machine model:

Finite Control (State Transition Diagram):
- The finite control represents the control unit of the Turing machine. It consists of a finite set of states and a transition function. Each state in the finite control corresponds to a specific behavior or operation the machine can perform. The transition function defines how the machine transitions from one state to another based on the current state and symbol read from the tape.
Tape:
- The tape is divided into an infinite number of cells, each capable of holding a symbol from the machine's alphabet (e.g., 0, 1, blank). The tape is used for both input and storage of intermediate results. The tape is typically one-dimensional and extends infinitely in both directions.
Read/Write Head:
- The read/write head is responsible for reading the symbol currently under it on the tape and writing new symbols to the tape. It can move left or right one cell at a time based on the transition rules.
Alphabet:
- The alphabet consists of symbols that the machine can read and write. This includes input symbols, blank symbols, and any other symbols used in the transition function.
Transition Rules:
- The transition rules define how the machine behaves. They specify which state the machine should transition to and what symbol to write on the tape based on the current state and symbol being read. Transition rules are at the core of the Turing machine's operation.

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