A "standard" single-tape Turing machine M has a one-way infinite tape; the set of valid tape head positions is N (nonnegative integers). A two-way-infinite Turing machine T is a single-tape Turing machine where the set of valid tape head positions is Z (integers). In other words, there is no "leftmost" tape cell; the tape head can move arbitrarily far to the left as well as arbitrarily far to the right. (See example T in part (b) below.) (a) Describe in general how an arbitrary configuration of a two-way-infinite Turing machine T can be represented as a configuration of a standard one-way-infinite Turing machine M.

A "standard" single-tape Turing machine M has a one-way infinite tape; the set of valid tape head positions is N (nonnegative integers). A two-way-infinite Turing machine T is a single-tape Turing machine where the set of valid tape head positions is Z (integers). In other words, there is no "leftmost" tape cell; the tape head can move arbitrarily far to the left as well as arbitrarily far to the right. (See example T in part (b) below.) (a) Describe in general how an arbitrary configuration of a two-way-infinite Turing machine T can be represented as a configuration of a standard one-way-infinite Turing machine M.

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

A "standard" single-tape Turing machine M has a one-way infinite tape; the set of valid tape head
positions is N (nonnegative integers). A two-way-infinite Turing machine T is a single-tape Turing
machine where the set of valid tape head positions is Z (integers). In other words, there is no
"leftmost" tape cell; the tape head can move arbitrarily far to the left as well as arbitrarily far to
the right. (See example 7 in part (b) below.)
(a) Describe in general how an arbitrary configuration of a two-way-infinite Turing machine T
can be represented as a configuration of a standard one-way-infinite Turing machine M.

(b) Show how your description in part (a) applies to the following example configuration of T:
T: (arrow shows position of tape head)
position
-5
-4
-3
-2
-14 0
1 2 3
content
L
g
h
i
j
k
1
U
M: (draw arrow at tape head position, and put symbols in cells as in your description above)
position 0
1 2
3
4 5
6 7 8 9 10 11
content
4 5

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