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MCS265
Homework set 6 solution
April 14, 2004
David Wolfe
Due: April 21, 2004
1. (Warmup) (Sipser 3.11) A
Turing machine with doubly infnite tape
is similar to an ordinary Turing machine
except that its tape is inFnite to the left as well as to the right.
The tape is initially Flled with blanks
except for the portion that contains the input. Computation is deFned as usual except that the head never
encounters an end to the tape as it moves leftward. Show that this type of Turing machine recognizes the class
of Turingrecognizable languages.
It suﬃces to convert a Turing machine with doubly inFnite tape,
M
, into a regular Turing machine
M
0
accepting
the same language. The idea is simply to “fold” the doublyinFnite tape over. If
M
has tape alphabet Γ and
states
Q
,
M
0
will have tape alphabet Γ
×
Γandstates
Q
×{
L,R
}
.
M
0
stores in tape location
n
two symbols:
Location
n
of
M
and location
−
n
of
M
. The state space is doubled so that
M
0
can remember whether its
simulating the left or right side of
M
’s tape. The transition function is easily adapted.
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This note was uploaded on 02/22/2010 for the course CS 881 taught by Professor H.f. during the Spring '10 term at Shahid Beheshti University.
 Spring '10
 H.F.

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