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The Turing Machine
Quiz description by James Edward G. II
The Turing Machine is a simple computing architecture dating all the
way back to the 1930s. While extremely primitive compared to any
modern machine, there has been a lot of research showing that a Turing
Machine is capable of just about anything the fancier machines can do
(although much less efficiently, of course).
This week’s task is to build a Turing Machine, so we can play around
with the architecture.
A Turing Machine has but three simple parts:
* A single state register.
* An infinite tape of memory cells that can hold one character
each, with a
read/write head that points to one of these cells at any given
time. The
tape is filled with an infinite run of blank characters in
either
direction.
* A finite set of program instructions. The program is just a big
table of
state transitions. The Turing Machine will look up an
instruction based
the current value of the state register and the current
character under
head of the tape. That instruction will provide a state for
the
register, a character to place in the current memory cell, and
an order to
move the head to the left or the right.
To keep our Turning Machine simple, let’s say that our state register
can contain words matching the regular expression /\w+/ and the tape
only contains characters that match the expression /\w/. We will
call our blank tape cell character the underscore.
Program lines will be of the form:
CurrentState _ NewState C R
The above translates to: if the current state is CurrentState and the
character under the tape head is our blank character, set the state to
NewState, replace the blank character with a C, and move the tape head
to the right one position. All five elements will be present in each
line and separated by one or more whitespace characters. Allow for
trailing comments (using #) on a line, comment only lines, and blank
lines in the program by ignoring all three.
The initial state of your Turing machine should be set to the
CurrentState mentioned on the first line of the program. Optionally,
the initial contents of the tape can be provided when the program is
load, but it will default to an all blank tape. The program runs
until it fails to find an instruction for the CurrentState and the
character currently under the tape head, at which point it prints the
current contents of the tape head from the first non-blank character
to the last non-blank character and exits.
Here’s a sample run of a simple program through my Turing Machine so
you can see how this plays out:
$ cat palindrome.tm
# Report whether a string of 0 and 1 (ie. a binary
# number) is a palindrome.
look_first 0 go_end_0 _ R
look_first 1 go_end_1 _ R
look_first _ write_es Y R
go_end_0 0 go_end_0 0 R
go_end_0 1 go_end_0 1 R
go_end_0 _ check_end_0 _ L
go_end_1 0 go_end_1 0 R
go_end_1 1 go_end_1 1 R
go_end_1 _ check_end_1 _ L
check_end_0 0 ok_rewind _ L
check_end_0 1 fail_rewind _ L
check_end_0 _ ok_rewind _ L
check_end_1 0 fail_rewind _ L
check_end_1 1 ok_rewind _ L
check_end_1 _ ok_rewind _ L
ok_rewind 0 ok_rewind 0 L
ok_rewind 1 ok_rewind 1 L
ok_rewind _ look_first _ R
fail_rewind 0 fail_rewind _ L
fail_rewind 1 fail_rewind _ L
fail_rewind _ write_o N R
write_es _ write_s e R
write_o _ done o R
write_s _ done s R
$ ruby tm.rb palindrome.tm 011010110
Yes
$ ruby tm.rb palindrome.tm 01101
No
Just kidding…
Just kidding…
