Turing machine - Revision history

Jnc: Bold 'Turing complete' (for use as a target)

2024-04-10T04:21:03Z

Bold 'Turing complete' (for use as a target)

Jnc: Add category, some external links to toy physical ones, etc

2024-04-08T18:13:41Z

Add category, some external links to toy physical ones, etc

Jonathanjo: From wanted pages

2024-04-07T12:45:27Z

From wanted pages

New page

[[File:Minksy-computation-fig-6.0.1.png|right|thumb|A blank Turing machine from Minsky's ''Computation: Finite and Infinite Machines'']]

A '''Turing Machine''' is a kind of abstract computer, devised by mathematician [[Alan Turing]] in 1936, to develop theories of ''computability'' -- that which can, and which cannot, be computed.

The classic introduction to this kind of machine is MIT professor Marvin Minksy's ''Computation: Finite and Infinite Machines'' (Prentice-Hall 1967):

<blockquote>
A Turing machine is a finite-state machine associated with an external
storage or memory medium. This medium has the form of a sequence of
''squares'', marked of on a linear ''tape''. The machine is couple to the tape
through a ''head'', which is situated, at each moment, on some square of the
tape (see fig). The head has three functions, all of which are exercised
in each operation cycle of the finite-state machine. The functions are:
''reading'' the square of the tape beeing "scanned," ''writing'' on the scanned
square, and ''moving'' the machine to an adjacent square (which becomes the
scanned square in the next operation cycle).
</blockquote>

The basic operation is that each square can have a single symbol from a finite
set of symbols; each step possibly changes the symbol and moves the tape to the
left or the right.

They are comprehensively covered in computing literature, with endless variations, including a large number of physical implementations.

A number of very important theoretical results came from study of these machines:

* A Turing machine is adequate to simulate any other kind of automata, ignoring specified size and speed constraints.
* A machine which can simulate a Turing machine can therefore simulate ''any'' machine and is said to be ''Turing complete''.

@@ Line 17: / Line 17: @@
 </blockquote>
-The basic operation is that each square can have a single symbol from a finite
+The basic operation is that each square can have a single symbol from a finite set of symbols; each step possibly changes the symbol and moves the tape to the left or the right.
 They are comprehensively covered in computing literature, with endless variations, including a large number of physical implementations.
@@ Line 25: / Line 23: @@
 A number of very important theoretical results came from study of these machines:
-* A Turing machine is adequate to simulate any other kind of automata, ignoring specified size and speed constraints.
+* A Turing machine is adequate to simulate any other kind of [[automata]], ignoring specified size and speed constraints.
-* A machine which can simulate a Turing machine can therefore simulate ''any'' machine and is said to be ''Turing complete''.
+* A machine which can simulate a Turing machine can therefore simulate ''any'' machine and is said to be '''Turing complete'''.
 {{semi-stub}}

@@ Line 1: / Line 1: @@
-[[File:Minksy-computation-fig-6.0.1.png|right|thumb|A blank Turing machine from Minsky's ''Computation: Finite and Infinite Machines'']]
+[[File:Minksy-computation-fig-6.0.1.png|right|thumb|250px|A blank Turing machine from Minsky's ''Computation: Finite and Infinite Machines'']]
-A '''Turing Machine''' is a kind of abstract computer, devised by mathematician [[Alan Turing]] in 1936, to develop theories of ''computability'' -- that which can, and which cannot, be computed.
+A '''Turing machine''' is an abstract [[computer]] (ironically, created before the first real computer), devised by mathematician [[Alan Turing]] in 1936, to develop theories of ''computability'' -- that which can, and which cannot, be computed.
-The classic introduction to this kind of machine is MIT professor Marvin Minksy's ''Computation: Finite and Infinite Machines'' (Prentice-Hall 1967):
+The classic introduction to this kind of machine is MIT professor [[Marvin Minksy]]'s ''Computation: Finite and Infinite Machines'' (Prentice-Hall 1967):
 <blockquote>
@@ Line 12: / Line 12: @@
 tape (see fig).  The head has three functions, all of which are exercised
 in each operation cycle of the finite-state machine.  The functions are:
-''reading'' the square of the tape beeing "scanned," ''writing'' on the scanned
+''reading'' the square of the tape being ''scanned'', ''writing'' on the scanned
 square, and ''moving'' the machine to an adjacent square (which becomes the
 scanned square in the next operation cycle).
@@ Line 27: / Line 27: @@
 * A Turing machine is adequate to simulate any other kind of automata, ignoring specified size and speed constraints.
 * A machine which can simulate a Turing machine can therefore simulate ''any'' machine and is said to be ''Turing complete''.