turing_machine 1.0

Turing Machine as a Python Generator.

This is a simulator of a Turing machine with a singly-infinite tape. The simulator allows one to execute a machine step-by step, check whether a machine accepts or rejects a particular input and see it’s execution.

Contents

• Installation

• Using the simulator in the IPython notebook

• Using the simulator inside of a Python script

• The API

  • Input acceptance

  • Step by step execution

  • Infinite execution

  • Debugging

Installation

There are several ways of getting the simulator.

• PyPi: great if you want to use the package as part of your application:

  pip install turing_machine

• git: if you want to get all the files, most importantly the notebook:

  git clone https://github.com/dimazest/turing_machine.git

• github: if you don’t bother using git:

  wget https://github.com/dimazest/turing_machine/archive/master.zip

Using the simulator in the IPython notebook

The notebook (Turing machine.ipynb) is a great way to run the machine interactively. You need to have a fresh version of IPython installed (>=3.0). Check out these IPython installation instructions using miniconda if you don’t have it installed yet.

Using the simulator inside of a Python script

If you dont want to be bother with IPython, you can use the simulator inside of your own script, see w_hash_w.py, for example:

python w_hash_w.py
q0                             [1]0#10
FindDelimiter1                 X[0]#10
FindDelimiter1                 X0[#]10

...    MANY OTHER CONFIGURATIONS   ...

qa                             XX#XX[]

The API

The package provides the `TuringMachine class which is instantiated with particular transitions. Once a Turing Machine is instantiated it can be executed. Here is an example of a machine that accepts language w#w (two identical words separated by #).

>>> from turing_machine import TuringMachine

>>> w_hash_w = TuringMachine(
...     {
...         ('q0', '#'): ('End', '#', 'R'),
...         ('End', ''): ('qa', '', 'R'),
...
...         ('q0', '0'): ('FindDelimiter0', 'X', 'R'),
...         ('FindDelimiter0', '#'): ('Check0', '#', 'R'),
...         ('Check0', '0'): ('FindLeftmost', 'X', 'L'),
...
...         ('q0', '1'): ('FindDelimiter1', 'X', 'R'),
...         ('FindDelimiter1', '#'): ('Check1', '#', 'R'),
...         ('Check1', '1'): ('FindLeftmost', 'X', 'L'),
...
...         ('FindLeftmost', '0'): ('FindLeftmost', '0', 'L'),
...         ('FindLeftmost', '1'): ('FindLeftmost', '1', 'L'),
...         ('FindLeftmost', 'X'): ('FindLeftmost', 'X', 'L'),
...         ('FindLeftmost', '#'): ('FindLeftmost', '#', 'L'),
...         ('FindLeftmost', ''): ('FindNext', '', 'R'),
...
...         ('FindNext', 'X'): ('FindNext', 'X', 'R'),
...         ('FindNext', '0'): ('FindDelimiter0', 'X', 'R'),
...         ('FindNext', '1'): ('FindDelimiter1', 'X', 'R'),
...         ('FindNext', '#'): ('End', '#', 'R'),
...
...         ('FindDelimiter0', '0'): ('FindDelimiter0', '0', 'R'),
...         ('FindDelimiter0', '1'): ('FindDelimiter0', '1', 'R'),
...         ('FindDelimiter1', '0'): ('FindDelimiter1', '0', 'R'),
...         ('FindDelimiter1', '1'): ('FindDelimiter1', '1', 'R'),
...
...         ('Check0', 'X'): ('Check0', 'X', 'R'),
...         ('Check1', 'X'): ('Check1', 'X', 'R'),
...
...         ('End', 'X'): ('End', 'X', 'R'),
...     }
... )

Input acceptance

Once we got a machine, we can check whether it accepts a particular string:

>>> w_hash_w.accepts('#')
True
>>> w_hash_w.accepts('1#1')
True
>>> w_hash_w.accepts('1#10')
False

or rejects:

>>> w_hash_w.rejects('##')
True
>>> w_hash_w.rejects('#')
False

Step by step execution

The .run() method returns a generator that executes the machine and yields the configuration together with he acceptance decision:

>>> execution = w_hash_w.run('1#1')
>>> action, context = next(execution)
>>> context['state']
'q0'

Infinite execution

Because execution is done in a generator, it’s possible to have infinite executions but the acceptance checks are limited by the number of steps they are allowed to perform.

>>> go_right = TuringMachine(
...     {
...         ('q0', ''): ('q0', '', 'R'),
...     }
... )

If the step limit is reached, None is returned:

>>> go_right.accepts('') is None
True

Do 2000 steps:

>>> go_right.accepts('', step_limit=2000) is None
True

Debugging

Another nice feature is the ability to debug the machine by observing it’s configuration.

>>> w_hash_w.debug('1#1')
q0                             [1]#1
FindDelimiter1                 X[#]1
Check1                         X#[1]
FindLeftmost                   X[#]X
FindLeftmost                   [X]#X
FindLeftmost                   []X#X
FindNext                       [X]#X
FindNext                       X[#]X
End                            X#[X]
End                            X#X[]
qa                             X#X[]