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.

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[]