Turing Machine as a Python Generator.
Project description
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[]
