AALpy is a light-weight active automata learning library written in pure Python. By implementing a single method and a few lines of configuration, you can start learning automata.

Whether you work with regular languages or you would like to learn models of reactive systems, AALpy supports a wide range of modeling formalisms, including deterministic, non-deterministic, and stochastic automata. You can use it to learn deterministic finite automata, Moore machines, and Mealy machines of deterministic systems. If the system that you would like to learn shows non-deterministic or stochastic behavior, AALpy allows you to learn observable nondeterministic finite-state machines, Markov decision processes, or stochastic transducers.

AALpy enables efficient learning by providing a large array of equivalence oracles, implementing various conformance testing strategies. Learning is mostly based on Angluin's L* algorithm, for which AALpy supports a selection of optimizations, including efficient counterexample processing. Finally, support for learning abstracted non-deterministic Mealy machines enables efficient learning of system models with large input space.

If you miss a specific feature in AALpy, you can easily extend it.


Use the package manager pip to install AALpy.

pip install aalpy

The minimum required version of Python is 3.6.
Ensure that you have Graphviz installed and added to your path if you want to visualize models.

For manual installation, clone the master and install the following dependency.

pip install pydot
# and to install the library
python setup.py install

Documentation and Wiki

If you are interested in automata learning or would like to understand the automata learning process in more detail,
please check out our Wiki. On Wiki, you will find more detailed examples on how to use AALpy.

For the official documentation of all classes and methods, check out:

Interactive examples can be found in the notebooks folder.
If you would like to interact/change those examples in the browser, click on the following badge. (Navigate to the notebooks folder and select one notebook)


Examples.py contains many examples demonstrating all AALpy functionality are presented.


All automata learning procedures follow this high-level approach:

If you would like to learn a black-box Date Validator's behavior, your AALpy configuration would look something like this:

from aalpy.base import SUL
from aalpy.utils import visualize_automaton, DateValidator
from aalpy.oracles import StatePrefixEqOracle
from aalpy.learning_algs import run_Lstar

class DateSUL(SUL):
    An example implementation of a system under learning that 
    can be used to learn the behavior of the date validator.

    def __init__(self):
        # DateValidator is a black-box class used for date string verification
        # The ormat of the dates is %d/%m/%Y'
        # Its method is_date_accepted returns True if date is accepted, False otherwise
        self.dv = DateValidator()
        self.string = ""

    def pre(self):
        # reset the string used for testing
        self.string = ""

    def post(self):

    def step(self, letter):
        # add the input to the current string
        if letter is not None:
            self.string += str(letter)

        # test if the current sting is accepted
        return self.dv.is_date_accepted(self.string)

# instantiate the SUL
sul = DateSUL()

# define the input alphabet
alphabet = list(range(0, 9)) + ['/']

# define a equivalence oracle

eq_oracle = StatePrefixEqOracle(alphabet, sul, walks_per_state=500, walk_len=15)

# run the learning algorithm

learned_model = run_Lstar(alphabet, sul, eq_oracle, automaton_type='dfa')
# visualize the automaton

The following snippet demonstrates a short example in which an automaton is either loaded or randomly generated and then learned.

from aalpy.utils import load_automaton_from_file, save_automaton_to_file, visualize_automaton, generate_random_dfa
from aalpy.SULs import DfaSUL
from aalpy.oracles import RandomWalkEqOracle
from aalpy.learning_algs import run_Lstar

# load an automaton
automaton = load_automaton_from_file('path_to_the_file.dot', automaton_type='dfa')

# or randomly generate one
random_dfa = generate_random_dfa(alphabet=[1,2,3,4,5],num_states=20, num_accepting_states=8)
big_random_dfa = generate_random_dfa(alphabet=[1,2,3,4,5],num_states=2000, num_accepting_states=500)

# get input alphabet of the automaton
alphabet = random_dfa.get_input_alphabet()

# create a SUL instance for the automaton/system under learning
sul = DfaSUL(random_dfa)

# define the equivalence oracle
eq_oracle = RandomWalkEqOracle(alphabet, sul, num_steps=5000, reset_prob=0.09)

# start learning
learned_dfa = run_Lstar(alphabet, sul, eq_oracle, automaton_type='dfa')

# save automaton to file and visualize it
save_automaton_to_file(learned_dfa, path='Learned_Automaton', file_type='dot')

# visualize automaton
# or just print its DOT representation

To make experiments reproducible, define a random seed at the beginning of your program.

from random import seed
seed(2) # all experiments will be reproducible

For more detailed examples, check out:

Cite AALpy

If you use AALpy in your research, please cite:

To be announced, please contact [email protected]tria.com in the meantime. 

Research Contact

If you have research suggestions or need specific help concerning your research, feel free to contact [email protected].
We are happy to help you and consult you in applying automata learning in various domains.