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An Active Automata Learning Library

Python application CodeQL PyPI - Downloads

GitHub issues GitHub pull requests Python 3.6 PyPI - Wheel Binder Maintenance License: MIT

AALpy is a light-weight active automata learning library written in pure Python. You can start learning automata in just a few lines of code.

Whether you work with regular languages or you would like to learn models of (black-box) reactive systems, AALpy supports a wide range of modeling formalisms, including deterministic, non-deterministic, and stochastic automata.

Automata Type Supported Formalisms Features
Deterministic Deterministic Finite Automata
Mealy Machines
Moore Machines
Counterexample Processing
Seamless Caching
11 Equivalence Oracles
Non-Deterministic Observable Non-Deterministic FSM
Abstracted Non-Deterministic FSM
Size Reduction Trough Abstraction
Stochastic Markov Decision Processes
Stochastic Mealy Machines
Markov Chains
Counterexample Processing
Row/Cell Compatability Metrics
Model Checking with PRISM
Alergia Passive Learning

AALpy enables efficient learning by providing a large set 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 and caching.

AALpy also has an efficient implementation of the ALERGIA algorithm, suited for passive learning of Markov Chains and Markov Decision processes. With ALERGIA, one can also passively learn deterministic Moore machines.


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 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)

Binder contains many examples and it is a great starting point.


All automata learning procedures follow this high-level approach:

For more detailed examples, check out: contains examples covering almost the whole AALpy's functionality, and it is a great starting point/reference. Wiki has a step-by-step guide to using AALpy and can help you understand AALpy and automata learning in general.

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('', 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()

# loaded or randomly generated automata are considered as BLACK-BOX that is queried
# learning algorithm has no knowledge about its structure
# 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

Selected Applications

AALpy has been used to:

Cite AALpy and Research Contact

If you use AALpy in your research, please cite:

	title = {{AALpy}: An Active Automata Learning Library},
	author = {Edi Mu\v{s}kardin and Bernhard K. Aichernig and Ingo Pill and Andrea Pferscher and Martin Tappler},
	booktitle = {Automated Technology for Verification and Analysis - 19th International
	Symposium, {ATVA} 2021, Gold Coast, Australia, October 18-22, 2021, Proceedings},
	series    = {Lecture Notes in Computer Science},  
	publisher = {Springer},
	year      = {2021},

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


Pull requests are welcome. For significant changes, please open an issue first to discuss what you would like to change. In case of any questions or possible bugs, please open issues.