A pure-Python (Python >= 3.11) package for manipulating:

• Binary decision diagrams (BDDs).
• Multi-valued decision diagrams (MDDs).

as well as Cython bindings to the C libraries:

• CUDD (also read the introduction, and note that the original link for CUDD is http://vlsi.colorado.edu/~fabio/CUDD/)
• Sylvan (multi-core parallelization)
• BuDDy

These bindings expose almost identical interfaces as the Python implementation. The intended workflow is:

• develop your algorithm in pure Python (easy to debug and introspect),
• use the bindings to benchmark and deploy

Your code remains the same.

Contains:

• All the standard functions defined, e.g., by Bryant.
• Dynamic variable reordering using Rudell's sifting algorithm.
• Reordering to obtain a given order.
• Parser of quantified Boolean expressions in either TLA+ or Promela syntax.
• Pre/Image computation (relational product).
• Renaming variables.
• Zero-omitted binary decision diagrams (ZDDs) in CUDD
• Conversion from BDDs to MDDs.
• Conversion functions to networkx and DOT graphs.
• BDDs have methods to dump and load them using JSON, or pickle.
• BDDs dumped by CUDD's DDDMP can be loaded using fast iterative parser.
• Garbage collection that combines reference counting and tracing

If you prefer to work with integer variables instead of Booleans, and have BDD computations occur underneath, then use the module omega.symbolic.fol from the omega package.

If you are interested in computing minimal covers (two-level logic minimization) then use the module omega.symbolic.cover of the omega package. The method omega.symbolic.fol.Context.to_expr converts BDDs to minimal formulas in disjunctive normal form (DNF).

In the Markdown file doc.md.

The changelog is in the file CHANGES.md.

The module dd.autoref wraps the pure-Python BDD implementation dd.bdd. The API of dd.cudd is almost identical to dd.autoref. You can skip details about dd.bdd, unless you want to implement recursive BDD operations at a low level.

from dd.autoref import BDD

bdd = BDD()
bdd.declare('x', 'y', 'z', 'w')

# conjunction (in TLA+ syntax)
u = bdd.add_expr(r'x /\ y')
    # symbols `&`, `|` are supported too
    # note the "r" before the quote,
    # which signifies a raw string and is
    # needed to allow for the backslash
print(u.support)
# substitute variables for variables (rename)
rename = dict(x='z', y='w')
v = bdd.let(rename, u)
# substitute constants for variables (cofactor)
values = dict(x=True, y=False)
v = bdd.let(values, u)
# substitute BDDs for variables (compose)
d = dict(x=bdd.add_expr(r'z \/ w'))
v = bdd.let(d, u)
# as Python operators
v = bdd.var('z') & bdd.var('w')
v = ~ v
# quantify universally ("forall")
u = bdd.add_expr(r'\A x, y:  (x /\ y) => y')
# quantify existentially ("exist")
u = bdd.add_expr(r'\E x, y:  x \/ y')
# less readable but faster alternative,
# (faster because of not calling the parser;
# this may matter only inside innermost loops)
u = bdd.var('x') | bdd.var('y')
u = bdd.exist(['x', 'y'], u)
assert u == bdd.true, u
# inline BDD references
u = bdd.add_expr(rf'x /\ {v}')
# satisfying assignments (models):
# an assignment
d = bdd.pick(u, care_vars=['x', 'y'])
# iterate over all assignments
for d in bdd.pick_iter(u):
    print(d)
# how many assignments
n = bdd.count(u)
# write to and load from JSON file
filename = 'bdd.json'
bdd.dump(filename, roots=dict(res=u))
other_bdd = BDD()
roots = other_bdd.load(filename)
print(other_bdd.vars)

To run the same code with CUDD installed, change the first line to:

from dd.cudd import BDD

Most useful functionality is available via methods of the class BDD. A few of the functions can prove useful too, among them to_nx(). Use the method BDD.dump to write a BDD to a pickle file, and BDD.load to load it back. A CUDD dddmp file can be loaded using the function dd.dddmp.load.

A Function object wraps each BDD node and decrements its reference count when disposed by Python's garbage collector. Lower-level details are discussed in the documentation.

For using ZDDs, change the first line to

from dd.cudd_zdd import ZDD as BDD

From the Python Package Index (PyPI) using the package installer pip:

pip install dd

or from the directory of source files:

pip install .

For graph layout, install also graphviz.

The dd package requires Python 3.11 or later. For Python 2.7, use dd == 0.5.7.

To compile also the module dd.cudd (which interfaces to CUDD) when installing from PyPI, run:

pip install --upgrade wheel cython
export DD_FETCH=1 DD_CUDD=1
pip install dd -vvv --use-pep517 --no-build-isolation

(DD_FETCH=1 DD_CUDD=1 pip install dd also works, when the source tarball includes cythonized code.)

To confirm that the installation succeeded:

python -c 'import dd.cudd'

The environment variables above mean:

• DD_FETCH=1: download CUDD v3.0.0 sources from the internet, unpack the tarball (after checking its hash), and make CUDD.
• DD_CUDD=1: build the Cython module dd.cudd

More about environment variables that configure the C extensions of dd is described in the file doc.md

Wheel files are available from PyPI, which contain the module dd.cudd, with the CUDD library compiled and linked. If you have a Linux system and Python version compatible with one of the PyPI wheels, then pip install dd will install also dd.cudd.

These notes apply to the compiled modules dd.cudd and dd.cudd_zdd that are contained in the wheel file on PyPI (namely the files dd/cudd.cpython-39-x86_64-linux-gnu.so and dd/cudd_zdd.cpython-39-x86_64-linux-gnu.so in the *.whl file, which can be obtained using unzip). These notes do not apply to the source code of the modules dd.cudd and dd.cudd_zdd. The source distribution of dd on PyPI is distributed under a 3-clause BSD license.

The following libraries and their headers were used when building the modules dd.cudd and dd.cudd_zdd that are included in the wheel:

• Python: https://www.python.org/ftp/python/3.A.B/Python-3.A.B.tgz (where A and B the numerals of the corresponding Python version used; for example 10 and 2 to signify Python 3.10.2). CPython releases are described at: https://www.python.org/downloads/
• CUDD.

The licenses of Python and CUDD are included in the wheel archive.

Cython does not add its license to C code that it generates.

GCC was used to compile the modules dd.cudd and dd.cudd_zdd in the wheel, and the GCC runtime library exception applies.

The modules dd.cudd and dd.cudd_zdd in the wheel dynamically link to the:

• Linux kernel (in particular linux-vdso.so.1), which allows system calls (read the kernel's file COPYING and the explicit syscall exception in the file LICENSES/exceptions/Linux-syscall-note)
• GNU C Library (glibc) (in particular libpthread.so.0, libc.so.6, /lib64/ld-linux-x86-64.so.2), which uses the LGPLv2.1 that allows dynamic linking, and other licenses. These licenses are included in the wheel file and apply to the GNU C Library that is dynamically linked.

Use pytest. Run with:

pushd tests/
pytest -v --continue-on-collection-errors .
popd

Tests of Cython modules that were not installed will fail. The code is covered well by tests.

BSD-3, read file LICENSE.