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Library of decision diagrams and algorithms on them, in pure Python, as well as Cython bindings to CUDD, Sylvan, and BuDDy.

Project Description
[![Build Status][build_img]][travis]
[![Coverage Status][coverage]][coveralls]


A pure-Python (3 and 2) package for manipulating:

- [Binary decision diagrams]( (BDDs).
- [Multi-valued decision diagrams]( (MDDs).

as well as [Cython]( bindings to the C libraries:

- [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.


- 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.
- Conversion from BDDs to MDDs.
- Conversion functions to [`networkx`]( and
[`pydot`]( graphs.
- BDDs have methods to `dump` and `load` them using `pickle`.
- BDDs dumped by CUDD's DDDMP can be loaded using fast iterative parser.
- Garbage collection using reference counting

If you prefer to work with integer variables instead of Booleans, and have
BDD computations occur underneath, then use the module
from the [`omega` package](


In the [Markdown]( file


Two interfaces are available:

- convenience: the module
[`dd.autoref`]( wraps
`dd.bdd` and takes care of reference counting
using [`__del__`](

- "low level": the module
[`dd.bdd`]( requires that
the user in/decrement the reference counters associated with nodes that
are used outside of a `BDD`.

## Automated reference counting

The module `dd.autoref` wraps the pure-Python BDD implementation in `dd.bdd`.
A `Function` object wraps a node and decrements its reference count when
disposed by Python's garbage collector:

from dd.autoref import BDD, Function

bdd = BDD()
[bdd.add_var(var) for var in ['x', 'y']]
u = bdd.add_expr('x => y') # TLA+ syntax
u = bdd.add_expr('x -> y') # Promela syntax

# alternative
x = bdd.var('x')
not_x = ~ x
y = bdd.var('y')
v = not_x | y
assert u == v


The interface to CUDD in `dd.cudd` looks similar to `dd.autoref`,
including automated reference counting:

from dd import cudd

bdd = cudd.BDD()
[bdd.add_var(var) for var in ['x', y'']]
u = bdd.add_expr('\E x, y: x /\ y')
assert u == bdd.true, u

# longer alternative
xy = bdd.add_expr('x /\ y')
u = bdd.exist(['x', 'y'], xy)
assert u == bdd.true, u

## Reference counting by the user

The pure-Python module `dd.bdd` can be used directly,
which allows access more extensive than `dd.autoref`.
The `n` variables in a `dd.bdd.BDD` are ordered
from `0` (top level) to `n-1` (bottom level).
The terminal node `1` is at level `n`.

from dd.bdd import BDD

ordering = dict(x=0, y=1)
bdd = BDD(ordering)

Boolean expressions can be added with the method `BDD.add_expr`:

# using TLA+ syntax
u = bdd.add_expr('x \/ y')
v = bdd.add_expr('~ x \/ z')
w = bdd.apply('/\\', u, v)
r = bdd.apply('=>', u, w)

# using Promela syntax
u = bdd.add_expr('x | y')
v = bdd.add_expr('!x | z')
w = bdd.apply('&', u, v)
r = bdd.apply('->', u, w)

# w = bdd.apply('and', u, v) # also available

Garbage collection is triggered either explicitly by the user, or
when invoking the reordering algorithm.
If we invoked garbage collection next,
then the nodes `u`, `v`, `w` would be deleted.
To prevent this from happening, their reference counts should be incremented.
For example, if we want to prevent `w` from being collected as garbage, then


To decrement the reference count:


The more useful functions in `dd.bdd` are:
`image`, `preimage`, `reorder`, `to_nx`, `to_pydot`.

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`.


## pure-Python

Recommended to use `pip`, because the latest version will install
dependencies before `dd`:

pip install dd


python install

If you use the latter, remember to install `ply` before `dd`.
If `ply` is absent, then the parser tables will not be cached, affecting performance.
For graph layout with `pydot`,
[graphviz]( needs to be installed.

## Cython bindings

### `dd` fetching CUDD

By default, the package installs only the Python modules.
You can select to install any Cython extensions using
the `` options:

- `--cudd`
- `--sylvan`
- `--buddy`

Pass `--fetch` to `` to tell it to download, unpack, and `make` CUDD v3.0.0. For example:

pip download dd --no-deps
tar xzf dd-*.tar.gz
cd dd-*
python install --fetch --cudd

The path to an existing CUDD build directory can be passed as an argument:

python install --cudd="/home/user/cudd"

If you prefer defining installation directories, then follow [Cython's instructions]( to define `CFLAGS` and `LDFLAGS` before running ``. You need to have copied `CuddInt.h` to the installation's include location (CUDD omits it).

If building from the repository, then first install `cython`.
For example:

git clone
cd dd
pip install cython # not needed if building from PyPI distro
python install --fetch --cudd

The above options can be passed to `pip` too, using the
in a requirements file, for example:

dd >= 0.1.1 --install-option="--fetch" --install-option="--cudd"

The command line behavior of `pip` [is currently different](, so

pip install --install-option="--fetch" dd

will propagate option `--fetch` to dependencies, and so raise an error.

### User installing build dependencies

If you build and install CUDD, Sylvan, or BuDDy yourself, then ensure that:

- the header files and libraries are present, and
- suitable compiler, include, linking, and library flags are passed,
either by setting [environment variables](
prior to calling `pip`, or by editing the file [``](

Currently, `` expects to find Sylvan under `dd/sylvan` and built with [Autotools]( (for an example, see `.travis.yml`).
If the path differs in your environment, remember to update it.


Require [`nose`]( and the extras. Run with:

cd tests/

If the extension module `dd.cudd` has not been compiled and installed,
then the CUDD tests will fail.

[BSD-3](, see file `LICENSE`.

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