Fold-BDD

Library for folding (or reducing) over a Reduced Ordered Binary Decision Diagram.

Installation

If you just need to use fold_bdd, you can just run:

$ pip install fold-bdd

For developers, note that this project uses the poetry python package/dependency management tool. Please familarize yourself with it and then run:

$ poetry install

Usage

The fold-bdd library supports two types of folds:

1. Folding over the DAG of a BDD starting at the root and then recursively merging the low and high branches until the True/False leaves. This is simply a compressed variant of a post-order traversal.

2. Folding over a path in the DAG, starting at the root and moving the the corresponding leaf (left fold).

In both cases, local context such as the levels of the parent and child nodes are passed in.

As input, each of these take in a bdd, from the dd library and function for accumulating or merging.

The following example illustrates how to use fold_bdd to count the number of solutions to a predicate using post_order and evaluate a path using fold_path.

Create ROBDD

# Create BDD.
from dd.cudd import BDD

manager = BDD()
manager.declare('x', 'y')
manager.reorder({'x': 1, 'y': 0})
manger.configure(reordering=False)

bexpr = manager.add_expr('x | y')

Post-Order Examples

from fold_bdd import post_order

Count Number of Nodes in BDD

def merge1(ctx, low=None, high=None):
    return 1 if low is None else low + high

def dag_size(bexpr):
    return post_order(bexpr, merge1)

assert bexpr.dag_size == dag_size(bexpr)

Count Number of Solutions to bexpr.

def merge2(ctx, low, high):
    if ctx.is_leaf:
        return ctx.skipped_paths if ctx.node_val else 0
    return (low + high) * ctx.skipped_paths

def count_solutions(bexpr):
    return post_order(bexpr, merge2)

assert count_solutions(bexpr) == 3

Fold Path Examples

Count nodes along path.

def merge(ctx, val, acc):
    return acc + 1

def count_nodes(bexpr, vals):
    return fold_path(merge, bexpr, vals, initial=0)

assert count_nodes(bexpr, (False, False)) == 3
assert count_nodes(bexpr, (True, False)) == 2

Count paths corresponding to BDD path

def merge(ctx, val, acc):
    return acc * ctx.skipped_paths

def count_paths(bexpr, vals):
    return fold_path(merge, bexpr, vals, initial=1)

assert count_paths(bexpr, (False, True)) == 1
assert count_paths(bexpr, (True, False)) == 2

Context Object Attributes

The Context object contains exposes attributes

• node_val: Union[str, bool] # Node name or leaf value.
• negated: bool # Is the edge to prev node negated.
• max_lvl: int # How many decision variables are there.
• curr_lvl: int # Which decision is this.
• prev_lvl: Optional[int] # Which decision was the parent. None if root.
• low_lvl: Optional[int] # Which decision does the False edge point to. None if leaf.
• high_lvl: Optional[int] # Which decision does the True edge point to. None if leaf.
• is_leaf: bool # Is the current node a leaf.
• skipped: int # How many decisions were skipped on edge to this node.