pyddlib

pyddlib is a Python3 library for manipulating decision diagrams (DD).

It is intended to follow (as much as possible) the notation and overall construction proposed in the following papers:

[1] Bryant, Randal E. Graph-based algorithms for boolean function manipulation. Computers, IEEE Transactions on 100, no. 8 (1986): 677-691.

[2] Brace, Karl S., Richard L. Rudell, and Randal E. Bryant. Efficient implementation of a BDD package. In Proceedings of the 27th ACM/IEEE design automation conference, pp. 40-45. ACM, 1991.

[3] Bahar, R. Iris, Erica A. Frohm, Charles M. Gaona, Gary D. Hachtel, Enrico Macii, Abelardo Pardo, and Fabio Somenzi. Algebraic decision diagrams and their applications. Formal methods in system design 10, no. 2-3 (1997): 171-206.

Install

It is required to have Python3 installed.

$ pip3 install pyddlib

Usage

Binary Decision Diagrams (BDDs)

You create BDDs from constants and variables by composing boolean functions with logical operations AND (&), OR (|), XOR (^) and NOT (-).

from pyddlib.bdd import BDD

one  = BDD.one()
zero = BDD.zero()
print("== True ==")
print(one)
print("== False ==")
print(zero)

x1 = BDD.variable(1)
x2 = BDD.variable(2)
x3 = BDD.variable(3)
print("=== x1 ===")
print(x1)

print("=== NOT x1 ===")
print(~x1)

print("=== x1 AND x2 ===")
print(x1 & x2)

print("=== x1 OR x2 ===")
print(x1 | x2)

print("=== x1 XOR x2 ===")
print(x1 ^ x2)

bdd1 = ~x1 | (x2 ^ ~x3)
if (bdd1 & one) == bdd1:
    print('True is the neutral element for AND operation!')

bdd2 = ~(~x2) ^ (~(x1 | x3))
if (bdd2 | zero) == bdd2:
    print('False is the neutral element for OR operation!')

bdd3 = x1 & ~x1
if bdd3.is_zero():
    print('You can check contradiction with is_zero() funtion!')

bdd4 = x1 | ~x1
if bdd4.is_one():
    print('You can check tautology with is_one() function!')

bdd5 = ~(x1 | ~(x2 & ~x3))
if (bdd5 ^ bdd5).is_zero():
    print('You can check equivalence with XOR!')

if (x1 & x2) == (x2 & x1):
    print('Commutative law works for boolean functions!')

if x1 & (x2 & x3) == (x1 & x2) & x3:
    print('Associative law works for boolean functions!')

if (x1 & (x2 | x3)) == ((x1 & x2) | (x1 & x3)):
    print('Distributivity law works: AND distributes over OR!')

if (x1 | (x2 & x3)) == ((x1 | x2) & (x1 | x3)):
    print('Distributivity law works: OR distributes over AND!')

bdd6 = ~(x1 & ~(~x2 | x3))
valuation1 = { 1: True, 2: True, 3: False }

if bdd6.restrict(valuation1).is_zero():
    print('You can evaluate the function with restrict!')

valuation2 = { 1: True }
if bdd6.restrict(valuation2) == (~x2 | x3):
    print('You can also partially evaluate the function with restrict!')

Algebraic Decision Diagrams (ADDs)

You create ADDs from constants and variables by composing arithmetic operations functions +, -, *, /.

from pyddlib.add import ADD

c0 = ADD.constant(0.0)
c1 = ADD.constant(1.0)
c2 = ADD.constant(2.0)
print("=== c1 ===")
print(c1)
print("=== c2 ===")
print(c2)

x1 = ADD.variable(1)
x2 = ADD.variable(2)
x3 = ADD.variable(3)
print("=== x1 ===")
print(x1)

print("=== NOT x1 ===")
print(~x1)

print("=== x1 * x2 * c1 ===")
print(x1 * x2 * c2)

print("=== (x1 + x2) * c2 ===")
print((x1 + x2) * c2)

print("=== x1 - x2 ===")
print(x1 - x2)

add1 = ~x1 + (x2 * ~x3)
if (add1 * c1) == add1:
    print('ADD.constant(1.0) is the neutral element for multiplication!')

add2 = ~(~x2) * (~(x1 + x3))
if (add2 + c0) == add2:
    print('ADD.constant(0.0) is the neutral element for addition!')

add3 = x1 * ~x1
if add3 == c0:
    print('You can check contradiction by comparing with ADD.constant(0.0) !')

add4 = x1 + ~x1
if add4 == c1:
    print('You can check tautology by comparing with ADD.constant(1.0) !')

if (x1 * x2) == (x2 * x1) and (x1 + x2) == (x2 + x1):
    print('Commutative law works for multiplication and addition!')

if x1 * (x2 * x3) == (x1 * x2) * x3 and x1 + (x2 + x3) == (x1 + x2) + x3:
    print('Associative law works for multiplication and addition!')

if (x1 * (x2 + x3)) == ((x1 * x2) + (x1 * x3)):
    print('Distributivity law works: multiplication distributes over addition!')

add5 = x1 * x2 + x3 * c2
valuation = { 1: True, 2: False, 3: True }

if add5.restrict(valuation).value == 2.0:
    print('You can evaluate the function with restrict!')

valuation2 = { 1: True }
if add5.restrict(valuation2) == (x2 + x3 * c2):
    print('You can also partially evaluate the function with restrict!')

LICENSE

pyddlib is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

pyddlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with pyddlib. If not, see http://www.gnu.org/licenses/

thiagopbueno / pyddlib