Package: pyddlib
pyddlib=======pyddlib is a Python3 library for manipulating decision diagrams (DD).It is intended to follow (as much as possible) the notation and overallconstruction proposed in the following papers:[1] Bryant, Randal E. **Graph-based algorithms for boolean functionmanipulation**. Computers, IEEE Transactions on 100, no. 8 (1986):677-691.[2] Brace, Karl S., Richard L. Rudell, and Randal E. Bryant. **Efficientimplementation of a BDD package**. In Proceedings of the 27th ACM/IEEEdesign 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 decisiondiagrams 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 pyddlibUsage-----Binary Decision Diagrams (BDDs)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~You create BDDs from constants and variables by composing booleanfunctions with logical operations AND (&), OR (\|), XOR (^) and NOT (-)... code:: pythonfrom pyddlib.bdd import BDDone  = 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 & ~x1if bdd3.is_zero():print('You can check contradiction with is_zero() funtion!')bdd4 = x1 | ~x1if 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 +, -, *, /... code:: pythonfrom pyddlib.add import ADDc0 = 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 * ~x1if add3 == c0:print('You can check contradiction by comparing with ADD.constant(0.0) !')add4 = x1 + ~x1if 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 * c2valuation = { 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-------Copyright (c) 2017 Thiago Pereira Bueno All Rights Reserved.pyddlib is free software: you can redistribute it and/or modify it underthe terms of the GNU Lesser General Public License as published by theFree Software Foundation, either version 3 of the License, or (at youroption) any later version.pyddlib is distributed in the hope that it will be useful, but WITHOUT ANYWARRANTY; without even the implied warranty of MERCHANTABILITY orFITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General PublicLicense for more details.You should have received a copy of the GNU Lesser General Public Licensealong with pyddlib. If not, see http://www.gnu.org/licenses/