pcerman / bdd-racket

Implementation of the Binary Decision Diagrams in Racket

Binary Decision Diagrams (bdd-racket)

This is experimental library which implements Binary Decision Diagrams (BDD) in Racket programming language. This is not production library. It will be changed without preserving backward compatibility in the future. Library implements Reduced Ordered Binary Decision Diagrams (ROBDD) and Zero-Suppressed Binary Decision Diagrams (ZDD). My intent is to add implementation of functions transforming ROBDD into ZDD and vice versa. I was inspired by papers [1], [2].

License

This code is released under MIT License.
Copyright (c) 2016 Peter Cerman (https://github.com/pcerman)

Example of use

ROBDD

(require "bdd.rkt" "robdd.rkt")

(define ex '(xor (xor x y) z))

;; create ROBDD for this boolean expression
(define bdd (make-robdd ex '(x y z)))

;; create graph representation of this ROBDD and write it into the file
(bdd->tgf bdd "bdd.tgf" '(x y z))

;; count number of solutions which evaluates to boolean value true
(robdd-sat-count bdd 3)
;; it returns: 4

;; transform ROBDD into boolean expression
(robdd->b-expr bdd '(x y z))
;; it returns: '(or (and x (or (and y z) (and (not y) (not z))))
;;                  (and (not x) (or (and y (not z)) (and (not y) z))))

Graph representation of the ROBDD from example:

ZDD

(require "bdd.rkt" "zdd.rkt")

(define ex '(xor (xor x y) z))

;; create ZDD for this boolean expression
(define zdd (make-zdd ex '(x y z)))

;; create graph representation of this ZDD and write it into the file
(bdd->tgf zdd "zdd.tgf" '(x y z))

;; count number of solutions which evaluates to boolean value true
(zdd-count zdd)
;; it returns: 4

;; transform ZDD into boolean expression
(zdd->b-expr zdd '(x y z))
;; it returns: '(or (and x (or (and y z) (and (not y) (not z))))
;;                  (and (not x) (or (and y (not z)) (and (not y) z))))

Graph representation of the ZDD from example. It represents subset { {x}, {y}, {z}, {x,y,z} } of powerset from {x,y,z}.

References

1. Henrik Reif Andersen, An Introduction to Binary Decision Diagrams, Lecture notes for 49285 Advanced Algorithms E97, October 1997, Department of Information Technology, Technical University of Denmark
2. Shin-ichi Minato, Zero-suppressed BDDs and their applications, International Journal on Software Tools for Technology Transfer, May 2001, Volume 3, Issue 2, pp 156–170, doi:10.1007/s100090100038