3.17 delta : Exclusive-OR operation

Format

.delta()

Description

Find out the exclusive-OR (XOR) operation on on the itemset from the ZDD object which contains and , and return the result of ZDD object as .

For example, XOR operations on itemset abc and bcd are as follows.

abc.delta(bcd) = abcbcd = ad

Find out the XOR operation between multiple itemsets.

(abc + a).delta(bcd + b) = abcbcd + abcb + abcd + ab

= ad + ac + abcd + ab

The weight is computed by expanding the same itemset to multiple instances.

(2abc).delta(bcd) = (abc+abc).delta(bcd) = ad + ad = 2ad

In addition, when is changed to (intersection operation), it becomes delta function.

Example

Example 1: Basic Example

In the following, using items a,b,c, find out the exclusive OR on itemsets 2ab + a + 3b, abc + 2ab + bc + 1, ab+a.

> require 'zdd'
# First, define the itemsets
> a=ZDD::itemset("a")
> b=ZDD::itemset("b")
> c=ZDD::itemset("c")
> f=2*a*b+a+3*b
> f.show
 2 a b + a + 3 b

(2ab + a + 3b)a = 3ab + 2b + 1

> f.delta(a).show
 3 a b + 2 b + 1

(2ab + a + 3b)b = ab + 2a + 3

> f.delta(b).show
 a b + 2 a + 3

(2ab + a + 3b)ab = 3a + b + 2

> f.delta(a*b).show
 3 a + b + 2

(2ab + a + 3b)1 = 2ab+a+3b Since constant 1 is an empty itemset, it is remained in the original set for solving XOR operation.

> f.delta(1).show
 2 a b + a + 3 b

The operation result of the each term in (abc + 2ab + bc + 1)(2ab + a) are as follows:

• abc 2ab = 2c

• 2ab 2ab = 4

• bc 2ab = 2ac

• 1 2ab = 2ab

• abc a = bc

• 2ab a = 2b

• bc a = abc

• 1 a = a

The result is summarized as a b c + 2 a b + 2 a c + a + b c + 2 b + 2 c + 4.

> g=((a*b*c)+2*(a*b)+(b*c)+1)
> h=2*a*b + a
> g.show
 a b c + 2 a b + b c + 1
> h.show
 2 a b + a
> g.delta(h).show
 a b c + 2 a b + 2 a c + a + b c + 2 b + 2 c + 4

See Also