*This is exercise 7.1.4-12 in TAoCP. It is easy, but somehow I liked the solution.*

A BDD (**b**inary **d**ecision **d**iagram) is a data structure
that encodes boolean functions. Each node has a *variable* and two
children, *low* and *high*. To make it concrete, let's pick a
C-language structure.

struct dd_node { int V; // variable, at least 1 and at most N int L, H; // indexes in nodes }; struct dd_node nodes[nodes_size];

A valid BDD representation obeys a few constraints.

- nodes[k].L!=nodes[k].H for k≥2
- nodes[k].L==nodes[k].H==k for k<2
- nodes[nodes[k].X].V>nodes[k].V for k≥2 and X either L or R
- nodes[k]==nodes[kk] implies k==kk
- For all 2≤k<nodes_size there is a kk such that nodes[kk].L==k || nodes[kk].R==k.

Each such node basically encodes a (!v?l:h) expression. For example, if value[V] is the value of variable V then the represented boolean function is evaluated by eval(value, nodes_size-1).

int eval(int* value, int k) { if (k < 2) return k; return !value[nodes[k].V]? eval(value, nodes[k].L) : eval(value, nodes[k].H); }

Here comes the problem. Suppose you are given two BDDs, nodes1 of size s1 and nodes2 of size s2. Design an algorithm to decide if they represent the same boolean function. And, by the way, do not use a stack, not even the call stack.

## No comments:

## Post a Comment

Note: (1) You need to have third-party cookies enabled in order to comment on Blogger. (2) Better to copy your comment before hitting publish/preview. Blogger sometimes eats comments on the first try, but the second works. Crazy Blogger.