Recursive methods on CUDD

Question

This is a follow-up to a suggestion by @DCTLib in the post below.

Cudd_PrintMinterm, accessing the individual minterms in the sum of products

I've been pursuing part (b) of the suggestion and will share some pseudo-code in a separate post.

Meanwhile, in his part (b) suggestion, @DCTLib posted a link to https://github.com/VerifiableRobotics/slugs/blob/master/src/BFAbstractionLibrary/BFCudd.cpp. I've been trying to read this program. There is a recursive function in the classic Somenzi paper, Binary Decision Diagrams, which describes an algo to compute the number of satisfying assignments (below, Fig. 7). I've been trying to compare the two, slugs and Fig. 7. But having a hard time seeing any similarities. But then C is mostly inscrutable to me. Do you know if slugs BFCudd is based on Somenze fig 7, @DCTLib?

Thanks, Gui

Answer 1

It's not exactly the same algorithm.

There are two main differences:

First, the "SatHowMany" function does not take a cube of variables to consider for counting. Rather, that function considers all variables. The fact that "recurse_getNofSatisfyingAssignments" supports cubes manifest in the function potentially returning NaN (not a number) if a variable is found in the BDD that does not appear in the cube. The rest of the differences seem to stem from this support.

Second, SatHowMany returns the number of satisfying assignments to all n variables for a node. This leads, for instance, to the division by 2 in line -4. "recurse_getNofSatisfyingAssignments" only returns the number of assignments for the remaining variables to be considered.

Both algorithms cache information - in "SatHowMany", it's called a table, in "recurse_getNofSatisfyingAssignments" it's called a buffer. Note that in line 24 of "recurse_getNofSatisfyingAssignments", there is a constant string thrown. This means that either the function does not work, or the code is never reached. Most likely it's the latter.

Function "SatHowMany" seems to assume that it gets a BDD node - it cannot be a pointer to a complemented BDD node. Function "recurse_getNofSatisfyingAssignments" works correctly with complemented nodes, as a DdNode* may store a pointer to a complemented node.

Due to the support for cubes, "recurse_getNofSatisfyingAssignments" supports flexible variable ordering (hence the lookup of "cuddI" which denotes for a variable where it is in the current BDD variable ordering). For function SatHowMany, the variable ordering does not make a difference.