ApproxMC6: Approximate Model Counter

ApproxMCv6 is a state-of-the-art approximate model counter using Arjun and CryptoMiniSat to give probabilistic approximate model counts to problems of size and complexity that were not possible before.

This work is the culmination of work by a number of people, including but not limited to, Mate Soos, Jiong Yang, Stephan Gocht, Yash Pote, and Kuldeep S. Meel. Publications: published in AAAI-19, in CAV2020, and in CAV2023.

ApproxMC handles CNF formulas and performs approximate counting.

1. If you are interested in exact model counting, visit our exact counter Ganak
2. If you are instead interested in DNF formulas, visit our approximate DNF counter Pepin.

Installation

We recommend using a prebuilt binary from our release page which contains binaries for many different platforms. The second best thing to use is Nix. Simply install nix and then:

nix profile install github:meelgroup/approxmc

Then you will have approxmc binary available and ready to use.

Providing a Projection Set

For some applications, one is not interested in solutions over all the variables and instead interested in counting the number of unique solutions to a subset of variables, called sampling set (also called a "projection set"). ApproxMC allows you to specify the sampling set using the following modified version of DIMACS format:

$ cat myfile.cnf
c p show 1 3 4 6 7 8 10 0
p cnf 500 1
3 4 0

Above, using the c p show line, we declare that only variables 1, 3, 4, 6, 7, 8 and 10 form part of the sampling set out of the CNF's 500 variables 1,2...500. This line must end with a 0. The solution that ApproxMC will be giving is essentially answering the question: how many different combination of settings to this variables are there that satisfy this problem? Naturally, if your sampling set only contains 7 variables, then the maximum number of solutions can only be at most 2^7 = 128. This is true even if your CNF has thousands of variables.

Running ApproxMC

In our case, the maximum number of solutions could at most be 2^7=128, but our CNF should be restricting this. Let's see:

$ approxmc --seed 5 myfile.cnf
c ApproxMC version 3.0
[...]
c CryptoMiniSat SHA revision [...]
c Using code from 'When Boolean Satisfiability Meets Gauss-E. in a Simplex Way'
[...]
[appmc] using seed: 5
[appmc] Sampling set size: 7
[appmc] Sampling set: 1, 3, 4, 6, 7, 8, 10,
[appmc] Using start iteration 0
[appmc] [    0.00 ] bounded_sol_count looking for   73 solutions -- hashes active: 0
[appmc] [    0.01 ] bounded_sol_count looking for   73 solutions -- hashes active: 1
[appmc] [    0.01 ] bounded_sol_count looking for   73 solutions -- hashes active: 0
[...]
[appmc] FINISHED ApproxMC T: 0.04 s
c [appmc] Number of solutions is: 48*2**1
s mc 96

ApproxMC reports that we have approximately 96 (=48*2) solutions to the CNF's independent support. This is because for variables 3 and 4 we have banned the false,false solution, so out of their 4 possible settings, one is banned. Therefore, we have 2^5 * (4-1) = 96 solutions.

Guarantees

ApproxMC provides so-called "PAC", or Probably Approximately Correct, guarantees. In less fancy words, the system guarantees that the solution found is within a certain tolerance (called "epsilon") with a certain probability (called "delta"). The default tolerance and probability, i.e. epsilon and delta values, are set to 0.8 and 0.2, respectively. Both values are configurable.

How to use the Python interface

Install using pip:

pip install pyapproxmc

Then you can use it as:

import pyapproxmc
c = pyapproxmc.Counter()
c.add_clause([1,2,3])
c.add_clause([3,20])
count = c.count()
print("Approximate count is: %d*2**%d" % (count[0], count[1]))

The above will print that Approximate count is: 11*2**16. Since the largest variable in the clauses was 20, the system contained 2**20 (i.e. 1048576) potential models. However, some of these models were prohibited by the two clauses, and so only approximately 11*2**16 (i.e. 720896) models remained.

If you want to count over a projection set, you need to call count(projection_set), for example:

import pyapproxmc
c = pyapproxmc.Counter()
c.add_clause([1,2,3])
c.add_clause([3,20])
count = c.count(range(1,10))
print("Approximate count is: %d*2**%d" % (count[0], count[1]))

This now prints Approximate count is: 7*2**6, which corresponds to the approximate count of models, projected over variables 1..10.

Library usage

The system can be used as a library:

#include <approxmc/approxmc.h>
#include <vector>
#include <cassert>

using std::vector;
using namespace ApproxMC;
using namespace CMSat;

int main() {
    AppMC appmc;
    appmc.new_vars(10);

    vector<Lit> clause;

    //add "-3 4 0"
    clause.clear();
    clause.push_back(Lit(2, true));
    clause.push_back(Lit(3, false));
    appmc.add_clause(clause);

    //add "3 -4 0"
    clause.clear();
    clause.push_back(Lit(2, false));
    clause.push_back(Lit(3, true));
    appmc.add_clause(clause);

    SolCount c = appmc.count();
    uint32_t cnt = std::pow(2, c.hashCount)*c.cellSolCount;
    assert(cnt == std::pow(2, 9));

    return 0;
}

ApproxMC5: Sparse-XOR based Approximate Model Counter

Note: this is beta version release, not recommended for general use. We are currently working on a tight integration of sparse XORs into ApproxMC based on our LICS-20 paper. You can turn on the sparse XORs using the flag --sparse 1 but beware as reported in LICS-20 paper, this may slow down solving in some cases. It is likely to give a significant speedup if the number of solutions is very large.

Issues, questions, bugs, etc.

Please click on "issues" at the top and create a new issue. All issues are responded to promptly.

How to Cite

If you use ApproxMC, please cite the following papers: AAAI-19, in CAV2020, and in CAV2023. CAV20, AAAI19 and IJCAI16. If you use sparse XORs, please also cite the LICS20 paper. ApproxMC builds on a series of papers on hashing-based approach: Related Publications

The benchmarks used in our evaluation can be found here.