Cardinality-CDCL

CDCL with native cardinality constraint handling.

Solver and Checker:

• CaDiCaL (https://github.com/arminbiere/cadical Commit a5f15211db36c3956764e18194dd5bd63bf3b5e6)
• Drat-trim (https://github.com/marijnheule/drat-trim)

Build

To build use

sh build.sh

To clean use

sh clean.sh

General Usage

Solver configurations include:

• CCDCL: cardinality-based CDCL solver (native propagation on cardinality constraints)
• CCDCL+: cardinality-based CDCL solver with reencoded constraints (Hybrid mode from the paper)
• ReEncode: basic CaDiCaL CDCL solver with reencoded constraints

For general usage with a KNF formula as input, you can use the cardinality CDCL solver directly with:

> ./cardinality-cadical/build/cadical <KNF> <Proof> --no-binary

Where <Proof> --no-binary can be left off if you do not need proof logging.

If you want to extract cardinality constraints from a CNF, or use one of the configurations that reencodes cardinality constraints into clauses, you should use one of the scripts below.

The scripts also provide proof checking.

KNF format

Header : p knf <nVariables> <nKlauses>

Cardinality Constraint : k <bound> [<lit>] 0

x1 + x3 + -x5 >= 2 : k 2 1 3 -5 0

Clauses written in standard dimacs format

(x1 OR x2 OR -x5) : 1 2 -5 0

Note, KNF does not support duplicate literals or opposing literals in cardinality constraints.

Remove opposing literals and update the bound appropriately in a preprocessing step before calling the solver.

E.g., x1 + -x1 + x2 + x3 >= 2 can be replaced by x2 + x3 >= 1.

Duplicate literals can be replaced by new variables in a preprocessing step before calling the solver.

E.g., x1 + x1 + x2 >= 1 can be replaced by x3 + x4 + x2 >= 1 AND x1 <-> x3 AND x1 <-> x4.

Running Scripts

Proof checking is enabled with 1 and disabled with 0.

To run configurations from the paper (on input CNF), and check result (as described in the paper):

• CaDiCaL: > sh scripts/cadical <CNF> <ProofChecking>
• CCDCL: > sh scripts/ccdcl <CNF> <ProofChecking>
• CCDCL+ (Hybrid mode): > sh scripts/ccdclPlus <CNF> <ProofChecking>
• ReEncode: > sh scripts/ReEncode <CNF> <ProofChecking>

e.g. with proog checking, sh scripts/ccdcl.sh benchmarks/cnf/php8.cnf 1

To run configurations from the paper (on input KNF), and check result (as described in the paper):

• CCDCL: > sh scripts/ccdcl <KNF> <ProofChecking>
• CCDCL+ (Hybrid mode): > sh scripts/ccdclPlus <KNF> <ProofChecking>
• ReEncode: > sh scripts/ReEncode <KNF> <ProofChecking>

e.g. with proog checking, sh scripts/ccdcl.sh benchmarks/knf/php8.knf 1

The folder tmp will contain formulas and proofs when executing the scripts.

To extract a KNF from a CNF, use

sh scripts/Extract.sh <CNF> <OUT.knf>

To reencode a KNF into CNF, for the Linear encoding of AMO use

./Tools/knf2cnf <KNF> > <OUT.cnf>

for the pairwise encoding of AMO constraints use

./Tools/pairwise <KNF> > <OUT.cnf>

To generate the derivation for the Linear AMO reencoding, use

./Tools/derivation <KNF> > <OUT.drat>

Encoding KNFs with PySAT Encodings

First install the PySAT module (https://pysathq.github.io/docs/html/api/card.html)

python3 Tools/pysat_encode.py -k <KNF input> -c <CNF output> -e <encoding type [seqcounter, totalizer, sortnetwrk, cardnetwrk, mtotalizer, kmtotalizer]>

Example execution

python3 Tools/pysat_encode.py -k Benchmarks/KNF/magicsq-3.knf -c magicsq-3.cnf -e kmtotalizer

Data

For extraction and solving on the SAT Annivesary track benchmarks, as well as an extractor compariosn on PySAT.Card encodings, refer to the CAV24 repository: https://github.com/jreeves3/CAV24-FromClausesToKlauses and paper: https://www.cs.cmu.edu/~jereeves/research/cav24-paper.pdf