splr 0.11.0

A modern SAT Solver for Propositional Logic in Rust

Splr is a modern SAT solver in Rust, based on Glucose 4.1. It adopts various research results on modern SAT solvers:

• CDCL, watch literals, LBD and so on from Glucose, Minisat and the ancestors
• Glucose-like dynamic blocking/forcing restarts
• pre/in-processor to simplify CNF
• branching variable selection based on Learning Rate Based Branching with Reason Side Rewarding or EVSIDS
• chronological backtrack
• CaDiCaL-like extended phase saving
• restart stabilization inspired by CadiCaL
• clause vivification

Many thanks to SAT researchers.

Please check ChangeLog about recent updates.

Correctness

Though Splr comes with ABSOLUTELY NO WARRANTY, I'd like to show some results.

Version 0.11.0

• all the certifications of UUF250 were correct and verified with Grad.
• SAT Race 2019, Benchmarks -- splr-0.11.0 RC (84895b21) solved with a 300 sec timeout:
  • 43 satisfiable problems: all the solutions were correct.
  • 7 unsatisfiable problems: all the certifications were verified with Grad.

Install

Just run cargo install splr after installing the latest cargo. Two executables will be installed:

• splr -- the solver
• dmcr -- a very simple model checker to verify a satisfiable assignment set generated by splr.

Alternatively, Nix users can use nix build.

Usage

Splr is a standalone program, taking a CNF file. The result will be saved to a file, which format is defined by SAT competition 2011 rules.

unif-k3-r4.25-v360-c1530-S1293537826-039.cnf       360,1530 |time:   251.06
 #conflict:    2402204, #decision:      4410993, #propagate:      129058093
  Assignment|#rem:      351, #fix:        0, #elm:        9, prg%:   2.5000
      Clause|Remv:    70187, LBD2:      613, BinC:        2, Perm:     1523
     Restart|#BLK:        0, #RST:     3655, *scl:        1, sclM:       32
         LBD|avrg:   9.9065, trnd:   0.7834, depG:   3.0248, /dpc:     1.17
    Conflict|tASG:   0.9294, cLvl:    16.08, bLvl:    14.93, /ppc:    56.35
        misc|vivC:      861, subC:        0, core:      125, /cpr:  2900.25
      Result|file: ./ans_unif-k3-r4.25-v360-c1530-S1293537826-039.cnf
s SATISFIABLE: cnfs/unif-k3-r4.25-v360-c1530-S1293537826-039.cnf

$ cat ans_unif-k3-r4.25-v360-c1530-S1293537826-039.cnf
c This file was generated by splr-0.11.0 for cnfs/unif-k3-r4.25-v360-c1530-S1293537826-039.cnf
c 
c unif-k3-r4.25-v360-c1530-S1293537826-039.cnf, #var:      360, #cls:     1530
c  #conflict:    2402204, #decision:      4410993, #propagate:      129058093,
c   Assignment|#rem:      351, #fix:        0, #elm:        9, prg%:   2.5000,
c       Clause|Remv:    70187, LBD2:      613, BinC:        2, Perm:     1523,
c      Restart|#BLK:        0, #RST:     3655, *scl:        1, sclM:       32,
c          LBD|avrg:   9.9065, trnd:   0.7834, depG:   3.0248, /dpc:     1.17,
c     Conflict|tASG:   0.9294, cLvl:    16.08, bLvl:    14.93, /ppc:    56.35,
c         misc|vivC:       90, subC:        0, core:      125, /cpr:  2900.25,
c     Strategy|mode:  generic, time:   251.07,
c 
c   config::ChronoBtThreshold                      100
c   config::ClauseRewardDecayRate                 0.95
c   config::InprocessorInterval                  10000
c   config::RestartAsgThreshold                    0.6
c   config::RestartLbdThreshold                    1.6
c   config::VarRewardDecayRate                    0.94
c   assign::NumConflict                        2402204
c   assign::NumDecision                        4410993
c   assign::NumPropagation                   129058093
c   assign::NumRephase                              56
c   assign::NumRestart                            3656
c   assign::NumVar                                 360
c   assign::NumAssertedVar                           0
c   assign::NumEliminatedVar                         9
c   assign::NumUnassertedVar                       351
c   assign::NumUnassignedVar                       351
c   assign::NumUnreachableVar                        0
c   assign::RootLevel                                0
c   assign::DecisionPerConflict                      1.168
c   assign::PropagationPerConflict                  56.349
c   assign::ConflictPerRestart                    2944.588
c   assign::ConflictPerBaseRestart                2944.588
c   assign::BestPhaseDivergenceRate                  0.187
c   clause::NumBiClause                              2
c   clause::NumBiClauseCompletion                    0
c   clause::NumBiLearnt                              2
c   clause::NumClause                            71710
c   clause::NumLBD2                                613
c   clause::NumLearnt                            70187
c   clause::NumReduction                            88
c   clause::NumReRegistration                        0
c   clause::Timestamp                          2402204
c   clause::DpAverageLBD                             3.025
c   processor::NumFullElimination                   90
c   processor::NumSubsumedClause                     0
c   restart::NumBlock                                0
c   restart::NumCycle                                5
c   restart::NumRestart                           3656
c   restart::NumStage                               88
c   restart::IntervalScale                           1
c   restart::IntervalScaleMax                       32
c   state::NumDecisionConflict                 1209918
c   state::NumProcessor                             89
c   state::Vivification                             89
c   state::VivifiedClause                          861
c   state::VivifiedVar                               0
c   state::BackjumpLevel                            14.934
c   state::ConflictLevel                            16.077
c 
s SATISFIABLE
v 1 -2 3 4 5 6 -7 -8 9 -10 -11 -12 13 -14 ...  -360 0

$ dmcr cnfs/unif-k3-r4.25-v360-c1530-S1293537826-039.cnf
A valid assignment set for cnfs/unif-k3-r4.25-v360-c1530-S1293537826-039.cnf is found in ans_unif-k3-r4.25-v360-c1530-S1293537826-039.cnf

If you want to certificate unsatisfiability, use --certify or -c and use proof checker like Grid.

1. Run splr with the certificate option.

$ splr -c cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf
unif-k3-r4.25-v360-c1530-S1028159446-096.cnf       360,1530 |time:   129.90
 #conflict:    1752264, #decision:      2887321, #propagate:       90608546
  Assignment|#rem:      350, #fix:        2, #elm:        8, prg%:   2.7778
      Clause|Remv:   214899, LBD2:      652, BinC:      491, Perm:     1974
     Restart|#BLK:        0, #RST:     4467, *scl:        1, sclM:       32
         LBD|avrg:   2.0147, trnd:   0.2924, depG:   2.2306, /dpc:     1.05
    Conflict|tASG:   0.9935, cLvl:     7.65, bLvl:     6.52, /ppc:    49.02
        misc|vivC:      690, subC:        0, core:      350, /cpr:   882.87
      Result|file: ./ans_unif-k3-r4.25-v360-c1530-S1028159446-096.cnf
 Certificate|file: proof.drat
s UNSATISFIABLE: cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf

2. Convert the generated DRAT file to a GRAT file.

$ gratgen cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf proof.drat -o proof.grat
roof.gratgratgen cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf proof.drat
c sizeof(cdb_t) = 4
c sizeof(cdb_t*) = 8
c Using RAT run heuristics
c Parsing formula ... 1ms
c Parsing proof (ASCII format) ... 13977ms
c Forward pass ... 1671ms
c Starting Backward pass
c Single threaded mode
c Waiting for aux-threads ...done
c Lemmas processed by threads: 1560280 mdev: 0
c Finished Backward pass: 56677ms
c Writing combined proof ... 15791ms
s VERIFIED
c Timing statistics (ms)
c Parsing:  13979
c Checking: 58371
c   * bwd:  56677
c Writing:  15791
c Overall:  88168
c   * vrf:  72377

c Lemma statistics
c RUP lemmas:  1560280
c RAT lemmas:  0
c   RAT run heuristics:   0
c Total lemmas:  1560280

c Size statistics (bytes)
c Number of clauses: 1762685
c Clause DB size:  128927268
c Item list:       52911152
c Pivots store:    8388608

3. Verify it with gratchk.

$ gratchk unsat cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf proof.grat

Calling Splr from Rust programs

Since 0.4.0, you can use Splr in your programs.

use splr::*;
use std::convert::TryFrom;

fn main() {
    let v: Vec<Vec<i32>> = vec![vec![1, 2], vec![-1, 3], vec![1, -3], vec![-1, 2]];
    match Certificate::try_from(v) {
        Ok(Certificate::SAT(ans)) => println!("s SATISFIABLE: {:?}", ans),
        Ok(Certificate::UNSAT) => println!("s UNSATISFIABLE"),
        Err(e) => panic!("s UNKNOWN; {}", e),
    }
}

All solutions SAT solver

use splr::*;
use std::{convert::TryFrom, env::args};

fn main() {
    let cnf = args().nth(1).expect("takes an arg");
    let assigns: Vec<i32> = Vec::new();
    println!("#solutions: {}", run(&cnf, &assigns));
}

#[cfg(feature = "incremental_solver")]
fn run(cnf: &str, assigns: &[i32]) -> usize {
    let mut solver = Solver::try_from(cnf).expect("panic at loading a CNF");
    for n in assigns.iter() {
        solver.add_assignment(*n).expect("panic at assertion");
    }
    let mut count = 0;
    loop {
        match solver.solve() {
            Ok(Certificate::SAT(ans)) => {
                count += 1;
                println!("s SATISFIABLE({}): {:?}", count, ans);
                let ans = ans.iter().map(|i| -i).collect::<Vec<i32>>();
                match solver.add_clause(ans) {
                    Err(SolverError::Inconsistent) => {
                        println!("c no answer due to level zero conflict");
                        break;
                    }
                    Err(e) => {
                        println!("s UNKNOWN; {:?}", e);
                        break;
                    }
                    Ok(_) => solver.reset(),
                }
            }
            Ok(Certificate::UNSAT) => {
                println!("s UNSATISFIABLE");
                break;
            }
            Err(e) => {
                println!("s UNKNOWN; {}", e);
                break;
            }
        }
    }
    count
}

Since 0.4.1, Solver has iter(). So you can iterate on satisfiable 'solution: Vec<i32>'s as:

#[cfg(feature = "incremental_solver")]
for (i, v) in Solver::try_from(cnf).expect("panic").iter().enumerate() {
    println!("{}-th answer: {:?}", i, v);
}

Mnemonics used in the progress message

Command line options

$ splr --help
A modern CDCL SAT solver in Rust
Activated features: best phase tracking, binary clause completion, clause elimination, clause vivification, Learning-Rate based rewarding, Luby stabilization, reason side rewarding, stage-based rephase

USAGE:
  splr [FLAGS] [OPTIONS] <cnf-file>
FLAGS:
  -h, --help                Prints help information
  -C, --no-color            Disable coloring
  -q, --quiet               Disable any progress message
  -c, --certify             Writes a DRAT UNSAT certification file
  -j, --journal             Shows sub-module logs
  -l, --log                 Uses Glucose-like progress report
  -V, --version             Prints version information
OPTIONS (red options depend on features in Cargo.toml):
      --cbt <c-cbt-thr>     Dec. lvl to use chronoBT              100
      --cdr <crw-dcy-rat>   Clause reward decay rate                0.95
      --cl <c-cls-lim>      Soft limit of #clauses (6MC/GB)         0
      --ii <c-ip-int>       #cls to start in-processor          10000
  -t, --timeout <timeout>   CPU time limit in sec.               5000
      --ecl <elm-cls-lim>   Max #lit for clause subsume            18
      --evl <elm-grw-lim>   Grow limit of #cls in var elim.         0
      --evo <elm-var-occ>   Max #cls for var elimination        20000
  -o, --dir <io-outdir>     Output directory                         .
  -p, --proof <io-pfile>    DRAT Cert. filename                 proof.drat
  -r, --result <io-rfile>   Result filename/stdout                       
      --ral <rst-asg-len>   Length of assign. fast EMA             24
      --ras <rst-asg-slw>   Length of assign. slow EMA           8192
      --rat <rst-asg-thr>   Blocking restart threshold              0.60
      --rll <rst-lbd-len>   Length of LBD fast EMA                  8
      --rls <rst-lbd-slw>   Length of LBD slow EMA               8192
      --rlt <rst-lbd-thr>   Forcing restart threshold               1.60
      --rs  <rst-step>      #conflicts between restarts             2
      --srd <stg-rwd-dcy>   Decay rate for staged var reward        0.50
      --srv <stg-rwd-val>   Extra reward for staged vars            1.00
      --vdr <vrw-dcy-rat>   Var reward decay rate                   0.94
      --vds <vrw-dcy-stp>   Var reward decay change step            0.10
ARGS:
  <cnf-file>    DIMACS CNF file

Solver description

Splr-0.11.0 adopts the following features by default:

• Learning-rate based var rewarding and clause rewarding[3]
• Reason-side var rewarding[3]
• chronological backtrack and non-chronological backtrack[4]
• clause vivification[5]
• dynamic restart blocking based on the number of remaining vars[2]
• dynamic restart based on average LBDs of learnt clauses[1]
• clause elimination and subsumption as pre-processor and in-processor
• stabilization based on Luby series, or Luby Stabilization
• re-phase the best phases

As shown in the blow, Splr calls in-processor very frequently.

Luby stabilization is an original mechanism to make long periods without restarts, which are called stabilized modes. This method updates the restart interval, which usually has a constant value, as follows:

restart_interval = luby(n) * base_interval;

where n represents the number of updates, and luby(n) is a function returning n-th number of Luby series. The longer the solver searches, the larger the average value is. So we can periodically explore the search space more deeply. Here is an example.

Note: the mechanism explained here is different from that used in Splr-0.10.0.

Bibliography

• [1] G. Audemard and L. Simon, "Predicting learnt clauses quality in modern SAT solvers," in International Joint Conference on Artificial Intelligence 2009, pp. 399–404, 2009.

• [2] G. Audemard and L. Simon, "Refining restarts strategies for SAT and UNSAT," in Lecture Notes in Computer Science, vol.7513, pp.118–126, 2012.

• [3] J. H. Liang, V. Ganesh, P. Poupart, and K. Czarnecki, "Learning Rate Based Branching Heuristic for SAT Solvers," in Lecture Notes in Computer Science, vol.9710, pp.123–140, 2016.

• [4] A. Nadel and V. Ryvchin, "Chronological Backtracking," in Theory and Applications of Satisfiability Testing - SAT 2018, June 2018, pp.111–121, 2018.

• [5] C. Piette, Y. Hamadi, and L. Saïs, "Vivifying propositional clausal formulae," Front. Artif. Intell. Appl., vol.178, pp.525–529, 2008.

License

This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0. If a copy of the MPL was not distributed with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

2020-2021, Narazaki Shuji