splr 0.14.0 - Docs.rs

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 the given CNF
branching variable selection based on Learning Rate Based Branching with Reason Side Rewarding or EVSIDS
CaDiCaL-like extended phase saving
restart stabilization inspired by CadiCaL
clause vivification
trail saving

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 0.14.0

SAT Competition 2021, Benchmarks main truck -- splr-0.14.0 RC (d92ced26d) solved with a 400 sec timeout:
- 41 satisfiable problems: all the solutions were correct.
- 35 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.

$ splr cnfs/unif-k3-r4.25-v360-c1530-S1293537826-039.cnf 
unif-k3-r4.25-v360-c1530-S1293537826-039.cnf       360,1530 |time:   471.38
 #conflict:    3889091, #decision:      5538290, #propagate:      205562077
  Assignment|#rem:      351, #fix:        0, #elm:        9, prg%:   2.5000
      Clause|Remv:   114491, LBD2:      674, BinC:        0, Perm:     1521
     Restart|#BLK:        0, #RST:    19441, *scl:        1, sclM:       32
         LBD|trnd:   1.1441, avrg:  15.4832, depG:   3.0733, /dpc:     1.17
    Conflict|tASG:   0.9577, cLvl:    17.85, bLvl:    16.70, /ppc:    56.88
        misc|vivC:     2046, subC:        0, core:      125, /cpr:    67.30
      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-0.14.0 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:    3889091, #decision:      5538290, #propagate:      205562077,
c   Assignment|#rem:      351, #fix:        0, #elm:        9, prg%:   2.5000,
c       Clause|Remv:   114491, LBD2:      674, BinC:        0, Perm:     1521,
c      Restart|#BLK:        0, #RST:    19441, *scl:        1, sclM:       32,
c          LBD|avrg:  15.4832, trnd:   1.1441, depG:   3.0733, /dpc:     1.17,
c     Conflict|tASG:   0.9577, cLvl:    17.85, bLvl:    16.70, /ppc:    56.88,
c         misc|vivC:      114, subC:        0, core:      125, /cpr:    67.30,
c     Strategy|mode:  generic, time:   471.39,
c 
c   config::ChronoBtThreshold                      100.000
c   config::ClauseRewardDecayRate                    0.950
c   config::InprocessorInterval                  10000.000
c   config::RestartAsgThreshold                      0.600
c   config::RestartLbdThreshold                      1.600
c   config::VarRewardDecayRate                       0.960
c   assign::NumConflict                        3889091
c   assign::NumDecision                        5538290
c   assign::NumPropagation                   205562077
c   assign::NumRephase                              69
c   assign::NumRestart                           19442
c   assign::NumVar                                 360
c   assign::NumAssertedVar                           0
c   assign::NumEliminatedVar                         9
c   assign::NumReconflict                          232
c   assign::NumRepropagation                    709713
c   assign::NumUnassertedVar                       351
c   assign::NumUnassignedVar                       351
c   assign::NumUnreachableVar                        0
c   assign::RootLevel                                0
c   assign::DecisionPerConflict                      1.175
c   assign::PropagationPerConflict                  56.876
c   assign::ConflictPerRestart                      69.289
c   assign::ConflictPerBaseRestart                  69.289
c   assign::BestPhaseDivergenceRate                  0.000
c   clause::NumBiClause                              0
c   clause::NumBiClauseCompletion                    0
c   clause::NumBiLearnt                              0
c   clause::NumClause                           116012
c   clause::NumLBD2                                674
c   clause::NumLearnt                           114491
c   clause::NumReduction                           112
c   clause::NumReRegistration                        0
c   clause::Timestamp                          3889091
c   clause::DpAverageLBD                             3.073
c   processor::NumFullElimination                  114
c   processor::NumSubsumedClause                     0
c   restart::NumBlock                                0
c   restart::NumCycle                                5
c   restart::NumRestart                          19442
c   restart::NumStage                              112
c   restart::IntervalScale                           1
c   restart::IntervalScaleMax                       32
c   state::NumNoDecisionConflict                     0
c   state::NumProcessor                            113
c   state::Vivification                            113
c   state::VivifiedClause                         2046
c   state::VivifiedVar                               0
c   state::BackjumpLevel                            16.704
c   state::ConflictLevel                            17.846
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.

Firstly run splr with the certificate option -c.

$ splr -c cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf
unif-k3-r4.25-v360-c1530-S1028159446-096.cnf       360,1530 |time:   188.78
 #conflict:    1878094, #decision:      3632102, #propagate:       95497554
  Assignment|#rem:      346, #fix:        6, #elm:        8, prg%:   3.8889
      Clause|Remv:    22937, LBD2:      618, BinC:       97, Perm:     1500
     Restart|#BLK:        0, #RST:    11799, *scl:        8, sclM:       32
         LBD|trnd:   0.2960, avrg:   2.2538, depG:   2.4044, /dpc:     1.03
    Conflict|tASG:   1.0390, cLvl:     8.63, bLvl:     7.51, /ppc:    48.37
        misc|vivC:     1008, subC:        0, core:      346, /cpr:   178.13
      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

A: Verify with drat-trim

$ drat-trim cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf proof.drat              
c parsing input formula with 360 variables and 1530 clauses
c finished parsing
c detected empty clause; start verification via backward checking
c 1530 of 1530 clauses in core                            
c 1588714 of 1889628 lemmas in core using 54190641 resolution steps
c 0 RAT lemmas in core; 808781 redundant literals in core lemmas
s VERIFIED
c verification time: 100.177 seconds

B: Verify with gratchk

Firstly you have to 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 
c sizeof(cdb_t) = 4
c sizeof(cdb_t*) = 8
c Using RAT run heuristics
c Parsing formula ... 1ms
c Parsing proof (ASCII format) ... 16602ms
c Forward pass ... 3092ms
c Starting Backward pass
c Single threaded mode
c Waiting for aux-threads ...done
c Lemmas processed by threads: 1587582 mdev: 0
c Finished Backward pass: 65581ms
c Writing combined proof ... 16102ms
s VERIFIED
c Timing statistics (ms)
c Parsing:  16604
c Checking: 68699
c   * bwd:  65581
c Writing:  16102
c Overall:  101411
c   * vrf:  85308

c Lemma statistics
c RUP lemmas:  1587582
c RAT lemmas:  0
c   RAT run heuristics:   0
c Total lemmas:  1587582

c Size statistics (bytes)
c Number of clauses: 1891157
c Clause DB size:  144045664
c Item list:       60101264
c Pivots store:    8388608

Then verify it with gratchk.

$ gratchk unsat cnfs/unif-k3-r4.25-v360-c1530-S1028159446-096.cnf proof.grat
c Reading cnf
c Reading proof
c Done
c Verifying unsat
s VERIFIED UNSAT

Calling Splr from Rust programs

Since 0.4.0, you can use Splr in your programs. (Here I suppose that you uses Rust 2021.)

use splr::*;

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::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

mnemonic	meaning
`#var`	the number of variables used in the given CNF file
`#cls`	the number of clauses used in the given CNF file
`time`	elapsed CPU time in seconds (or wall-clock time if CPU time is not available)
`#conflict`	the number of conflicts
`#decision`	the number of decisions
`#propagate`	the number of propagates (its unit is literal)
`#rem`	the number of remaining variables
`#fix`	the number of asserted variables (which has been assigned a value at decision level zero)
`#elm`	the number of eliminated variables
`prg%`	the percentage of `remaining variables / total variables`
`Remv`	the current number of learnt clauses that are not bi-clauses
`LBD2`	the accumulated number of learnt clauses which LBDs are 2
`BinC`	the current number of binary learnt clauses
`Perm`	the current number of given clauses and binary learnt clauses
`#BLK`	the number of blocking restarts
`#RST`	the number of restarts
`*scl`	the scaling factor for restart interval used in Luby stabilization
`sclM`	the largest scaling factor so far
`avrg`	the EMA, Exponential Moving Average, of LBD of learnt clauses
`trnd`	the current trend of the LBD's EMA
`depG`	the EMA of LBD of the clauses used in conflict analysis
`/dpc`	the EMA of decisions per conflict
`tASG`	the current trend of the number of assigned vars after restart
`cLvl`	the EMA of decision levels at which conflicts occur
`bLvl`	the EMA of decision levels to which backjumps go
`/ppc`	the EMA of propagations per conflict
`vivC`	the number of the vivified clauses
`subC`	the number of the clauses subsumed by clause elimination processor
`core`	the number of unreachable vars
`/cpr`	the EMA of conflicts per restart
`mode`	Selected strategy's id
`time`	the elapsed CPU time in seconds

Command line options

$ splr --help
A modern CDCL SAT solver in Rust
Activated features: best phase tracking, clause elimination, clause vivification, dynamic restart threshold, Learning-Rate Based rewarding, Luby stabilization, reason-side rewarding, stage-based rephase, trail saving, unsafe access

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            64
      --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             16
      --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
      --vdr <vrw-dcy-rat>   Var reward decay rate                   0.96
      --vds <vrw-dcy-stp>   Var reward decay change step            0.00
ARGS:
  <cnf-file>    DIMACS CNF file

Solver description

Splr-0.14.0 adopts the following features by default:

Learning-rate based (LRB) var rewarding and clause rewarding[4]
Reason-side var rewarding[4]
~~chronological backtrack[5]~~ disabled since 0.12 due to incorrect UNSAT certificates.
clause vivification[6]
dynamic restart based on average LBDs of learnt clauses[1]
dynamic restart blocking based on the number of remaining vars[2]
clause elimination and subsumption as pre-processor and in-processor
stabilization based on Luby series, or Luby Stabilization
re-phase the best phases
trail saving extended with reason refinement based on clause quality[3]

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

search algorithm in Splr 0.14

Luby stabilization is an original mechanism to make long periods without restarts, which are called stabilized modes. In this method, every clause reduction 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 value 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.

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 LNCS, vol.7513, pp.118–126, 2012.
[3] R. Hickey and F. Bacchus, "Trail Saving on Backtrack", SAT 2020, LNCS, vol. 12178, pp.46-61, 2020.
[4] J. H. Liang, V. Ganesh, P. Poupart, and K. Czarnecki, "Learning Rate Based Branching Heuristic for SAT Solvers," in LNCS, vol.9710, pp.123–140, 2016.
[5] A. Nadel and V. Ryvchin, "Chronological Backtracking," in Theory and Applications of Satisfiability Testing - SAT 2018, June 2018, pp.111–121, 2018.
[6] 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