Skip to main content
  • Home
  • Development
  • Documentation
  • Donate
  • Operational login
  • Browse the archive

swh logo
SoftwareHeritage
Software
Heritage
Archive
Features
  • Search

  • Downloads

  • Save code now

  • Add forge now

  • Help

https://github.com/TakehideSoh/SAF
18 January 2026, 11:53:51 UTC
  • Code
  • Branches (4)
  • Releases (0)
  • Visits
    • Branches
    • Releases
    • HEAD
    • refs/heads/dev
    • refs/heads/main
    • refs/tags/v1.0-cmsb2023
    • refs/tags/v1.1-CMSB2023
    No releases to show
  • 5153fb6
  • /
  • cadical
  • /
  • src
  • /
  • vivify.cpp
Raw File Download Save again
Take a new snapshot of a software origin

If the archived software origin currently browsed is not synchronized with its upstream version (for instance when new commits have been issued), you can explicitly request Software Heritage to take a new snapshot of it.

Use the form below to proceed. Once a request has been submitted and accepted, it will be processed as soon as possible. You can then check its processing state by visiting this dedicated page.
swh spinner

Processing "take a new snapshot" request ...

To reference or cite the objects present in the Software Heritage archive, permalinks based on SoftWare Hash IDentifiers (SWHIDs) must be used.
Select below a type of object currently browsed in order to display its associated SWHID and permalink.

  • content
  • directory
  • revision
  • snapshot
origin badgecontent badge
swh:1:cnt:324f43a26085a17b17a3753b2a3b13ebcafdb8bc
origin badgedirectory badge
swh:1:dir:01d80ce94d8f49344a6b25660f682eedd134ff96
origin badgerevision badge
swh:1:rev:3b45819df15225431050eeb48c1a31ffdd580af7
origin badgesnapshot badge
swh:1:snp:d3fcf0e446f52630e867f11dee4c2c828bf46951

This interface enables to generate software citations, provided that the root directory of browsed objects contains a citation.cff or codemeta.json file.
Select below a type of object currently browsed in order to generate citations for them.

  • content
  • directory
  • revision
  • snapshot
Generate software citation in BibTex format (requires biblatex-software package)
Generating citation ...
Generate software citation in BibTex format (requires biblatex-software package)
Generating citation ...
Generate software citation in BibTex format (requires biblatex-software package)
Generating citation ...
Generate software citation in BibTex format (requires biblatex-software package)
Generating citation ...
Tip revision: 3b45819df15225431050eeb48c1a31ffdd580af7 authored by Daniel Le Berre on 22 June 2023, 20:02:19 UTC
Typo in README
Tip revision: 3b45819
vivify.cpp
#include "internal.hpp"

namespace CaDiCaL {

/*------------------------------------------------------------------------*/

// Vivification is a special case of asymmetric tautology elimination (ATE)
// and asymmetric literal elimination (ALE).  It strengthens and removes
// clauses proven redundant through unit propagation.
//
// The original algorithm is due to a paper by Piette, Hamadi and Sais
// published at ECAI'08.  We have an inprocessing version, e.g., it does not
// necessarily run-to-completion.  Our version also performs conflict
// analysis and uses a new heuristic for selecting clauses to vivify.

// Our idea is to focus on clauses with many occurrences of its literals in
// other clauses first.  This both complements nicely our implementation of
// subsume, which is bounded, e.g., subsumption attempts are skipped for
// very long clauses with literals with many occurrences and also is
// stronger in the sense that it enables to remove more clauses due to unit
// propagation (AT checks).

// While first focusing on irredundant clause we then added a separate phase
// upfront which focuses on strengthening also redundant clauses in spirit
// of the ideas presented in the IJCAI'17 paper by M. Luo, C.-M. Li, F.
// Xiao, F. Manya, and Z. Lu.

// There is another very similar approach called 'distilliation' published
// by Han and Somenzi in DAC'07, which reorganizes the CNF in a trie data
// structure to reuse decisions and propagations along the trie.  We used
// that as an inspiration but instead of building a trie we simple sort
// clauses and literals in such a way that we get the same effect.  If a new
// clause is 'distilled' or 'vivified' we first check how many of the
// decisions (which are only lazily undone) can be reused for that clause.
// Reusing can be improved by picking a global literal order and sorting the
// literals in all clauses with respect to that order.  We favor literals
// with more occurrences first.  Then we sort clauses lexicographically with
// respect to that literal order.

/*------------------------------------------------------------------------*/

// For vivification we have a separate dedicated propagation routine, which
// prefers to propagate binary clauses first.  It also uses its own
// assignment procedure 'vivify_assign', which does not mess with phase
// saving during search nor the conflict and other statistics and further
// can be inlined separately here.  The propagation routine needs to ignore
// (large) clauses which are currently vivified.

inline void Internal::vivify_assign (int lit, Clause * reason) {
  require_mode (VIVIFY);
  const int idx = vidx (lit);
  assert (!vals[idx]);
  assert (!flags (idx).eliminated () || !reason);
  Var & v = var (idx);
  v.level = level;                      // required to reuse decisions
  v.trail = (int) trail.size ();        // used in 'vivify_better_watch'
  v.reason = level ? reason : 0;        // for conflict analysis
  if (!level) learn_unit_clause (lit);
  const signed char tmp = sign (lit);
  vals[idx] = tmp;
  vals[-idx] = -tmp;
  assert (val (lit) > 0);
  assert (val (-lit) < 0);
  trail.push_back (lit);
  LOG (reason, "vivify assign %d", lit);
}

// Assume negated literals in candidate clause.

void Internal::vivify_assume (int lit) {
  require_mode (VIVIFY);
  level++;
  control.push_back (Level (lit, trail.size ()));
  LOG ("vivify decide %d", lit);
  assert (level > 0);
  assert (propagated == trail.size ());
  vivify_assign (lit, 0);
}

// Dedicated routine similar to 'propagate' in 'propagate.cpp' and
// 'probe_propagate' with 'probe_propagate2' in 'probe.cpp'.  Please refer
// to that code for more explanation on how propagation is implemented.

bool Internal::vivify_propagate () {
  require_mode (VIVIFY);
  assert (!unsat);
  START (propagate);
  int64_t before = propagated2 = propagated;
  for (;;) {
    if (propagated2 != trail.size ()) {
      const int lit = -trail[propagated2++];
      LOG ("vivify propagating %d over binary clauses", -lit);
      Watches & ws = watches (lit);
      for (const auto & w : ws) {
        if (!w.binary ()) continue;
        const signed char b = val (w.blit);
        if (b > 0) continue;
        if (b < 0) conflict = w.clause;                 // but continue
        else vivify_assign (w.blit, w.clause);
      }
    } else if (!conflict && propagated != trail.size ()) {
      const int lit = -trail[propagated++];
      LOG ("vivify propagating %d over large clauses", -lit);
      Watches & ws = watches (lit);
      const const_watch_iterator eow = ws.end ();
      const_watch_iterator i = ws.begin ();
      watch_iterator j = ws.begin ();
      while (i != eow) {
        const Watch w = *j++ = *i++;
        if (w.binary ()) continue;
        if (val (w.blit) > 0) continue;
        if (w.clause->garbage) { j--; continue; }
        if (w.clause == ignore) continue;
        literal_iterator lits = w.clause->begin ();
        const int other = lits[0]^lits[1]^lit;
        const signed char u = val (other);
        if (u > 0) j[-1].blit = other;
        else {
          const int size = w.clause->size;
          const const_literal_iterator end = lits + size;
          const literal_iterator middle = lits + w.clause->pos;
          literal_iterator k = middle;
          signed char v = -1;
          int r = 0;
          while (k != end && (v = val (r = *k)) < 0)
            k++;
          if (v < 0) {
            k = lits + 2;
            assert (w.clause->pos <= size);
            while (k != middle && (v = val (r = *k)) < 0)
              k++;
          }
          w.clause->pos = k - lits;
          assert (lits + 2 <= k), assert (k <= w.clause->end ());
          if (v > 0) j[-1].blit = r;
          else if (!v) {
            LOG (w.clause, "unwatch %d in", r);
            lits[0] = other;
            lits[1] = r;
            *k = lit;
            watch_literal (r, lit, w.clause);
            j--;
          } else if (!u) {
            assert (v < 0);
            vivify_assign (other, w.clause);
          } else {
            assert (u < 0);
            assert (v < 0);
            conflict = w.clause;
            break;
          }
        }
      }
      if (j != i) {
        while (i != eow)
          *j++ = *i++;
        ws.resize (j - ws.begin ());
      }
    } else break;
  }
  int64_t delta = propagated2 - before;
  stats.propagations.vivify += delta;
  if (conflict) LOG (conflict, "conflict");
  STOP (propagate);
  return !conflict;
}

/*------------------------------------------------------------------------*/

// Check whether a literal occurs less often.  In the implementation below
// (search for 'int64_t score = ...' or '@4') we actually compute a
// weighted occurrence count similar to the Jeroslow Wang heuristic.

struct vivify_more_noccs {

  Internal * internal;

  vivify_more_noccs (Internal * i) : internal (i) { }

  bool operator () (int a, int b) {
    int64_t n = internal->noccs (a);
    int64_t m = internal->noccs (b);
    if (n > m) return true;     // larger occurrences / score first
    if (n < m) return false;    // smaller occurrences / score last
    if (a == -b) return a > 0;  // positive literal first
    return abs (a) < abs (b);   // smaller index first
  }
};

// Sort candidate clauses by the number of occurrences (actually by their
// score) of their literals, with clauses to be vivified first last.   We
// assume that clauses are sorted w.r.t. more occurring (higher score)
// literals first (with respect to 'vivify_more_noccs').
//
// For example if there are the following (long irredundant) clauses
//
//   1 -3 -4      (A)
//  -1 -2  3 4    (B)
//   2 -3  4      (C)
//
// then we have the following literal scores using Jeroslow Wang scores and
// normalizing it with 2^12 (which is the same as 1<<12):
//
//  nocc ( 1) = 2^12 * (2^-3       ) =  512  3.
//  nocc (-1) = 2^12 * (2^-4       ) =  256  6.
//  nocc ( 2) = 2^12 * (2^-3       ) =  512  4.
//  nocc (-2) = 2^12 * (2^-4       ) =  256  7.                 @1
//  nocc ( 3) = 2^12 * (2^-4       ) =  256  8.
//  nocc (-3) = 2^12 * (2^-3 + 2^-3) = 1024  1.
//  nocc ( 4) = 2^12 * (2^-3 + 2^-4) =  768  2.
//  nocc (-4) = 2^12 * (2^-3       ) =  512  5.
//
// which gives the literal order (according to 'vivify_more_noccs')
//
//  -3, 4, 1, 2, -4, -1, -2, 3
//
// Then sorting the literals in each clause gives
//
//  -3  1 -4     (A')
//   4 -1 -2  3  (B')                                           @2
//  -3  4  2     (C')
//
// and finally sorting those clauses lexicographically w.r.t. scores is
//
//  -3  4  2     (C')
//  -3  1 -4     (A')                                           @3
//   4 -1 -2  3  (B')
//
// This order is defined by 'vivify_clause_later' which returns 'true' if
// the first clause should be vivified later than the second.

struct vivify_clause_later {

  Internal * internal;

  vivify_clause_later (Internal * i) : internal (i) { }

  bool operator () (Clause * a, Clause * b) const {

    // First focus on clauses scheduled in the last vivify round but not
    // checked yet since then.
    //
    if (!a->vivify && b->vivify) return true;
    if (a->vivify && !b->vivify) return false;

    // Among redundant clauses (in redundant mode) prefer small glue.
    //
    if (a->redundant) {
      assert (b->redundant);
      if (a->glue > b->glue) return true;
      if (a->glue < b->glue) return false;
    }

    // Then prefer shorter size.
    //
    if (a->size > b->size) return true;
    if (a->size < b->size) return false;

    // Now compare literals in the clauses lexicographically with respect to
    // the literal order 'vivify_more_noccs' assuming literals are sorted
    // decreasingly with respect to that order.
    //
    const auto eoa = a->end (), eob = b->end ();
    auto j = b->begin ();
    for (auto i = a->begin (); i != eoa && j != eob; i++, j++)
      if (*i != *j) return vivify_more_noccs (internal) (*j, *i);

    return j == eob;    // Prefer shorter clauses to be vivified first.
  }
};

/*------------------------------------------------------------------------*/

// Attempting on-the-fly subsumption during sorting when the last line is
// reached in 'vivify_clause_later' above turned out to be trouble some for
// identical clauses.  This is the single point where 'vivify_clause_later'
// is not asymmetric and would require 'stable' sorting for determinism.  It
// can also not be made 'complete' on-the-fly.  Instead of on-the-fly
// subsumption we thus go over the sorted scheduled in a linear scan
// again and remove certain subsumed clauses (the subsuming clause is
// syntactically a prefix of the subsumed clause), which includes
// those troublesome syntactically identical clauses.

struct vivify_flush_smaller {

  bool operator () (Clause * a, Clause * b) const {

    const auto eoa = a->end (), eob = b->end ();
    auto i = a->begin (), j = b->begin ();
    for (; i != eoa && j != eob; i++, j++)
      if (*i != *j) return *i < *j;

    return j == eob && i != eoa;
  }
};

void Internal::flush_vivification_schedule (Vivifier & vivifier) {

  auto & schedule = vivifier.schedule;

  stable_sort (schedule.begin (), schedule.end (), vivify_flush_smaller ());

  const auto end = schedule.end ();
  auto j = schedule.begin (), i = j;

  Clause * prev = 0;
  int64_t subsumed = 0;
  for (; i != end; i++) {
    Clause * c = *j++ = *i;
    if (!prev || c->size < prev->size) { prev = c; continue; }
    const auto eop = prev->end ();
    auto k = prev->begin ();
    for (auto l = c->begin (); k != eop; k++, l++)
      if (*k != *l) break;
    if (k == eop) {
      LOG (c, "found subsumed");
      LOG (prev, "subsuming");
      assert (!c->garbage);
      assert (!prev->garbage);
      assert (c->redundant || !prev->redundant);
      mark_garbage (c);
      subsumed++;
      j--;
    } else prev = c;
  }

  if (subsumed)
    PHASE ("vivify", stats.vivifications,
       "flushed %" PRId64 " subsumed scheduled clauses", subsumed);

  stats.vivifysubs += subsumed;

  if (subsumed) {
    schedule.resize (j - schedule.begin ());
    shrink_vector (schedule);
  } else assert (j == end);
}

/*------------------------------------------------------------------------*/

// Depending on whether we try to vivify redundant or irredundant clauses,
// we schedule a clause to be vivified.  For redundant clauses we only try
// to vivify them if they are likely to survive the next 'reduce' operation.

bool Internal::consider_to_vivify_clause (Clause * c,
                                          bool redundant_mode) {
  if (c->garbage) return false;
  if (c->redundant != redundant_mode) return false;
  if (opts.vivifyonce >= 1 && c->redundant && c->vivified) return false;
  if (opts.vivifyonce >= 2 && !c->redundant && c->vivified) return false;
  if (c->redundant && !likely_to_be_kept_clause (c)) return false;
  return true;
}

// Conflict analysis from 'start' which learns a decision only clause.

void Internal::vivify_analyze_redundant (Vivifier & vivifier,
                                         Clause * start,
                                         bool & only_binary_reasons)
{
  LOG ("analyzing conflict in redundant mode");

  only_binary_reasons = true;

  auto & stack = vivifier.stack;
  stack.clear ();

  stack.push_back (start);
  while (!stack.empty ()) {
    Clause * c = stack.back ();
    if (c->size > 2) only_binary_reasons = false;
    stack.pop_back ();
    LOG (c, "vivify analyze");
    for (const auto & lit : *c) {
      Var & v = var (lit);
      if (!v.level) continue;
      Flags & f = flags (lit);
      if (f.seen) continue;
      assert (val (lit) < 0);
      f.seen = true;
      analyzed.push_back (lit);
      if (v.reason) stack.push_back (v.reason);
      else LOG ("vivify seen %d", lit);
    }
  }

  if (only_binary_reasons) LOG ("all reasons are binary");
}

// Check whether we assigned all literals to false and none is implied.

bool Internal::vivify_all_decisions (Clause * c, int subsume) {

  // assert (redundant_mode);

  for (const auto & other : *c) {
    if (other == subsume) continue;
    if (val (other) >= 0) return false;
    Var & v = var (other);
    if (!v.level) continue;
    if (v.reason) return false;
    if (!flags (other).seen) return false;
  }

  return true;
}

// After conflict analysis (in redundant mode) we check whether all literals
// in the candidate clause 'c' are actually decisions.  If that is case we do
// not subsume the clause 'c'.  Otherwise we go over it and add literals to
// the global learned clause which should be kept.  Thus the result of this
// function is communicated through the global 'clause'.  If it becomes empty,
// we do not learn it and subsumption fails.   The 'subsume' literal is used
// to force keeping that literal (see case '@5' below, where we found this
// positively implied literal).

void Internal::vivify_post_process_analysis (Clause * c, int subsume) {

  // assert (redundant_mode);

  if (vivify_all_decisions (c, subsume)) {

    LOG ("analyzed literals are all decisions thus no strengthening");

    clause.clear ();    // Do not subsume nor strengthen (case '@7').

  } else {              // Otherwise prepare subsuming learned clause.

    for (const auto & other : *c) {

      enum { FLUSH, IGNORE, KEEP } action;

           if (other == subsume)     action = KEEP;
      else if (val (other) >= 0)     action = FLUSH;
      else {
        Var & v = var (other);
             if (!v.level)           action = IGNORE;
        else if (v.reason)           action = FLUSH;
        else if (flags (other).seen) action = KEEP;
        else                         action = FLUSH;
      }

      if (action == KEEP) clause.push_back (other);
#ifdef LOGGING
      if (action == KEEP)   LOG ("keeping literal %d", other);
      if (action == FLUSH)  LOG ("flushing literal %d", other);
      if (action == IGNORE) LOG ("ignoring literal %d", other);
#endif
    }
  }
}

/*------------------------------------------------------------------------*/

// In a strengthened clause the idea is to move non-false literals to the
// front, followed by false literals.  Literals are further sorted by
// reverse assignment order.  The goal is to use watches which require to
// backtrack as few as possible decision levels.

struct vivify_better_watch {

  Internal * internal;

  vivify_better_watch (Internal * i) : internal (i) { }

  bool operator () (int a, int b) {

    const signed char av = internal->val (a), bv = internal->val (b);

    if (av >= 0 && bv < 0) return true;
    if (av < 0 && bv >= 0) return false;

    return internal->var (a).trail > internal->var (b).trail;
  }
};

// Common code to actually strengthen a candidate clause.  The resulting
// strengthened clause is communicated through the global 'clause'.

void Internal::vivify_strengthen (Clause * c) {

  assert (!clause.empty ());
  stats.vivifystrs++;

  if (clause.size () == 1) {

    backtrack ();
    const int unit = clause[0];
    LOG (c, "vivification shrunken to unit %d", unit);
    assert (!val (unit));
    assign_unit (unit);
    stats.vivifyunits++;

    bool ok = propagate ();
    if (!ok) learn_empty_clause ();

  } else {

    // See explanation before 'vivify_better_watch' above.
    //
    sort (clause.begin (), clause.end (), vivify_better_watch (this));

    int new_level = level;

    const int lit0 = clause[0];
    signed char val0 = val (lit0);
    if (val0 < 0) {
      const int level0 = var (lit0).level;
      LOG ("1st watch %d negative at level %d", lit0, level0);
      new_level = level0 - 1;
    }

    const int lit1 = clause[1];
    const signed char val1 = val (lit1);
    if (val1 < 0 &&
        !(val0 > 0 && var (lit0).level <= var (lit1).level)) {
      const int level1 = var (lit1).level;
      LOG ("2nd watch %d negative at level %d", lit1, level1);
      new_level = level1 - 1;
    }

    if (new_level < level) backtrack (new_level);

    assert (val (lit0) >= 0);
    assert (val (lit1) >= 0 ||
            (val (lit0) > 0 &&
             val (lit1) < 0 &&
             var (lit0).level <= var (lit1).level));

    Clause * d = new_clause_as (c);
    LOG (c, "before vivification");
    LOG (d, "after vivification");
    (void) d;
  }
  clause.clear ();
  mark_garbage (c);
}

/*------------------------------------------------------------------------*/

// Main function: try to vivify this candidate clause in the given mode.

void Internal::vivify_clause (Vivifier & vivifier, Clause * c) {

  const bool redundant_mode = vivifier.redundant_mode;

  assert (redundant_mode || !c->redundant);
  assert (c->size > 2);                       // see (NO-BINARY) below

  c->vivify = false;                          // mark as checked / tried
  c->vivified = true;                         // and globally remember

  if (c->garbage) return;

  // First check whether the candidate clause is already satisfied and at
  // the same time copy its non fixed literals to 'sorted'.  The literals
  // in the candidate clause might not be sorted anymore due to replacing
  // watches during propagation, even though we sorted them initially
  // while pushing the clause onto the schedule and sorting the schedule.
  //
  int satisfied = 0;
  auto & sorted = vivifier.sorted;
  sorted.clear ();

  for (const auto & lit : *c) {
    const int tmp = fixed (lit);
    if (tmp > 0) { satisfied = lit; break; }
    else if (!tmp) sorted.push_back (lit);
  }

  if (satisfied) {
    LOG (c, "satisfied by propagated unit %d", satisfied);
    mark_garbage (c);
    return;
  }

  sort (sorted.begin (), sorted.end (), vivify_more_noccs (this));

  // The actual vivification checking is performed here, by assuming the
  // negation of each of the remaining literals of the clause in turn and
  // propagating it.  If a conflict occurs or another literal in the
  // clause becomes assigned during propagation, we can stop.
  //
  LOG (c, "vivification checking");
  stats.vivifychecks++;

  // If the decision 'level' is non-zero, then we can reuse decisions for
  // the previous candidate, and avoid re-propagating them.  In preliminary
  // experiments this saved between 30%-50% decisions (and thus
  // propagations), which in turn lets us also vivify more clauses within
  // the same propagation bounds, or terminate earlier if vivify runs to
  // completion.
  //
  if (level) {
#ifdef LOGGING
    int orig_level = level;
#endif
    // First check whether this clause is actually a reason for forcing
    // one of its literals to true and then backtrack one level before
    // that happened.  Otherwise this clause might be incorrectly
    // considered to be redundant or if this situation is checked then
    // redundancy by other clauses using this forced literal becomes
    // impossible.
    //
    int forced = 0;

    // This search could be avoided if we would eagerly set the 'reason'
    // boolean flag of clauses, which however we do not want to do for
    // binary clauses (during propagation) and thus would still require
    // a version of 'protect_reason' for binary clauses during 'reduce'
    // (well binary clauses are not collected during 'reduce', but again
    // this exception from the exception is pretty complex and thus a
    // simply search here is probably easier to understand).

    for (const auto & lit : *c) {
      const signed char tmp = val (lit);
      if (tmp < 0) continue;
      if (tmp > 0 && var (lit).reason == c) forced = lit;
      break;
    }
    if (forced) {
      LOG ("clause is reason forcing %d", forced);
      assert (var (forced).level);
      backtrack (var (forced).level - 1);
    }

    // As long the (remaining) literals of the sorted clause match
    // decisions on the trail we just reuse them.
    //
    if (level) {

      int l = 1;        // This is the decision level we want to reuse.

      for (const auto & lit : sorted) {
	if (fixed (lit)) continue;
	const int decision = control[l].decision;
	if (-lit == decision) {
	  LOG ("reusing decision %d at decision level %d", decision, l);
	  stats.vivifyreused++;
	  if (++l > level) break;
	} else {
	  LOG ("literal %d does not match decision %d at decision level %d",
	    lit, decision, l);
	  backtrack (l-1);
	  break;
	}
      }
    }

    LOG ("reused %d decision levels from %d", level, orig_level);
  }

  LOG (sorted, "sorted size %zd probing schedule", sorted.size ());

  // Make sure to ignore this clause during propagation.  This is not that
  // easy for binary clauses (NO-BINARY), e.g., ignoring binary clauses,
  // without changing 'propagate'. Actually, we do not want to remove binary
  // clauses which are subsumed.  Those are hyper binary resolvents and
  // should be kept as learned clauses instead, unless they are transitive
  // in the binary implication graph, which in turn is detected during
  // transitive reduction in 'transred'.
  //
  ignore = c;

  int subsume = 0;            // determined to be redundant / subsumed
  int remove = 0;             // at least literal 'remove' can be removed

  // If the candidate is redundant, i.e., we are in redundant mode, the
  // clause is subsumed (in one of the two cases below where 'subsume' is
  // assigned) and further all reasons involved are only binary clauses,
  // then this redundant clause is what we once called a hidden tautology,
  // and even for redundant clauses it makes sense to remove the candidate.
  // It does not add anything to propagation power of the formula.  This is
  // the same argument as removing transitive clauses in the binary
  // implication graph during transitive reduction.
  //
  bool only_binary_reasons = false;

  // Go over the literals in the candidate clause in sorted order.
  //
  for (const auto & lit : sorted) {

    // Exit loop as soon a literal is positively implied (case '@5' below)
    // or propagation of the negation of a literal fails ('@6').
    //
    if (subsume) break;

    // We keep on assigning literals, even though we know already that we
    // can remove one (was negatively implied), since we either might run
    // into the 'subsume' case above or more false literals become implied.
    // In any case this might result in stronger vivified clauses.  As a
    // consequence continue with this loop even if 'remove' is non-zero.

    const signed char tmp = val (lit);

    if (tmp) {                // literal already assigned

      const Var & v = var (lit);

      if (!v.level) { LOG ("skipping fixed %d", lit); continue; }
      if (!v.reason) { LOG ("skipping decision %d", lit); continue; }

      if (tmp > 0) {          // positively implied

        LOG ("subsumed since literal %d already true", lit);

        subsume = lit;        // will be able to subsume candidate '@5'

        // In redundant mode we want to strengthen clauses instead of
        // subsuming them (actually incorrect for irredundant candidates).
        // Thus we perform resolutions to find such a strengthening.
        //
        if (redundant_mode) {

          assert (c->redundant);
          assert (clause.empty ());
          assert (analyzed.empty ());

          // We start the analysis by adding the negation of the implied
          // literal to the global 'clause'.
          //
          flags (lit).seen = true;
          analyzed.push_back (-lit);
          LOG ("vivify seen %d", -lit);
          assert (v.reason);

          // Continue the analysis with the reason of the implied literal.
          //
          vivify_analyze_redundant (vivifier, v.reason, only_binary_reasons);
          if (!only_binary_reasons) {
            vivify_post_process_analysis (c, subsume);
            if (!clause.empty ()) stats.vivifystred2++;
          }
          clear_analyzed_literals ();

          backtrack (level - 1);
          assert (!conflict);

          break;
        }

      } else {                // negatively implied

        assert (tmp < 0);
        LOG ("literal %d is already false and can be removed", lit);

        remove = lit;         // will be able to remove this literal
      }

    } else {                  // still unassigned

      stats.vivifydecs++;
      vivify_assume (-lit);
      LOG ("negated decision %d score %" PRId64 "", lit, noccs (lit));

      if (vivify_propagate ()) continue;        // hot-spot

      LOG ("subsumed since propagation produced conflict");

      subsume = INT_MIN;      // will be able to subsume candidate '@6'

      // Again try to strengthen instead of subsuming in redundant mode.
      //
      if (redundant_mode) {

        assert (c->redundant);
        assert (clause.empty ());
        assert (analyzed.empty ());

        vivify_analyze_redundant (vivifier, conflict, only_binary_reasons);
        if (!only_binary_reasons) {
          vivify_post_process_analysis (c, subsume);
          if (!clause.empty ()) stats.vivifystred3++;
        }
        clear_analyzed_literals ();
      }

      backtrack (level - 1);
      conflict = 0;

      break;
    }
  }

  assert (ignore == c);
  ignore = 0;

  if (subsume) {

    if (redundant_mode && !only_binary_reasons) {

      assert (c->redundant);

      if (!clause.empty ()) {

        LOG ("strengthening instead of subsuming clause");
        vivify_strengthen (c);

      } else {  // triggered by '@7'

        // In redundant mode, where candidates might be redundant and we
        // allow to propagate over redundant clauses too, we do not remove
        // unit implied clauses which we failed to strengthen.

        LOG (c, "ignoring asymmetric tautology in redundant mode");

        if (c->redundant) {

          assert (redundant_mode);
          assert (!c->vivify);

        } else {

          // For an irredundant clause the situation is different, since we
          // might be able to remove it even if we only propagate over
          // irredundant clauses.  Thus we schedule it again.

          LOG (c, "rescheduling for irredundant round");
          assert (!c->vivify);

          c->vivify = true;
        }
      }

    } else {

      stats.vivifysubs++;
      LOG (c, "redundant asymmetric tautology");
      mark_garbage (c);

    }

  } else if (remove) {

    assert (level);
    assert (clause.empty ());

    // There might be other literals implied to false (or even root level
    // falsified).  Those should be removed in addition to 'remove'.
    //
    for (const auto & other : *c) {
      assert (val (other) < 0);
      Var & v = var (other);
      if (!v.level) continue; // Remove root-level fixed literals.
      if (v.reason) {         // Remove all negative implied literals.
        assert (v.level);
        assert (v.reason);
        LOG ("flushing literal %d", other);
      } else {                                // Decision or unassigned.
        LOG ("keeping literal %d", other);
        clause.push_back (other);
      }
    }

    if (redundant_mode) stats.vivifystred1++;
    else                stats.vivifystrirr++;

    vivify_strengthen (c);

  } else {
    LOG ("vivification failed");
  }
}

/*------------------------------------------------------------------------*/

// There are two modes of vivification, one using all clauses and one
// focusing on irredundant clauses only.  The latter variant working on
// irredundant clauses only can also remove irredundant asymmetric
// tautologies (clauses subsumed through unit propagation), which in
// redundant mode is incorrect (due to propagating over redundant clauses).

void Internal::vivify_round (bool redundant_mode, int64_t propagation_limit) {

  if (unsat) return;
  if (terminated_asynchronously ()) return;

  PHASE ("vivify", stats.vivifications,
    "starting %s vivification round propagation limit %" PRId64 "",
    redundant_mode ? "redundant" : "irredundant", propagation_limit);

  // Disconnect all watches since we sort literals within clauses.
  //
  if (watching ()) clear_watches ();

  // Count the number of occurrences of literals in all clauses,
  // particularly binary clauses, which are usually responsible
  // for most of the propagations.
  //
  init_noccs ();

  for (const auto & c : clauses) {

    if (!consider_to_vivify_clause (c, redundant_mode)) continue;

    // This computes an approximation of the Jeroslow Wang heuristic score
    //
    //       nocc (L) =     sum       2^(12-|C|)
    //                   L in C in F
    //
    // but we cap the size at 12, that is all clauses of size 12 and larger
    // contribute '1' to the score, which allows us to use 'long' numbers.
    // See the example above (search for '@1').
    //
    const int shift = 12 - c->size;
    const int64_t score = shift < 1 ? 1 : (1l << shift);           // @4

    for (const auto lit : *c)
      noccs (lit) += score;
  }

  // Refill the schedule every time.  Unchecked clauses are 'saved' by
  // setting their 'vivify' bit, such that they can be tried next time.
  //
  Vivifier vivifier (redundant_mode);

  // In the first round of filling the schedule check whether there are
  // still clauses left, which were scheduled but have not been vivified yet.
  // The second round is only entered if no such clause was found in the
  // first round.  Then the second round selects all clauses.
  //
  for (const auto & c : clauses) {

    if (c->size == 2) continue;       // see also (NO-BINARY) above

    if (!consider_to_vivify_clause (c, redundant_mode)) continue;

    // Literals in scheduled clauses are sorted with their highest score
    // literals first (as explained above in the example at '@2').  This
    // is also needed in the prefix subsumption checking below.
    //
    sort (c->begin (), c->end (), vivify_more_noccs (this));

    vivifier.schedule.push_back (c);
  }
  shrink_vector (vivifier.schedule);

  // Flush clauses subsumed by another clause with the same prefix, which
  // also includes flushing syntactically identical clauses.
  //
  flush_vivification_schedule (vivifier);

  // Sort candidates, with first to be tried candidate clause last, i.e.,
  // many occurrences and high score literals) as in the example explained
  // above (search for '@3').
  //
  stable_sort (vivifier.schedule.begin (), vivifier.schedule.end (),
    vivify_clause_later (this));

  // Remember old values of counters to summarize after each round with
  // verbose messages what happened in that round.
  //
  int64_t checked      = stats.vivifychecks;
  int64_t subsumed     = stats.vivifysubs;
  int64_t strengthened = stats.vivifystrs;
  int64_t units        = stats.vivifyunits;

  int64_t scheduled = vivifier.schedule.size ();
  stats.vivifysched += scheduled;

  PHASE ("vivify", stats.vivifications,
    "scheduled %" PRId64 " clauses to be vivified %.0f%%",
    scheduled, percent (scheduled, stats.current.irredundant));

  // Limit the number of propagations during vivification as in 'probe'.
  //
  const int64_t limit = stats.propagations.vivify + propagation_limit;

  connect_watches (!redundant_mode);       // watch all relevant clauses

  if (!unsat && !propagate ()) {
    LOG ("propagation after connecting watches in inconsistency");
    learn_empty_clause ();
  }

  while (!unsat &&
         !terminated_asynchronously () &&
         !vivifier.schedule.empty () &&
         stats.propagations.vivify < limit) {
    Clause * c = vivifier.schedule.back ();              // Next candidate.
    vivifier.schedule.pop_back ();
    vivify_clause (vivifier, c);
  }

  if (level) backtrack ();

  if (!unsat) {

    reset_noccs ();

    int64_t still_need_to_be_vivified = 0;
    for (const auto & c : vivifier.schedule)
      if (c->vivify)
        still_need_to_be_vivified++;

    // Preference clauses scheduled but not vivified yet next time.
    //
    if (still_need_to_be_vivified)
      PHASE ("vivify", stats.vivifications,
        "still need to vivify %" PRId64 " clauses %.02f%% of %" PRId64
        " scheduled", still_need_to_be_vivified,
        percent (still_need_to_be_vivified, scheduled),
        scheduled);
    else {
      PHASE ("vivify", stats.vivifications,
        "no previously not yet vivified clause left");
      for (const auto & c : vivifier.schedule)
        c->vivify = true;
    }

    vivifier.erase ();          // Reclaim  memory early.
  }

  clear_watches ();
  connect_watches ();

  if (!unsat) {

    // Since redundant clause were disconnected during propagating vivified
    // units in redundant mode, and further irredundant clauses are
    // arbitrarily sorted, we have to propagate all literals again after
    // connecting the first two literals in the clauses, in order to
    // reestablish the watching invariant.
    //
    propagated2 = propagated = 0;

    if (!propagate ()) {
      LOG ("propagating vivified units leads to conflict");
      learn_empty_clause ();
    }
  }

  checked      = stats.vivifychecks - checked;
  subsumed     = stats.vivifysubs   - subsumed;
  strengthened = stats.vivifystrs   - strengthened;
  units        = stats.vivifyunits  - units;

  PHASE ("vivify", stats.vivifications,
    "checked %" PRId64 " clauses %.02f%% of %" PRId64 " scheduled",
    checked, percent (checked, scheduled), scheduled);
  if (units)
    PHASE ("vivify", stats.vivifications,
      "found %" PRId64 " units %.02f%% of %" PRId64 " checked",
      units, percent (units, checked), checked);
  if (subsumed)
    PHASE ("vivify", stats.vivifications,
      "subsumed %" PRId64 " clauses %.02f%% of %" PRId64 " checked",
      subsumed, percent (subsumed, checked), checked);
  if (strengthened)
    PHASE ("vivify", stats.vivifications,
      "strengthened %" PRId64 " clauses %.02f%% of %" PRId64 " checked",
      strengthened, percent (strengthened, checked), checked);

  stats.subsumed     += subsumed;
  stats.strengthened += strengthened;

  last.vivify.propagations = stats.propagations.search;

  bool unsuccessful = !(subsumed + strengthened + units);
  report (redundant_mode ? 'w' : 'v', unsuccessful);
}

/*------------------------------------------------------------------------*/

void Internal::vivify () {

  if (unsat) return;
  if (terminated_asynchronously ()) return;
  if (!stats.current.irredundant) return;

  assert (opts.vivify);
  assert (!level);

  START_SIMPLIFIER (vivify, VIVIFY);
  stats.vivifications++;

  int64_t limit = stats.propagations.search;
  limit -= last.vivify.propagations;
  limit *= 1e-3 * opts.vivifyreleff;
  if (limit < opts.vivifymineff) limit = opts.vivifymineff;
  if (limit > opts.vivifymaxeff) limit = opts.vivifymaxeff;

  PHASE ("vivify", stats.vivifications,
    "vivification limit of twice %" PRId64 " propagations", limit);

  vivify_round (false, limit); // Vivify only irredundant clauses.

  limit *= 1e-3 * opts.vivifyredeff;

  vivify_round (true, limit);  // Vivify all clauses.

  STOP_SIMPLIFIER (vivify, VIVIFY);

  last.vivify.propagations = stats.propagations.search;
}

}

back to top

Software Heritage — Copyright (C) 2015–2026, The Software Heritage developers. License: GNU AGPLv3+.
The source code of Software Heritage itself is available on our development forge.
The source code files archived by Software Heritage are available under their own copyright and licenses.
Terms of use: Archive access, API— Content policy— Contact— JavaScript license information— Web API