code: ///////////////////////////////////////////////////////////////////////////
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  //                                                                       //
  //               The Next Generation Logic Library                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  //                                                                       //
  //  Copyright 2015-20xx Christoph Zengler                                //
  //                                                                       //
  //  Licensed under the Apache License, Version 2.0 (the "License");      //
  //  you may not use this file except in compliance with the License.     //
  //  You may obtain a copy of the License at                              //
  //                                                                       //
  //  http://www.apache.org/licenses/LICENSE-2.0                           //
  //                                                                       //
  //  Unless required by applicable law or agreed to in writing, software  //
  //  distributed under the License is distributed on an "AS IS" BASIS,    //
  //  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or      //
  //  implied.  See the License for the specific language governing        //
  //  permissions and limitations under the License.                       //
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  ///////////////////////////////////////////////////////////////////////////
  
  package org.logicng.primecomputation;
  
  import static org.logicng.handlers.Handler.aborted;
  import static org.logicng.handlers.Handler.start;
  
  import org.logicng.datastructures.Tristate;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.formulas.Literal;
  import org.logicng.handlers.SATHandler;
  import org.logicng.solvers.MiniSat;
  import org.logicng.solvers.SATSolver;
  import org.logicng.solvers.sat.MiniSatConfig;
  import org.logicng.util.FormulaHelper;
  
  import java.util.ArrayList;
  import java.util.List;
  import java.util.SortedSet;
  import java.util.TreeSet;
  
  /**
   * Naive implementation for reducing implicants and implicates to prime ones.
   * <p>
   * The computation is initialized with the formula for which
   * the prime implicants/implicates should be computed.
   * @version 2.1.0
   * @since 2.0.0
   */
  public final class NaivePrimeReduction {
  
      private final SATSolver implicantSolver;
      private final SATSolver implicateSolver;
  
      /**
       * Creates a new prime implicant computation for a given formula.
       * @param formula the formula
       */
      public NaivePrimeReduction(final Formula formula) {
          final FormulaFactory f = formula.factory();
          this.implicantSolver = MiniSat.miniSat(f, MiniSatConfig.builder().cnfMethod(MiniSatConfig.CNFMethod.PG_ON_SOLVER).build());
          this.implicantSolver.add(formula.negate());
          this.implicateSolver = MiniSat.miniSat(f, MiniSatConfig.builder().cnfMethod(MiniSatConfig.CNFMethod.PG_ON_SOLVER).build());
          this.implicateSolver.add(formula);
      }
  
      /**
       * Computes a prime implicant from the given implicant for the given formula.
       * Assumption: Given implicant is a satisfying assignment for the formula
       * @param implicant the implicant
       * @return a prime implicant
       */
      public SortedSet<Literal> reduceImplicant(final SortedSet<Literal> implicant) {
          return reduceImplicant(implicant, null);
      }
  
      /**
       * Computes a prime implicant from the given implicant for the given formula.
       * Assumption: Given implicant is a satisfying assignment for the formula
       * @param implicant the implicant
       * @param handler   a SAT handler for the underlying SAT Solver
       * @return a prime implicant or null if the computation was aborted by the handler
       */
      public SortedSet<Literal> reduceImplicant(final SortedSet<Literal> implicant, final SATHandler handler) {
          start(handler);
          final SortedSet<Literal> primeImplicant = new TreeSet<>(implicant);
          for (final Literal lit : implicant) {
              primeImplicant.remove(lit);
              final boolean sat = this.implicantSolver.sat(handler, primeImplicant) == Tristate.TRUE;
              if (aborted(handler)) {
                  return null;
              }
              if (sat) {
                  primeImplicant.add(lit);
              }
          }
          return primeImplicant;
      }
  
      /**
       * Computes a prime implicate from the given implicate for the given formula.
       * Assumption: Given implicate is a falsifying assignment for the formula, i.e. a satisfying assignment for the
       * negated formula
       * @param implicate the implicate
       * @return a prime implicate
       */
      public SortedSet<Literal> reduceImplicate(final SortedSet<Literal> implicate) {
          return reduceImplicate(implicate, null);
      }
  
      /**
       * Computes a prime implicate from the given implicate for the given formula.
       * Assumption: Given implicate is a falsifying assignment for the formula, i.e. a satisfying assignment for the
       * negated formula
       * @param implicate the implicate
       * @param handler   a SAT handler for the underlying SAT Solver
       * @return a prime implicate of null if the computation was aborted by the handler
       */
      public SortedSet<Literal> reduceImplicate(final SortedSet<Literal> implicate, final SATHandler handler) {
          start(handler);
          final SortedSet<Literal> primeImplicate = new TreeSet<>(implicate);
          for (final Literal lit : implicate) {
              primeImplicate.remove(lit);
              final List<Literal> assumptions = FormulaHelper.negateLiterals(primeImplicate, ArrayList::new);
              final boolean sat = this.implicateSolver.sat(handler, assumptions) == Tristate.TRUE;
              if (aborted(handler)) {
                  return null;
              }
              if (sat) {
                  primeImplicate.add(lit);
              }
          }
          return primeImplicate;
      }
  }
  