code: ///////////////////////////////////////////////////////////////////////////
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  //                 / /   / __ \/ __ `/ / ___/  |/ / / __                 //
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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.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  package org.logicng.transformations;
  
  import static org.logicng.formulas.FType.LITERAL;
  import static org.logicng.formulas.cache.TransformationCacheEntry.BDD_CNF;
  import static org.logicng.formulas.cache.TransformationCacheEntry.BDD_DNF;
  
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.formulas.FormulaTransformation;
  import org.logicng.knowledgecompilation.bdds.BDD;
  import org.logicng.knowledgecompilation.bdds.BDDFactory;
  import org.logicng.knowledgecompilation.bdds.jbuddy.BDDKernel;
  
  /**
   * Transformation of a formula in a normal form (DNF or CNF) by converting it to a BDD.
   * @version 2.3.0
   * @since 2.3.0
   */
  public abstract class BDDNormalFormTransformation implements FormulaTransformation {
  
      private final UnitPropagation up = UnitPropagation.get();
      private final BDDKernel kernel;
  
      /**
       * Constructs a new BDD-based normal form transformation with an optional BDD kernel.
       * <p>
       * Warning: You can use this object for arbitrarily many transformations, <b>but</b>
       * the number of different variables in all applied formulas <b>must not exceed</b>
       * the number of variables in the kernel.
       * @param kernel the optional BDD kernel
       */
      public BDDNormalFormTransformation(final BDDKernel kernel) {
          this.kernel = kernel;
      }
  
      /**
       * Constructs a new BDD-based normal form transformation for a given number of variables.
       * <p>
       * Warning: You can use this object for arbitrarily many transformations, <b>but</b>
       * the number of different variables in all applied formulas <b>must not exceed</b>
       * {@code numVars}.
       * <p>
       * To improve performance you might want to use {@link #BDDNormalFormTransformation(BDDKernel)},
       * where you have full control over the node and cache size in the used BDD kernel.
       * @param f       the formula factory to use
       * @param numVars the number of variables
       */
      public BDDNormalFormTransformation(final FormulaFactory f, final int numVars) {
          this.kernel = new BDDKernel(f, numVars, Math.max(numVars * 30, 20_000), Math.max(numVars * 20, 20_000));
      }
  
      /**
       * Computes the CNF or DNF from the given formula by using a BDD.
       * @param formula the formula to transform
       * @param cnf     {@code true} if a CNF should be computed, {@code false} if a canonical DNF should be computed
       * @param cache   indicates whether the result should be cached in this formula's cache
       * @return the normal form (CNF or DNF) of the formula
       */
      protected Formula compute(final Formula formula, final boolean cnf, final boolean cache) {
          if (formula.type().precedence() >= LITERAL.precedence()) {
              return formula;
          }
          if (hasNormalForm(formula, cnf)) {
              return formula;
          }
          final Formula cached = formula.transformationCacheEntry(cnf ? BDD_CNF : BDD_DNF);
          if (cache && cached != null) {
              return cached;
          }
          final BDD bdd = BDDFactory.build(formula, this.kernel, null);
          final Formula normalForm = cnf ? bdd.cnf() : bdd.dnf();
          final Formula simplifiedNormalForm;
          if (cnf) {
              simplifiedNormalForm = normalForm.transform(this.up);
          } else {
              // unit propagation simplification creates a CNF, so we use the negated DNF to negate the result back to DNF again
              simplifiedNormalForm = normalForm.negate().nnf().transform(this.up).negate().nnf();
          }
          if (cache) {
              formula.setTransformationCacheEntry(BDD_CNF, simplifiedNormalForm);
          }
          return simplifiedNormalForm;
      }
  
      private boolean hasNormalForm(final Formula formula, final boolean cnf) {
          return cnf ? formula.isCNF() : formula.isDNF();
      }
  }
  