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.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  package org.logicng.knowledgecompilation.bdds;
  
  import static org.assertj.core.api.Assertions.assertThat;
  
  import org.junit.jupiter.api.Test;
  import org.logicng.datastructures.Assignment;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.io.parsers.ParserException;
  import org.logicng.io.parsers.PseudoBooleanParser;
  import org.logicng.knowledgecompilation.bdds.orderings.VariableOrdering;
  import org.logicng.predicates.satisfiability.TautologyPredicate;
  
  /**
   * Unit tests for the BDD generation in the {@link org.logicng.formulas.Formula} class.
   * @version 2.3.0
   * @since 1.4.0
   */
  public class FormulaBDDTest {
  
      @Test
      public void testSimpleCases() {
          final FormulaFactory f = new FormulaFactory();
          BDD bdd = f.verum().bdd();
          assertThat(bdd.isTautology()).isTrue();
          bdd = f.falsum().bdd();
          assertThat(bdd.isContradiction()).isTrue();
          bdd = f.variable("A").bdd();
          assertThat(bdd.enumerateAllModels()).containsExactly(new Assignment(f.variable("A")));
      }
  
      @Test
      public void testBDDGeneration() throws ParserException {
          final FormulaFactory f = new FormulaFactory();
          final PseudoBooleanParser p = new PseudoBooleanParser(f);
          final Formula formula = p.parse("(A => ~B) & ((A & C) | (D & ~C)) & (A | Y | X) & (Y <=> (X | (W + A + F < 1)))");
          final BDD bddNoOrder = formula.bdd();
          final BDD bddBfs = formula.bdd(VariableOrdering.BFS);
          final BDD bddDfs = formula.bdd(VariableOrdering.DFS);
          final BDD bddMin2Max = formula.bdd(VariableOrdering.MIN2MAX);
          final BDD bddMax2Min = formula.bdd(VariableOrdering.MAX2MIN);
  
          assertThat(bddNoOrder.nodeCount()).isEqualTo(13);
          assertThat(bddBfs.nodeCount()).isEqualTo(14);
          assertThat(bddDfs.nodeCount()).isEqualTo(13);
          assertThat(bddMin2Max.nodeCount()).isEqualTo(14);
          assertThat(bddMax2Min.nodeCount()).isEqualTo(22);
  
          final TautologyPredicate tautology = new TautologyPredicate(f);
          assertThat(f.equivalence(bddNoOrder.cnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddBfs.cnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddDfs.cnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddMin2Max.cnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddMax2Min.cnf(), formula).holds(tautology)).isTrue();
  
          assertThat(f.equivalence(bddNoOrder.dnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddBfs.dnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddDfs.dnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddMin2Max.dnf(), formula).holds(tautology)).isTrue();
          assertThat(f.equivalence(bddMax2Min.dnf(), formula).holds(tautology)).isTrue();
      }
  
      @Test
      public void testNonNnfs() throws ParserException {
          final FormulaFactory f = new FormulaFactory();
          assertThat(f.parse("A + 2*B - C = 1").bdd()).isNotNull();
          assertThat(f.parse("(A & B & C | D & E & F) & (A - 2*B -D <= 0) | (C + 3*D - F > 0)").bdd()).isNotNull();
      }
  }
  