/// <summary> /// Determines the equivalence class of the specified node. /// </summary> /// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam> /// <param name="node">The node whose equivalence class to determine.</param> /// <param name="state">The state of the computation.</param> /// <param name="transformationRuleTree">The transformation rule tree.</param> /// <param name="settings">The computation settings.</param> /// <returns><see cref="EquivalenceClassResult.TooLongPath"/> if the equivalence class has /// not been computed before, <paramref name="settings"/> has /// <see cref="AnalysisSettings.UseMaxLength"/> equal to <see langword="true"/>, and a path /// of length (in arrows) strictly greater than /// <see cref="AnalysisSettings.MaxPathLength"/> of <paramref name="settings"/> is /// encountered during the equivalence class search. Otherwise, /// <see cref="EquivalenceClassResult.Zero"/> if the equivalence class is the zero /// class, and <see cref="EquivalenceClassResult.Nonzero"/> if the equivalence class is /// not the zero class.</returns> /// <remarks> /// <para>This method may modify the /// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.SearchTree"/>, /// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.EquivalenceClasses"/>, and /// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.LongestPathEncounteredNode"/> /// properties of the <paramref name="state"/> argument.</para> /// </remarks> private EquivalenceClassResult DetermineEquivalenceClass <TVertex>( SearchTreeNode <TVertex> node, AnalysisStateForSingleStartingVertex <TVertex> state, TransformationRuleTreeNode <TVertex> transformationRuleTree, MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings) where TVertex : IEquatable <TVertex>, IComparable <TVertex> { if (node.EquivalenceClassIsComputed) { return(state.NodeIsZeroEquivalent(node) ? EquivalenceClassResult.Zero : EquivalenceClassResult.Nonzero); } return(ComputeEquivalenceClass(node, state, transformationRuleTree, settings)); }
/// <summary> /// Explores the specified node in the equivalence class search. /// </summary> /// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam> /// <param name="node">The node to explore.</param> /// <param name="equivClassStack">The stack or queue of nodes to explore.</param> /// <param name="state">The state of the computation.</param> /// <param name="transformationRuleTree">The transformation rule tree.</param> /// <param name="settings">The computation settings.</param> /// <returns>A value of the <see cref="EquivalenceClassResult"/> enum indicating whether /// the node was <em>found</em> to be zero-equivalent. That is, the returned value is /// <see cref="EquivalenceClassResult.Zero"/> <em>only</em> if the node is zero-equivalent /// but may be <see cref="EquivalenceClassResult.Nonzero"/> even if the node is /// zero-equivalent. /// <remarks> /// <para>A node is found to be zero-equivalent either if its path can be killed or if /// the path is equivalent (up to replacement) to a path that has previously been /// determined to be zero-equivalent.</para> /// <para>This method may modify the /// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.SearchTree"/>, /// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.EquivalenceClasses"/>, and /// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.LongestPathEncounteredNode"/> /// properties of the <paramref name="state"/> argument.</para> /// </remarks> private EquivalenceClassResult ExploreNodeForEquivalenceClassSearch <TVertex>( SearchTreeNode <TVertex> node, Stack <SearchTreeNode <TVertex> > equivClassStack, AnalysisStateForSingleStartingVertex <TVertex> state, TransformationRuleTreeNode <TVertex> transformationRuleTree, MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings) where TVertex : IEquatable <TVertex>, IComparable <TVertex> { // A list of the vertices that appear after the path being considered from transformation. // The vertices are in reversed order. var trailingVertexPath = new List <TVertex>(); foreach (var endingNode in node.ReversePathOfNodes) // The vertex (i.e., last vertex) of endingNode is the last vertex in the subpath { var transformationNode = transformationRuleTree; foreach (var startingNode in endingNode.ReversePathOfNodes) // The vertex (i.e., last vertex) of startingNode is the first vertex in the subpath { var pathVertex = startingNode.Vertex; if (!transformationNode.Children.TryGetValue(pathVertex, out transformationNode)) { break; } if (transformationNode.CanBeKilled) { state.EquivalenceClasses.Union(node, state.ZeroDummyNode); return(EquivalenceClassResult.Zero); } // If replacement is possible, do the replacement on the subpath // and add a search tree node for the entire resulting path if (transformationNode.CanBeReplaced) { // Add search tree nodes for replacement path // This doesn't work when pathNode is the root ... // var lastUnreplacedNode = pathNode.Parent; // var curNode = lastUnreplacedNode; // ... so instead do the following (with Skip), which assumes that the replacement // path has the same first vertex (which it does for the semimonomial unbound // quivers under consideration) var firstNodeInTransformedPath = startingNode; var curNode = firstNodeInTransformedPath; foreach (var vertex in transformationNode.ReplacementPath.Vertices.Skip(1)) { curNode = state.GetInsertChildNode(curNode, vertex); } // Add search tree nodes for the trailing path foreach (var vertex in trailingVertexPath.Reversed()) { curNode = state.GetInsertChildNode(curNode, vertex); } // We now have the node obtained by applying the replacement rule. var transformedNode = curNode; // Do stuff with its path length. bool tooLong = DoPathLengthCheck(transformedNode, state, settings) == PathLengthCheckResult.TooLongPath; if (tooLong) { return(EquivalenceClassResult.TooLongPath); } if (state.NodeIsZeroEquivalent(transformedNode)) { state.EquivalenceClasses.Union(node, transformedNode); // Unioning with state.ZeroDummyNode would work equally well return(EquivalenceClassResult.Zero); } // If transformedNode.HasBeenDiscoveredDuringEquivalenceClassComputation // at this point, then it was discovered during this equivalence class // search (not during an earlier search that ended with zero equivalence), // and in this case, we should ignore it! if (!transformedNode.HasBeenDiscoveredDuringEquivalenceClassComputation) { transformedNode.HasBeenDiscoveredDuringEquivalenceClassComputation = true; state.EquivalenceClasses.Union(node, transformedNode); equivClassStack.Push(transformedNode); } } } trailingVertexPath.Add(endingNode.Vertex); } return(EquivalenceClassResult.Nonzero); }