/// <summary>
/// Computes 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
/// <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 ComputeEquivalenceClass <TVertex>(
SearchTreeNode <TVertex> startNode,
AnalysisStateForSingleStartingVertex <TVertex> state,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// The stack or queue of nodes to process
var equivClassStack = new Stack <SearchTreeNode <TVertex> >();
equivClassStack.Push(startNode);
startNode.HasBeenDiscoveredDuringEquivalenceClassComputation = true;
while (equivClassStack.Count > 0)
{
var node = equivClassStack.Pop();
var result = ExploreNodeForEquivalenceClassSearch(node, equivClassStack, state, transformationRuleTree, settings);
if (result == EquivalenceClassResult.TooLongPath)
{
return(EquivalenceClassResult.TooLongPath); // If too long, return "too long".
}
else if (result == EquivalenceClassResult.Zero)
{
return(EquivalenceClassResult.Zero); // If definitely zero-equivalent, return "zero"
}
}
return(EquivalenceClassResult.Nonzero);
}
/// <summary>
///
/// </summary>
/// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam>
/// <param name="quiver">The quiver.</param>
/// <param name="startingVertex">The starting vertex of the paths to look at.</param>
/// <param name="transformationRuleTree"></param>
/// <returns>The state of the search after it is done.</returns>
private AnalysisStateForSingleStartingVertex <TVertex> DoSearchInPathTree <TVertex>(
Quiver <TVertex> quiver,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// Set up for analysis/graph search
var state = new AnalysisStateForSingleStartingVertex <TVertex>(startingVertex);
// Analysis/graph search
// Keep a stack of "recently equivalence-class-computed" nodes
// In every iteration, pop a node from the stack and determine the equivalence classes
// of its child nodes.
// It would be cleaner to in every iteration determine the equivalence class of the
// *current* node and enqueue its child nodes (in other words, to have the queue
// contain nodes whose equivalence classes to explore), but this makes it non-trivial
// to keep track of the maximal nonzero equivalence classes
while (state.Stack.Count > 0)
{
var node = state.Stack.Pop();
bool isMaximalNonzero = true;
foreach (var nextVertex in quiver.AdjacencyLists[node.Vertex])
{
var child = state.GetInsertChildNode(node, nextVertex);
if (DoPathLengthCheck(child, state, settings) == PathLengthCheckResult.TooLongPath)
{
state.TooLongPathEncountered = true;
return(state);
}
var equivClassResult = DetermineEquivalenceClass(child, state, transformationRuleTree, settings);
if (equivClassResult == EquivalenceClassResult.Nonzero)
{
isMaximalNonzero = false;
state.Stack.Push(child);
}
else if (equivClassResult == EquivalenceClassResult.TooLongPath)
{
state.TooLongPathEncountered = true;
return(state);
}
}
if (isMaximalNonzero)
{
var representative = state.EquivalenceClasses.FindSet(node);
if (!state.maximalPathRepresentatives.Contains(representative))
{
state.maximalPathRepresentatives.Add(representative);
}
}
}
return(state);
}
/// <summary>
/// Essentially <see cref="ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt"/>
/// but with a more detailed, implementation-specific return value.
/// </summary>
/// <typeparam name="TVertex"></typeparam>
/// <param name="quiver"></param>
/// <param name="startingVertex"></param>
/// <param name="transformationRuleTree"></param>
/// <param name="settings"></param>
/// <returns></returns>
private AnalysisResultsForSingleStartingVertex <TVertex> AnalyzeWithStartingVertex <TVertex>(
Quiver <TVertex> quiver,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// Parameter validation
if (quiver is null)
{
throw new ArgumentNullException(nameof(quiver));
}
if (!quiver.Vertices.Contains(startingVertex))
{
throw new ArgumentException($"The quiver does not contain the starting vertex {startingVertex}.");
}
if (transformationRuleTree is null)
{
throw new ArgumentNullException(nameof(transformationRuleTree));
}
if (settings is null)
{
throw new ArgumentNullException(nameof(settings));
}
// Do search in the tree of all paths starting at startingVertex
AnalysisStateForSingleStartingVertex <TVertex> state = DoSearchInPathTree(quiver, startingVertex, transformationRuleTree, settings);
// Do cancellativity check
bool shouldDoCancellativityFailureDetection = settings.DetectCancellativityFailure && !state.TooLongPathEncountered;
bool cancellativityFailureDetected = shouldDoCancellativityFailureDetection ? DetectFailureOfCancellativity(state) : false;
bool shouldDoWeakCancellativityFailureDetection = settings.DetectWeakCancellativityFailure && !state.TooLongPathEncountered;
bool weakCancellativityFailureDetected = shouldDoWeakCancellativityFailureDetection ? DetectFailureOfWeakCancellativity(state) : false;
var cancellativityFailuresDetected = CancellativityTypes.None;
if (cancellativityFailureDetected)
{
cancellativityFailuresDetected |= CancellativityTypes.Cancellativity;
}
if (weakCancellativityFailureDetected)
{
cancellativityFailuresDetected |= CancellativityTypes.WeakCancellativity;
}
// Return results
var results = new AnalysisResultsForSingleStartingVertex <TVertex>(state, cancellativityFailuresDetected);
return(results);
}
/// <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>
/// Checks if the path is too long given the specified computation settings and also updates
/// the <see cref="AnalysisStateForSingleStartingVertex{TVertex}.LongestPathEncounteredNode"/>
/// property if necessary.
/// </summary>
/// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam>
/// <param name="node">The node whose corresponding path to check.</param>
/// <param name="state">The state of the computation.</param>
/// <param name="settings">The computation settings, which indicates whether to detect too
/// long paths.</param>
/// <returns>A value of the <see cref="PathLengthCheckResult"/> enum indicating whether the
/// path was too long.</returns>
private PathLengthCheckResult DoPathLengthCheck <TVertex>(
SearchTreeNode <TVertex> node,
AnalysisStateForSingleStartingVertex <TVertex> state,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
if (node.PathLength <= state.LongestPathEncounteredNode.Length)
{
return(PathLengthCheckResult.Fine);
}
// node.Path is slow, but this will be executed at most
// min(maxPathLength, largestPathLengthInQuiver) times or so
state.LongestPathEncounteredNode = node.Path;
return((settings.UseMaxLength && node.PathLength > settings.MaxPathLength) ? PathLengthCheckResult.TooLongPath : PathLengthCheckResult.Fine);
}
/// <inheritdoc/>
public MaximalNonzeroEquivalenceClassRepresentativesResults <TVertex> ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt <TVertex>(
Quiver <TVertex> quiver,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
var analysisResults = AnalyzeWithStartingVertex(quiver, startingVertex, transformationRuleTree, settings);
// The .ToList() call to eagerly evaluate the maximal path representatives is really
// important here; otherwise, the MaximalPathRepresentatives property of the
// MaximalNonzeroEquivalenceClassRepresentativesResult prevents the entire search tree
// of analysisResults from being freed.
var maximalPathRepresentatives = analysisResults.MaximalPathRepresentatives.Select(node => node.Path).ToList();
var outputResults = new MaximalNonzeroEquivalenceClassRepresentativesResults <TVertex>(
analysisResults.CancellativityFailuresDetected,
analysisResults.TooLongPathEncountered,
maximalPathRepresentatives,
analysisResults.LongestPathEncountered);
return(outputResults);
}
/// <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);
}