/// <summary>
/// For each state of the component, computes the total weight of all paths starting at that state.
/// Ending weights are taken into account.
/// </summary>
/// <remarks>The weights are computed using dynamic programming, going up from leafs to the root.</remarks>
private void ComputeWeightsToEnd()
{
// Iterate in the reverse topological order
for (int currentComponentIndex = 0; currentComponentIndex < this.components.Count; ++currentComponentIndex)
{
StronglyConnectedComponent currentComponent = this.components[currentComponentIndex];
// Update end weights in this component based on outgoing transitions to downward components
for (int stateIndex = 0; stateIndex < currentComponent.Size; ++stateIndex)
{
State state = currentComponent.GetStateByIndex(stateIndex);
// Aggregate weights of all the outgoing transitions from this state
Weight weightToAdd = state.EndWeight;
foreach (var transition in state.Transitions)
{
State destState = this.automaton.States[transition.DestinationStateIndex];
if (this.transitionFilter(transition) && !currentComponent.HasState(destState))
{
weightToAdd += transition.Weight * this.stateInfo[transition.DestinationStateIndex].WeightToEnd;
}
}
// We can go from any state of the component to the current state
if (!weightToAdd.IsZero)
{
for (int updatedStateIndex = 0; updatedStateIndex < currentComponent.Size; ++updatedStateIndex)
{
State updatedState = currentComponent.GetStateByIndex(updatedStateIndex);
CondensationStateInfo updatedStateInfo = this.stateInfo[updatedState.Index];
updatedStateInfo.WeightToEnd +=
currentComponent.GetWeight(updatedStateIndex, stateIndex) * weightToAdd;
this.stateInfo.Update(updatedState.Index, updatedStateInfo);
}
}
}
}
this.weightsToEndComputed = true;
}
/// <summary>
/// For each state of the component, computes the total weight of all paths starting at the root
/// and ending at that state. Ending weights are not taken into account.
/// </summary>
/// <remarks>The weights are computed using dynamic programming, going down from the root to leafs.</remarks>
private void ComputeWeightsFromRoot()
{
CondensationStateInfo rootInfo = this.stateIdToInfo[this.Root.Index];
rootInfo.UpwardWeightFromRoot = Weight.One;
this.stateIdToInfo[this.Root.Index] = rootInfo;
// Iterate in the topological order
for (int currentComponentIndex = this.components.Count - 1; currentComponentIndex >= 0; --currentComponentIndex)
{
StronglyConnectedComponent currentComponent = this.components[currentComponentIndex];
// Propagate weights inside the component
for (int srcStateIndex = 0; srcStateIndex < currentComponent.Size; ++srcStateIndex)
{
State srcState = currentComponent.GetStateByIndex(srcStateIndex);
CondensationStateInfo srcStateInfo = this.stateIdToInfo[srcState.Index];
if (srcStateInfo.UpwardWeightFromRoot.IsZero)
{
continue;
}
for (int destStateIndex = 0; destStateIndex < currentComponent.Size; ++destStateIndex)
{
State destState = currentComponent.GetStateByIndex(destStateIndex);
CondensationStateInfo destStateInfo = this.stateIdToInfo[destState.Index];
destStateInfo.WeightFromRoot = Weight.Sum(
destStateInfo.WeightFromRoot,
Weight.Product(srcStateInfo.UpwardWeightFromRoot, currentComponent.GetWeight(srcStateIndex, destStateIndex)));
this.stateIdToInfo[destState.Index] = destStateInfo;
}
}
// Compute weight contributions to downward components
for (int srcStateIndex = 0; srcStateIndex < currentComponent.Size; ++srcStateIndex)
{
State srcState = currentComponent.GetStateByIndex(srcStateIndex);
CondensationStateInfo srcStateInfo = this.stateIdToInfo[srcState.Index];
if (srcStateInfo.WeightFromRoot.IsZero)
{
continue;
}
// Aggregate weights of all the outgoing transitions from this state
for (int transitionIndex = 0; transitionIndex < srcState.TransitionCount; ++transitionIndex)
{
Transition transition = srcState.GetTransition(transitionIndex);
State destState = srcState.Owner.states[transition.DestinationStateIndex];
if (this.transitionFilter(transition) && !currentComponent.HasState(destState))
{
CondensationStateInfo destStateInfo = this.stateIdToInfo[destState.Index];
destStateInfo.UpwardWeightFromRoot = Weight.Sum(
destStateInfo.UpwardWeightFromRoot,
Weight.Product(srcStateInfo.WeightFromRoot, transition.Weight));
this.stateIdToInfo[transition.DestinationStateIndex] = destStateInfo;
}
}
}
}
this.weightsFromRootComputed = true;
}