internal static Automaton AddXSurroundedPaths(this Automaton automaton)
{
var states = new List <int>(automaton.States);
var symbols = new[] { Constants.RegularLanguage.R, Constants.RegularLanguage.S };
foreach (var fromState in states)
{
foreach (var symbol in symbols)
{
var toStates = new List <int>(automaton.TransitionMatrix.GetStates(fromState, symbol));
foreach (var toState in toStates)
{
// Add a new state before and after
int beforeState = automaton.AddState();
int afterState = automaton.AddState();
// Now add the new transitions between the states
automaton.AddTransition(fromState, beforeState, Constants.RegularLanguage.X);
automaton.AddTransition(beforeState, afterState, symbol);
automaton.AddTransition(afterState, toState, Constants.RegularLanguage.X);
}
}
}
// Add epsilon transitions between all new X states
bool changes = true;
while (changes)
{
changes = AddEpsilonStatesForXXSubPaths(automaton);
}
return(automaton);
}
private static bool AddEpsilonStatesForXXSubPaths(Automaton automaton)
{
var changes = false;
foreach (var state in automaton.States)
{
var states = automaton.GetStatesReachableFromStateWithSymbol(state, Constants.RegularLanguage.X, false);
foreach (var xReachableState in states)
{
var epsilonStates = automaton.GetStatesReachableFromStateWithSymbol(xReachableState, Constants.RegularLanguage.X, false, false);
foreach (var epsilonState in epsilonStates)
{
// Discard epsilon transition that loop back on the same state as they add no value
if (state != epsilonState)
{
if (automaton.AddTransition(state, epsilonState, Automaton.Epsilon))
{
changes = true;
}
}
}
}
}
return(changes);
}
private static bool AddTransitionsFromReachabilityStatus(Automaton automaton, int startState, int finalState, ReachabilityStatus reachabilityStatus)
{
bool changes = false;
if (reachabilityStatus.EvenReachable)
{
if (automaton.AddTransition(startState, finalState, Constants.RegularLanguage.X))
{
changes = true;
}
}
else if (reachabilityStatus.OddReachable)
{
// Odd reachable so add X transition
if (startState != finalState && automaton.AddTransition(startState, finalState, Automaton.Epsilon))
{
changes = true;
}
}
return(changes);
}
public static Automaton Parse(string file)
{
Automaton automaton = new Automaton();
int i = 0;
using (StreamReader sr = new StreamReader(file))
{
string[] inputs = new string[3];
while (!sr.EndOfStream)
{
var line = sr.ReadLine().Split(new string[] { "," }, StringSplitOptions.None);
i++;
if (i == 1)
{
automaton.EntryState = automaton.GetOrCreateState(line[1].Trim());
}
else if (i == 2)
{
automaton.ExitState = automaton.GetOrCreateState(line[1].Trim());
}
else if (i == 3)
{
automaton.DefaultOutput = line[1].Trim();
}
else if (i == 6)
{
inputs[0] = line[1].Trim();
inputs[1] = line[2].Trim();
inputs[2] = line[3].Trim();
}
else if (i > 6)
{
string from = line[0].Trim();
for (int col = 0; col < 3; col++)
{
string to = line[col + 1].Trim();
string input = inputs[col].Trim();
string output = line[col + 5].Trim();
automaton.AddTransition(automaton.GetOrCreateState(from), automaton.GetOrCreateState(to), input, output);
}
}
}
}
return(automaton);
}
internal static Automaton CreateLargeAutomataWithRandomTransitions(char[] alphabet, int states = 10000)
{
var automaton = new Automaton(alphabet);
var rng = new Random();
for (int i = 0; i < states; i++)
{
automaton.AddState();
}
automaton.SetAsStartState(0);
automaton.SetAsFinalState(states - 1);
for (int i = 0; i < states; i++)
{
foreach (var symbol in alphabet)
{
var state = rng.Next(states);
automaton.AddTransition(i, state, symbol);
}
}
return(automaton);
}
/// <summary>
/// Adds a transition to the internally stored canonical state substrings. Returns a list of all transitions that should be added directly resulting from this
/// </summary>
public IReadOnlyCollection <Transition> AddTransition(int stateFrom, char symbol, int stateTo)
{
// This process works as follows:
// - Check whether the transition already exists. If it already does, then just return.
// - Add the transition to the lookup
// - Calculate newly created transitions from the lookups
var outTransitionLookup = _outgoingTransitionLookup[stateFrom].GetTransitionDictionary(symbol);
var inTransitionLookup = _incomingTransitionLookup[stateTo].GetTransitionDictionary(symbol);
// Check whether the transition already exists, and add it if not.
// We will check the outgoing transition from the stateFrom, but we expect it to be consistent between the outgoing and incoming transition
// I.e. if s0 ----S----> s1, then we have S outgoing from s0 to s1, and S incoming on s1 from s0
// Therefore, if something breaks here then we know that our code has produced an inconsistent state
ReachabilityStatus fromReachabilityStatus;
if (outTransitionLookup.TryGetValue(stateTo, out var toReachabilityStatus))
{
fromReachabilityStatus = inTransitionLookup[stateFrom];
}
else
{
toReachabilityStatus = new ReachabilityStatus();
outTransitionLookup[stateTo] = toReachabilityStatus;
fromReachabilityStatus = new ReachabilityStatus();
inTransitionLookup[stateFrom] = fromReachabilityStatus;
}
if (symbol != Constants.RegularLanguage.X)
{
if (toReachabilityStatus.EvenReachable)
{
// Transition already exists
return(Array.Empty <Transition>());
}
else
{
fromReachabilityStatus.EvenReachable = true;
toReachabilityStatus.EvenReachable = true;
}
}
else
{
if (toReachabilityStatus.OddReachable)
{
// Transition already exists
return(Array.Empty <Transition>());
}
else
{
toReachabilityStatus.OddReachable = true;
fromReachabilityStatus.OddReachable = true;
}
}
var toAddTransitions = new List <Transition>();
Action <int, int, char> addTransition = (fromState, toState, symbol) =>
{
if (fromState == toState && symbol == Automaton.Epsilon)
{
return;
}
if (!_automaton.AddTransition(fromState, toState, symbol))
{
return;
}
toAddTransitions.Add(new Transition(fromState, toState, symbol));
};
// Adds an X or epsilon transition from a given state to another, based on an existing reachability status
Action <int, int, ReachabilityStatus, bool> addTransitionFromReachabilityStatus = (fromState, toState, reachabilityStatus, negated) =>
{
if ((reachabilityStatus.EvenReachable && negated) || (reachabilityStatus.OddReachable && !negated))
{
addTransition(fromState, toState, Constants.RegularLanguage.X);
}
if ((reachabilityStatus.OddReachable && negated) || (reachabilityStatus.EvenReachable && !negated))
{
addTransition(fromState, toState, Automaton.Epsilon);
}
};
Func <int, Dictionary <int, ReachabilityStatus> > getEpsilonReachabilityDictionary = (state) =>
{
var rightReachabilityDictionary = _outgoingTransitionLookup[state].EpsilonTransitions.ToDictionary(kv => kv.Key, kv => kv.Value);
ReachabilityStatus?reachabilityStatus = null;
if (!rightReachabilityDictionary.TryGetValue(stateTo, out reachabilityStatus))
{
reachabilityStatus = new ReachabilityStatus();
rightReachabilityDictionary[stateTo] = reachabilityStatus;
}
reachabilityStatus.EvenReachable |= true;
return(rightReachabilityDictionary);
};
// Adds transitions for each side combined together with the middle. Should only be called on combinations that make sense.
Action <Dictionary <int, ReachabilityStatus>, char, int, bool> combineWithBothSides =
(incomingReachabilityLookup, symbol, rightSymbolCount, negated) =>
{
var rightReachabilityDictionary = getEpsilonReachabilityDictionary(stateTo);
for (int i = 1; i <= rightSymbolCount; i++)
{
rightReachabilityDictionary = ApplyTransitionToReachabilityDictionary(rightReachabilityDictionary, symbol, i != rightSymbolCount);
}
foreach (var leftReachabilityStatus in incomingReachabilityLookup)
{
foreach (var rightReachabilityStatus in rightReachabilityDictionary)
{
var stateReachabilityStatus = leftReachabilityStatus.Value.Times(rightReachabilityStatus.Value);
addTransitionFromReachabilityStatus(leftReachabilityStatus.Key, rightReachabilityStatus.Key, stateReachabilityStatus, negated);
}
}
};
Action <Dictionary <int, ReachabilityStatus>, bool> combineLeft =
(incomingReachabilityLookup, negated) =>
{
foreach (var stateReachabilityLookup in incomingReachabilityLookup)
{
addTransitionFromReachabilityStatus(stateReachabilityLookup.Key, stateTo, stateReachabilityLookup.Value, negated);
}
};
Action <char, int, bool> combineRight =
(symbol, rightSymbolCount, negated) =>
{
var rightReachabilityDictionary = getEpsilonReachabilityDictionary(stateTo);
for (int i = 1; i <= rightSymbolCount; i++)
{
rightReachabilityDictionary = ApplyTransitionToReachabilityDictionary(rightReachabilityDictionary, symbol, i != rightSymbolCount);
}
foreach (var rightReachabilityLookup in rightReachabilityDictionary)
{
addTransitionFromReachabilityStatus(stateFrom, rightReachabilityLookup.Key, rightReachabilityLookup.Value, negated);
}
};
// Update a given transition set, by iterating through all possibilities specified in the iterate lookup
Action <int, Dictionary <int, ReachabilityStatus>, Func <StateTransitions, Dictionary <int, ReachabilityStatus> >, bool> updateTransitionSetEpsilon =
(inState, iterateReachabilityLookup, getToReachabilitySet, negated) =>
{
foreach (var stateReachabilityLookup in iterateReachabilityLookup)
{
var currentOutState = stateReachabilityLookup.Key;
var currentReachabilityStatus = stateReachabilityLookup.Value;
UpdateReachabilityStatus(currentOutState, currentReachabilityStatus, getToReachabilitySet(_incomingTransitionLookup[inState]), negated);
UpdateReachabilityStatus(inState, currentReachabilityStatus, getToReachabilitySet(_outgoingTransitionLookup[currentOutState]), negated);
}
};
Action <Dictionary <int, ReachabilityStatus>, Func <StateTransitions, Dictionary <int, ReachabilityStatus> >, bool> updateTransitionSetRight =
(iterateReachabilityLookup, getToReachabilitySet, negated) =>
{
foreach (var stateReachabilityLookup in iterateReachabilityLookup)
{
var currentReachabilityStatus = stateReachabilityLookup.Value;
UpdateReachabilityStatus(stateFrom, currentReachabilityStatus, getToReachabilitySet(_incomingTransitionLookup[stateReachabilityLookup.Key]), negated);
UpdateReachabilityStatus(stateReachabilityLookup.Key, currentReachabilityStatus, getToReachabilitySet(_outgoingTransitionLookup[stateFrom]), negated);
}
};
Action <Dictionary <int, ReachabilityStatus>, Func <StateTransitions, Dictionary <int, ReachabilityStatus> >, bool> updateTransitionSetLeft =
(iterateReachabilityLookup, getToReachabilitySet, negated) =>
{
foreach (var stateReachabilityLookup in iterateReachabilityLookup)
{
foreach (var epsilonReachability in getEpsilonReachabilityDictionary(stateTo))
{
var combinedReachability = stateReachabilityLookup.Value.Times(epsilonReachability.Value);
UpdateReachabilityStatus(epsilonReachability.Key, combinedReachability, getToReachabilitySet(_outgoingTransitionLookup[stateReachabilityLookup.Key]), false);
UpdateReachabilityStatus(stateReachabilityLookup.Key, combinedReachability, getToReachabilitySet(_incomingTransitionLookup[epsilonReachability.Key]), false);
}
}
};
Action <Dictionary <int, ReachabilityStatus>, Dictionary <int, ReachabilityStatus>, Func <StateTransitions, Dictionary <int, ReachabilityStatus> >, bool> updateTransitionSetBothSides =
(leftIterateSet, rightIterateSet, getToReachabilitySet, negated) =>
{
foreach (var lefStateReachabilityLookup in leftIterateSet)
{
foreach (var rightStateReachabilityLookup in rightIterateSet)
{
var leftState = lefStateReachabilityLookup.Key;
var rightState = rightStateReachabilityLookup.Key;
var currentReachabilityStatus = lefStateReachabilityLookup.Value.Times(rightStateReachabilityLookup.Value);
UpdateReachabilityStatus(leftState, currentReachabilityStatus, getToReachabilitySet(_incomingTransitionLookup[rightState]), negated);
UpdateReachabilityStatus(rightState, currentReachabilityStatus, getToReachabilitySet(_outgoingTransitionLookup[leftState]), negated);
}
}
};
// We have sk ---symbol---> sj.
// Now combine this with the incoming and outgoing transitions with sk and sjs
switch (symbol)
{
// For S Combine with S transitions on each side (S + S = X)
case Constants.RegularLanguage.S:
updateTransitionSetRight(_outgoingTransitionLookup[stateTo].EpsilonTransitions, (s) => s.STransitions, false);
// Combine new S transition with any incoming and outgoing S transitions
combineRight('S', 1, true);
combineLeft(_incomingTransitionLookup[stateFrom].STransitions, true);
break;
// For R Combine left with R and RR transitions on each side.(R + R = RR, RR + R = R + RR = X, R + R + R = X)
// In other words:
// For R + RR = X or RR + R = X add a transition
// For R + R + R = X add a transition
// For R + R = RR update the dictionaries.
case Constants.RegularLanguage.R:
// Update R + X/epsilon
updateTransitionSetRight(_outgoingTransitionLookup[stateTo].EpsilonTransitions, (s) => s.RTransitions, false);
// Update R + R transitions either side
updateTransitionSetLeft(_incomingTransitionLookup[stateFrom].RTransitions, (s) => s.RRTransitions, false);
updateTransitionSetRight(_outgoingTransitionLookup[stateTo].RTransitions, (s) => s.RRTransitions, false);
// Combine new R transition with any incoming RR transitions
combineRight('R', 2, true);
combineLeft(_incomingTransitionLookup[stateFrom].RRTransitions, true);
// Update incoming and outgoing transitions for R + R + R
combineWithBothSides(_incomingTransitionLookup[stateFrom].RTransitions, 'R', 1, true);
// Combine new R transition with any incoming R transitions
break;
case Constants.RegularLanguage.X:
case Automaton.Epsilon:
// For X and Epsilon Combine with X, S, R and RR transitions on each side
var even = true;
if (symbol == Constants.RegularLanguage.X)
{
// Update chains set
foreach (var chainEnd in _outgoingTransitionLookup[stateTo].EpsilonChains.Append(stateTo))
{
_outgoingTransitionLookup[stateFrom].XEpsilonChains.Add(chainEnd);
_incomingTransitionLookup[chainEnd].XEpsilonChains.Add(stateFrom);
}
even = false;
// Add epsilon transitions for X + X
// TODO: Potential optimisation:
// We shouldn't need to add the state to the queue here as the state should already be consistent at this point,
// so we should just add the state to the automaton, so long as it doesn't go to itself.
foreach (var xChainStart in _incomingTransitionLookup[stateFrom].XEpsilonChains)
{
addTransition(xChainStart, stateTo, Automaton.Epsilon);
}
var xStates = _automaton.GetStatesReachableFromStateWithSymbol(stateTo, 'X', true, false);
foreach (var xState in xStates)
{
addTransition(stateFrom, xState, Automaton.Epsilon);
}
}
else
{
// Update chains set
_outgoingTransitionLookup[stateFrom].EpsilonChains.Add(stateTo);
_incomingTransitionLookup[stateTo].EpsilonChains.Add(stateFrom);
foreach (var chainEnd in _outgoingTransitionLookup[stateTo].EpsilonChains.Append(stateTo))
{
foreach (var chainStart in _incomingTransitionLookup[stateFrom].XEpsilonChains)
{
_outgoingTransitionLookup[chainStart].XEpsilonChains.Add(chainEnd);
_incomingTransitionLookup[chainEnd].XEpsilonChains.Add(chainStart);
}
foreach (var chainStart in _incomingTransitionLookup[stateFrom].EpsilonChains)
{
_outgoingTransitionLookup[chainStart].EpsilonChains.Add(chainEnd);
_incomingTransitionLookup[chainEnd].EpsilonChains.Add(chainStart);
}
}
// Combine with X on each side X
var incomingXEpsilonChains = _incomingTransitionLookup[stateFrom].XEpsilonChains;
var xStates = _automaton.GetStatesReachableFromStateWithSymbol(stateTo, 'X', true, false);
var newTransitions = new List <(int from, int to)>();
foreach (var startXState in incomingXEpsilonChains)
{
foreach (var outgoingX in xStates)
{
// Both X. Combine.
newTransitions.Add((startXState, outgoingX));
}
}
foreach (var transition in newTransitions)
{
addTransition(transition.from, transition.to, Automaton.Epsilon);
}
}
// First update the Transition lookup.
// Update epsilon transitions
updateTransitionSetRight(_outgoingTransitionLookup[stateTo].EpsilonTransitions, (s) => s.EpsilonTransitions, !even);
// updateTransitionSetLeft(_incomingTransitionLookup[stateFrom].EpsilonTransitions, (s) => s.EpsilonTransitions, !even);
updateTransitionSetEpsilon(stateTo, _incomingTransitionLookup[stateFrom].EpsilonTransitions, (s) => s.EpsilonTransitions, !even);
// Combine with X,S,R,RR from front side. We only do the front side as the rules we are checking are XX, SXS, RXRXR.
foreach (var reachabilityLookup in _outgoingTransitionLookup[stateFrom].EpsilonTransitions)
{
if (reachabilityLookup.Value.EvenReachable)
{
updateTransitionSetEpsilon(reachabilityLookup.Key, _incomingTransitionLookup[stateFrom].STransitions, (s) => s.STransitions, false);
updateTransitionSetEpsilon(reachabilityLookup.Key, _incomingTransitionLookup[stateFrom].RTransitions, (s) => s.RTransitions, false);
updateTransitionSetEpsilon(reachabilityLookup.Key, _incomingTransitionLookup[stateFrom].RRTransitions, (s) => s.RRTransitions, false);
}
if (reachabilityLookup.Value.OddReachable)
{
updateTransitionSetEpsilon(reachabilityLookup.Key, _incomingTransitionLookup[stateFrom].STransitions, (s) => s.STransitions, true);
updateTransitionSetEpsilon(reachabilityLookup.Key, _incomingTransitionLookup[stateFrom].RTransitions, (s) => s.RTransitions, true);
updateTransitionSetEpsilon(reachabilityLookup.Key, _incomingTransitionLookup[stateFrom].RRTransitions, (s) => s.RRTransitions, true);
}
}
// Combine R + R
var rightReachability = getEpsilonReachabilityDictionary(stateTo);
rightReachability = ApplyTransitionToReachabilityDictionary(rightReachability, 'R', false);
foreach (var incomingRReachability in _incomingTransitionLookup[stateFrom].RTransitions)
{
foreach (var epsilonReachability in rightReachability)
{
var combinedReachability = incomingRReachability.Value.Times(epsilonReachability.Value);
UpdateReachabilityStatus(epsilonReachability.Key, combinedReachability, _outgoingTransitionLookup[incomingRReachability.Key].RRTransitions, !even);
UpdateReachabilityStatus(incomingRReachability.Key, combinedReachability, _incomingTransitionLookup[epsilonReachability.Key].RRTransitions, !even);
}
}
// Combine S + S
combineWithBothSides(_incomingTransitionLookup[stateFrom].STransitions, 'S', 1, even);
// Combine R + RR
combineWithBothSides(_incomingTransitionLookup[stateFrom].RTransitions, 'R', 2, even);
// Combine RR + R
combineWithBothSides(_incomingTransitionLookup[stateFrom].RRTransitions, 'R', 1, even);
break;
default:
throw new ArgumentException($"Character {symbol} has no understood implementation for canonicalisation");
}
return(toAddTransitions);
}
public static Automaton Build()
{
var automaton = new Automaton();
automaton.EntryState = automaton.GetOrCreateState("Nonexistant");
automaton.ExitState = automaton.GetOrCreateState("Discontinued");
automaton.AddTransition(automaton.GetOrCreateState("Nonexistant"), automaton.GetOrCreateState("Available"), "CreateAvailable", "Available");
automaton.AddTransition(automaton.GetOrCreateState("Nonexistant"), automaton.GetOrCreateState("Preorder"), "CreatePreorder", "Preorder");
automaton.AddTransition(automaton.GetOrCreateState("Preorder"), automaton.GetOrCreateState("Preorder"), "ToPreorder", "Preorder");
automaton.AddTransition(automaton.GetOrCreateState("Preorder"), automaton.GetOrCreateState("Available"), "ToAvailable", "Available");
automaton.AddTransition(automaton.GetOrCreateState("Preorder"), automaton.GetOrCreateState("OutOfStock"), "ToOutOfStock", "OutOfStock");
automaton.AddTransition(automaton.GetOrCreateState("Preorder"), automaton.GetOrCreateState("OnTheWay"), "ToOnTheWay", "OnTheWay");
automaton.AddTransition(automaton.GetOrCreateState("Preorder"), automaton.GetOrCreateState("Discontinued"), "ToDiscontinued", "Discontinued");
automaton.AddTransition(automaton.GetOrCreateState("Available"), automaton.GetOrCreateState("Available"), "ToAvailable", "Available");
automaton.AddTransition(automaton.GetOrCreateState("Available"), automaton.GetOrCreateState("OutOfStock"), "ToOutOfStock", "OutOfStock");
automaton.AddTransition(automaton.GetOrCreateState("Available"), automaton.GetOrCreateState("OnTheWay"), "ToOnTheWay", "OnTheWay");
automaton.AddTransition(automaton.GetOrCreateState("Available"), automaton.GetOrCreateState("Discontinued"), "ToDiscontinued", "Discontinued");
automaton.AddTransition(automaton.GetOrCreateState("OutOfStock"), automaton.GetOrCreateState("OutOfStock"), "ToOutOfStock", "OutOfStock");
automaton.AddTransition(automaton.GetOrCreateState("OutOfStock"), automaton.GetOrCreateState("Available"), "ToAvailable", "Available");
automaton.AddTransition(automaton.GetOrCreateState("OutOfStock"), automaton.GetOrCreateState("OnTheWay"), "ToOnTheWay", "OnTheWay");
automaton.AddTransition(automaton.GetOrCreateState("OutOfStock"), automaton.GetOrCreateState("Discontinued"), "ToDiscontinued", "Discontinued");
automaton.AddTransition(automaton.GetOrCreateState("OnTheWay"), automaton.GetOrCreateState("OnTheWay"), "ToOnTheWay", "OnTheWay");
automaton.AddTransition(automaton.GetOrCreateState("OnTheWay"), automaton.GetOrCreateState("Available"), "ToAvailable", "Available");
automaton.AddTransition(automaton.GetOrCreateState("OnTheWay"), automaton.GetOrCreateState("Discontinued"), "ToDiscontinued", "Discontinued");
//automaton.AddTransition(automaton.GetOrCreateState(""), automaton.GetOrCreateState(""), "", "");
return(automaton);
}
