internal static PDA <char, char> ParsePDAFromXmlPDA(XElement xmlPDA)
{
var properties = xmlPDA.Elements().Where(el => el.Name.LocalName == XmlNames.Properties).First();
var deterministic = bool.Parse(properties.Elements().Where(el => el.Name.LocalName == XmlNames.Determinism).First().Value);
var acceptanceCondition = AcceptanceCondition.GetAcceptanceConditionById(properties.Elements().Where(el => el.Name.LocalName == XmlNames.AcceptanceCondition).First().Value);
var allStackSymbolsAsStrings = properties.Elements().Where(el => el.Name.LocalName == XmlNames.StackAlphabet).First().Elements().Select(s => s.Value).ToList();
Assertion.Assert(allStackSymbolsAsStrings.All(s => s.Length == 1), "stack symbols must be chars");
var allStackSymbols = allStackSymbolsAsStrings.Select(s => s.First());
var firstStackSymbol = allStackSymbols.First();
//FIXME: what if all keys are used as stack symbols??
var initialState = xmlPDA.Elements().Where(el => el.Name.LocalName == XmlNames.Nodes).First().Elements().Where(el => el.Name.LocalName == XmlNames.InitialState).First();
Assertion.Assert(int.Parse(initialState.Attribute(XmlAttr.Id).Value) == PDA <char, char> .initialStateId, "the initial state has to have id " + PDA <char, char> .initialStateId);
var initialStateIsFinal = bool.Parse(initialState.Attribute(XmlAttr.IsFinal).Value);
var pda = new PDA <char, char>(acceptanceCondition, deterministic, firstStackSymbol, initialStateIsFinal, allStackSymbols, allStackAlphabetSymbols.First(k => !allStackSymbols.Contains(k)));
AddStatesToPda(pda, xmlPDA);
AddTransitionsToPda(pda, xmlPDA);
return(pda);
}
private static void AddInitialTransition(PDA <A, S> pda, PDA <A, S> newPDA, Func <int, int> transformer)
{
newPDA.AddTransition().From(newPDA.InitialState.Id).To(transformer(pda.InitialState.Id)).Read().Pop(newPDA.FirstStackSymbol).Push(new List <S>()
{
pda.FirstStackSymbol, newPDA.FirstStackSymbol
});
}
private static void AddEmptyingTransitions(PDA <A, S> newPDA, int newStateId)
{
foreach (var stackSymbol in newPDA.AllStackSymbols)
{
newPDA.AddTransition().From(newStateId).To(newStateId).Read().Pop(stackSymbol).Push();
}
}
private static void AddStatesToPda(PDA <char, char> pda, XElement xmlPDA)
{
foreach (var node in xmlPDA.Elements().Where(el => el.Name.LocalName == XmlNames.Nodes).First().Elements().Where(el => el.Name.LocalName == XmlNames.InnerState))
{
pda.AddState(int.Parse(node.Attribute(XmlAttr.Id).Value), Boolean.Parse(node.Attribute(XmlAttr.IsFinal).Value));
}
}
private static int AddNewState(PDA <A, S> newPDA)
{
var newStateId = newPDA.States.Max(n => n.Key) + 1;
newPDA.AddState(newStateId, false);
return(newStateId);
}
private static void AddStatesOfOriginalPDA(PDA <A, S> pda, PDA <A, S> newPDA, Func <int, int> transformer)
{
foreach (var state in pda.States)
{
newPDA.AddState(transformer(state.Key), false);
}
}
/// <summary>
/// Merges the both given DPDA with acceptance condition 'empty stack' into a new one, that simply contains both DPDAs. The initial state
/// of the result DPDA has two transitions, one to the initial state of pda1 and one to the initial state of pda2, each of these transitions
/// reads the corresponding given stack symbol. That means, for simulating pda1 with the merged one you just have to start the simulation
/// with the initialStackSymbol1 as start configuration
/// </summary>
/// <param name="dpda1">DPDA with empty stack</param>
/// <param name="dpda2">DPDA with empty stack</param>
/// <param name="initialStackSymbol1">the stack symbol that signals that the first DPDA should be simulated</param>
/// <param name="initialStackSymbol2">the stack symbol that signals that the second DPDA should be simulated</param>
/// <returns>the merged DPDA</returns>
public static PDA <A, S> MergeDPDAsWithEmptyStack(PDA <A, S> dpda1, PDA <A, S> dpda2, S initialStackSymbol1, S initialStackSymbol2)
{
Assertion.Assert(dpda1.Deterministic, NotDeterministicError);
Assertion.Assert(dpda2.Deterministic, NotDeterministicError);
Assertion.Assert(dpda1.AcceptanceCondition.IsEmptyStack(), NotEmptyStackError);
Assertion.Assert(dpda2.AcceptanceCondition.IsEmptyStack(), NotEmptyStackError);
Assertion.Assert(!initialStackSymbol1.Equals(initialStackSymbol2), "the both initial stack symbols must not be the same");
var newStackSymbols = dpda1.AllStackSymbols.Concat(dpda2.AllStackSymbols).Concat(new S[] { initialStackSymbol1, initialStackSymbol2 }).Distinct();
var res = new PDA <A, S>(new AcceptanceCondition.EmptyStack(), true, initialStackSymbol1, false, newStackSymbols);
int idTransformer1(int id) => id + 1;
int maxIdOfDPDA1 = dpda1.States.Max(s => s.Key) + 1;
int idTransformer2(int id) => idTransformer1(id + maxIdOfDPDA1);
AddStatesOfOriginalPDA(dpda1, res, idTransformer1);
AddStatesOfOriginalPDA(dpda2, res, idTransformer2);
AddTransitionsOfOriginalPDA(dpda1, res, idTransformer1);
AddTransitionsOfOriginalPDA(dpda2, res, idTransformer2);
res.AddTransition().From(res.InitialState.Id).To(idTransformer1(dpda1.InitialState.Id)).Read().Pop(initialStackSymbol1).Push(new List <S>()
{
dpda1.FirstStackSymbol
});
res.AddTransition().From(res.InitialState.Id).To(idTransformer2(dpda2.InitialState.Id)).Read().Pop(initialStackSymbol2).Push(new List <S>()
{
dpda2.FirstStackSymbol
});
return(res);
}
/// <summary>
/// runs an approximative equality test of a <see cref="pdaCorrect"/> and a <see cref="pdaAttempt"/>
/// </summary>
/// <param name="pdaCorrect">PDA assumed to be the correct PDA</param>
/// <param name="pdaAttempt">PDA to be testet if it equals the <see cref="pdaCorrect"/></param>
/// <param name="alphabet">alphabet of the both PDAs</param>
/// <param name="maximumWordLengthTested">the maximum length of words out of letters of the <see cref="alphabet"/>, which is tested for, if the PDAs accept them</param>
/// <param name="maximumNumberOfWords">an upper bound for number of words to be tested</param>
/// <param name="maximumMilliSeconds">an upper bound for the time the test should need</param>
public PDAEqualityResult(PDA <char, S> pdaCorrect, PDA <char, T> pdaAttempt, IEnumerable <char> alphabet, int maximumWordLengthTested, int maximumNumberOfWords, int maximumMilliSeconds)
{
this.pdaCorrect = pdaCorrect;
this.pdaAttempt = pdaAttempt;
this.alphabet = alphabet;
CheckWordsUntilLength(maximumWordLengthTested, maximumNumberOfWords, maximumMilliSeconds);
}
private static void AddTransitionsForAddedSymbol(PDA <A, S> pda, PDA <A, S> newPDA, S lowestStackSymbol, A addedSymbol, Func <int, int> transformer)
{
foreach (var state in pda.States.ToList())
{
var newId = transformer(state.Key);
newPDA.AddTransition().From(newId).To(newId).Read(Symbol <A> .SymbolIn(addedSymbol)).Pop(lowestStackSymbol).Push();
}
}
/// <summary>
/// creates a new PDA, that accepts the same language as the given PDA, but with empty stack as acceptance condition; the given PDA is assumed to have final state as acceptance condition
/// </summary>
/// <param name="pda"></param>
/// <returns></returns>
internal static PDA <A, S> ToPDAWithEmptyStack(PDA <A, S> pda)
{
int idTransformer(int id) => id + 1;
var pdaAndNewStateId = ToRawPDA(pda, idTransformer, false);
AddTransitionsToEmptyingState(pda, pdaAndNewStateId.Item1, pdaAndNewStateId.Item2, Symbol <A> .EpsilonIn(), idTransformer);
return(pdaAndNewStateId.Item1);
}
private static void AddTransitionsToEmptyingState(PDA <A, S> pda, PDA <A, S> newPDA, int newStateId, Symbol <A> symbolIn, Func <int, int> transformer)
{
foreach (var finalState in pda.States.Where(s => s.Value.Final).ToList())
{
foreach (var stackSymbol in newPDA.AllStackSymbols)
{
newPDA.AddTransition().From(transformer(finalState.Key)).To(newStateId).Read(symbolIn).Pop(stackSymbol).Push();
}
}
}
private static void AddTransitionsOfOriginalPDA(PDA <A, S> pda, PDA <A, S> newPDA, Func <int, int> transformer)
{
foreach (var state in pda.States)
{
var transitions = state.Value.Transitions;
foreach (var t in transitions)
{
newPDA.AddTransition().From(transformer(state.Key)).To(transformer(t.Target.Id)).Read(t.SymbolIn).Pop(t.StackSymbolIn).Push(t.StackSymbolsWritten);
}
}
}
public bool Equals(PDA <A, S> other)
{
var part1 = AcceptanceCondition.Equals(other.AcceptanceCondition);
var part2 = Deterministic == other.Deterministic;
var part3 = InitialState.Equals(other.InitialState);
var part4 = FirstStackSymbol.Equals(other.FirstStackSymbol);
var part5 = AllStackSymbols.OrderBy(s => s.ToString()).SequenceEqual(other.AllStackSymbols.OrderBy(s => s.ToString()));
var part6 = States.Values.OrderBy(s => s.Id).SequenceEqual(other.States.Values.OrderBy(s => s.Id));
return(part1 && part2 && part3 && part4 && part5 && part6);
}
/// <summary>
/// transforms the given DPDA d with acceptance condition 'final state' to a DPDA with acceptance condition 'empty stack',
/// that accepts the language {wa | w \element L(d)}, where "a" is the further alphabet symbol.
/// The added symbol is necessary to keep the determinism-property of the DPDA
/// </summary>
/// <param name="pda">the DPDA with acceptance condition 'final state', that should be transformed</param>
/// <param name="furtherAlphabetSymbol">the symbol, which is added to every word in the language of the given DPDA</param>
/// <returns>the transformed DPDA</returns>
public static PDA <A, S> ToDPDAWithEmptyStack(PDA <A, S> pda, A furtherAlphabetSymbol)
{
Assertion.Assert(pda.Deterministic, String.Format(NotDeterministicError, ""));
int idTransformer(int id) => id + 1;
var pdaAndNewStateId = ToRawPDA(pda, idTransformer, true);
AddTransitionsToEmptyingState(pda, pdaAndNewStateId.Item1, pdaAndNewStateId.Item2, Symbol <A> .SymbolIn(furtherAlphabetSymbol), idTransformer);
return(pdaAndNewStateId.Item1);
}
private static Tuple <PDA <A, S>, int> ToRawPDA(PDA <A, S> pda, Func <int, int> idTransformer, bool deterministic)
{
Assertion.Assert(pda.AcceptanceCondition.IsFinalState(), AlreadyEmptyStackError);
var res = new PDA <A, S>(new AcceptanceCondition.EmptyStack(), deterministic, pda.FurtherStackSymbol, false, pda.AllStackSymbols.Concat(new S[] { pda.FurtherStackSymbol }));
AddStatesOfOriginalPDA(pda, res, idTransformer);
var newStateId = AddNewState(res);
AddTransitionsOfOriginalPDA(pda, res, idTransformer);
AddInitialTransition(pda, res, idTransformer);
AddEmptyingTransitions(res, newStateId);
return(new Tuple <PDA <A, S>, int>(res, newStateId));
}
/// <summary>
/// transforms the given DPDA d into a new DPDA e with language L(e) = {wa | w \element L(d)}, where "a" is the added symbol
/// </summary>
/// <param name="dpda">the DPDA to transform</param>
/// <param name="addedSymbol">the symbol, which is added to every word in the language of the given DPDA</param>
/// <returns>the transformed DPDA</returns>
public static PDA <A, S> ToDPDAWithAddedAlphabetSymbol(PDA <A, S> dpda, A addedSymbol)
{
Assertion.Assert(dpda.Deterministic, NotDeterministicError);
Assertion.Assert(dpda.AcceptanceCondition.IsEmptyStack(), NotEmptyStackError);
Assertion.Assert(dpda.States.All(s => s.Value.Transitions.All(t => t.SymbolIn.IsEmpty() || !t.SymbolIn.GetSymbol().Equals(addedSymbol))), InvalidSymbolError);
var res = new PDA <A, S>(new AcceptanceCondition.EmptyStack(), true, dpda.FurtherStackSymbol, false, dpda.AllStackSymbols.Concat(new S[] { dpda.FurtherStackSymbol }));
int idTransformer(int id) => id + 1;
AddStatesOfOriginalPDA(dpda, res, idTransformer);
AddTransitionsOfOriginalPDA(dpda, res, idTransformer);
AddInitialTransition(dpda, res, idTransformer);
AddTransitionsForAddedSymbol(dpda, res, dpda.FurtherStackSymbol, addedSymbol, idTransformer);
return(res);
}
public PDA <A, S> Clone()
{
var res = new PDA <A, S>(AcceptanceCondition, true, FirstStackSymbol, InitialState.Final, AllStackSymbols.ToList());
foreach (var state in States.Where(s => s.Key != initialStateId).ToList())
{
res.AddState(state.Key, state.Value.Final);
}
foreach (var state in States)
{
foreach (var t in state.Value.Transitions)
{
res.AddTransition().From(t.Origin.Id).To(t.Target.Id).Read(t.SymbolIn).Pop(t.StackSymbolIn).Push(t.StackSymbolsWritten);
}
}
return(res);
}
private static void AddTransitionsToPda(PDA <char, char> pda, XElement xmlPDA)
{
//FIXME: if deterministic is true, but a transition violations the determinism property, then throw a suitable exception, which is catched in the Grader
foreach (var link in xmlPDA.Elements().Where(el => el.Name.LocalName == XmlNames.Links).First().Elements().Where(el => el.Name.LocalName == XmlNames.Link))
{
var start = int.Parse(link.Attribute(XmlAttr.Start).Value);
var target = int.Parse(link.Attribute(XmlAttr.End).Value);
foreach (var transition in link.Elements().Where(el => el.Name.LocalName == XmlNames.TransitionGroup).First().Elements().Where(el => el.Name.LocalName == XmlNames.Transition))
{
var inputSymbol = transition.Value[0] == Epsilon ? Symbol <char> .EpsilonIn() : Symbol <char> .SymbolIn(transition.Value[0]);
var inputStackSymbol = transition.Value[2];
var writtenStackSymbols = transition.Value.Skip(4);
pda.AddTransition().From(start).To(target).Read(inputSymbol).Pop(inputStackSymbol).Push(writtenStackSymbols);
}
}
}
static internal FromBuilder BuildTrasition(PDA <A, S> pda)
{
return(new FromBuilder(new TransitionBuilder <A, S>(pda)));
}
internal TransitionBuilder(PDA <A, S> pda)
{
this.pda = pda;
}
