/// <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);
}
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 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 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();
}
}
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 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);
}
}
}
