private static Tuple<PDA<A, S>, PDA<A, S>> ConvertDPDAsToEmptyStack(PDA<A, S> pda1, PDA<A, S> pda2, A furtherAlphabetSymbol)
{
if (pda1.AcceptanceCondition.IsEmptyStack() && pda2.AcceptanceCondition.IsEmptyStack())
{
return new Tuple<PDA<A, S>, PDA<A, S>>(pda1, pda2);
}
if (pda1.AcceptanceCondition.IsFinalState() && pda2.AcceptanceCondition.IsEmptyStack())
{
var newPda1 = PDATransformer<A, S>.ToDPDAWithEmptyStack(pda1, furtherAlphabetSymbol);
var newPda2 = PDATransformer<A, S>.ToDPDAWithAddedAlphabetSymbol(pda2, furtherAlphabetSymbol);
return new Tuple<PDA<A, S>, PDA<A, S>>(newPda1, newPda2);
}
if (pda1.AcceptanceCondition.IsEmptyStack() && pda2.AcceptanceCondition.IsFinalState())
{
var newPda1 = PDATransformer<A, S>.ToDPDAWithAddedAlphabetSymbol(pda1, furtherAlphabetSymbol);
var newPda2 = PDATransformer<A, S>.ToDPDAWithEmptyStack(pda2, furtherAlphabetSymbol);
return new Tuple<PDA<A, S>, PDA<A, S>>(newPda1, newPda2);
}
if (pda1.AcceptanceCondition.IsFinalState() && pda2.AcceptanceCondition.IsFinalState())
{
var newPda1 = PDATransformer<A, S>.ToDPDAWithEmptyStack(pda1, furtherAlphabetSymbol);
var newPda2 = PDATransformer<A, S>.ToDPDAWithEmptyStack(pda2, furtherAlphabetSymbol);
return new Tuple<PDA<A, S>, PDA<A, S>>(newPda1, newPda2);
}
throw new InvalidOperationException("the given pdas have wrong configuration");
}
internal static bool CheckEquivalence(PDA<A, S> pda1, PDA<A, S> pda2, S initialStackSymbol1, S initialStackSymbol2, A furtherAlphabetSymbol)
{
Assertion.Assert(pda1.Deterministic, String.Format(NotDeterministicError, "first"));
Assertion.Assert(pda2.Deterministic, String.Format(NotDeterministicError, "second"));
bool pdaDoesNotHaveSymbol(PDA<A, S> pda, A symbol) => pda.States.All(s => s.Value.Transitions.All(t => t.SymbolIn.IsEmpty() || !t.SymbolIn.GetSymbol().Equals(symbol)));
Assertion.Assert(pdaDoesNotHaveSymbol(pda1, furtherAlphabetSymbol) && pdaDoesNotHaveSymbol(pda2, furtherAlphabetSymbol), FurtherAlphabetSymbolInvalidError);
//TODO: the PDAs have both acceptance conditions, check also the equivalence of this pda with itself (and the other acceptance condition)
var convertedPDAs = ConvertDPDAsToEmptyStack(pda1, pda2, furtherAlphabetSymbol);
var mergedDPDA = PDATransformer<A, S>.MergeDPDAsWithEmptyStack(convertedPDAs.Item1, convertedPDAs.Item2, initialStackSymbol1, initialStackSymbol2);
var mergedDPDAInNormalForm = DPDAToNormalFormConverter<A, S>.ToNormalForm(mergedDPDA);
var initialStackSymbol1NormalForm = GetStackSymbol(mergedDPDAInNormalForm, initialStackSymbol1);
var initialStackSymbol2NormalForm = GetStackSymbol(mergedDPDAInNormalForm, initialStackSymbol2);
var determinisedSDAResult = DPDAInNormalFormToSDAConverter<A, StackSymbolSequence<S>>.ToDeterminisedSDA(mergedDPDAInNormalForm, initialStackSymbol1NormalForm, initialStackSymbol2NormalForm);
//TODO: create in the FromPDA-method already the partition (see Fact 3.2 in the paper) if it is necessary;
//maybe remove the own step of the creation of the SDA and integrate this into the determinisedSDA,
//as the partition depends on the DPDA that the SDA is created of
return false; //FIXME
}
public void MergeDPDAsWithEmptyStackTest()
{
var dpda1 = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), true, 'A', false, "ABC", 'Z');
dpda1.AddState(1, false);
dpda1.AddState(2, false);
dpda1.AddState(3, false);
dpda1.AddState(4, false);
dpda1.AddState(5, false);
dpda1.AddState(6, false);
dpda1.AddState(7, false);
dpda1.AddTransition().From(0).To(1).Read().Pop('A').Push("AAA");
dpda1.AddTransition().From(1).To(2).Read('a').Pop('A').Push();
dpda1.AddTransition().From(2).To(3).Read('a').Pop('A').Push();
dpda1.AddTransition().From(3).To(4).Read().Pop('A').Push("BBCC");
dpda1.AddTransition().From(4).To(4).Read('b').Pop('B').Push();
dpda1.AddTransition().From(4).To(4).Read('c').Pop('C').Push();
dpda1.AddTransition().From(1).To(5).Read().Pop('B').Push();
dpda1.AddTransition().From(2).To(6).Read().Pop('B').Push("B");
dpda1.AddTransition().From(6).To(7).Read().Pop('B').Push("B");
dpda1.AddTransition().From(7).To(6).Read().Pop('B').Push("B");
var dpda2 = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), true, 'A', false, "ABC", 'Z');
dpda2.AddState(1, false);
dpda2.AddState(2, false);
dpda2.AddState(3, false);
dpda2.AddState(4, false);
dpda2.AddTransition().From(0).To(1).Read().Pop('A').Push("AAA");
dpda2.AddTransition().From(1).To(2).Read('a').Pop('A').Push();
dpda2.AddTransition().From(2).To(3).Read('a').Pop('A').Push();
dpda2.AddTransition().From(3).To(4).Read().Pop('A').Push("BBCC");
dpda2.AddTransition().From(4).To(4).Read('b').Pop('B').Push();
dpda2.AddTransition().From(4).To(4).Read('c').Pop('C').Push();
var mergedDPDAForSimulationOf1 = PDATransformer <char, char> .MergeDPDAsWithEmptyStack(dpda1, dpda2, 'X', 'Y');
dpda1.CreateRunner();
mergedDPDAForSimulationOf1.CreateRunner();
var equalityResult1 = new PDAEqualityResult <char, char>(dpda1, mergedDPDAForSimulationOf1, "abc", 10, 400000, 3000);
Assert.IsTrue(equalityResult1.AreEqual);
var mergedDPDAForSimulationOf2 = PDATransformer <char, char> .MergeDPDAsWithEmptyStack(dpda2, dpda1, 'X', 'Y');
dpda2.CreateRunner();
mergedDPDAForSimulationOf2.CreateRunner();
var equalityResult2 = new PDAEqualityResult <char, char>(dpda2, mergedDPDAForSimulationOf2, "abc", 10, 400000, 3000);
Assert.IsTrue(equalityResult2.AreEqual);
}
private static SimulationPath <A, char> RunSimulationWithCFGForFinalState(PDA <A, char> pda, A[] word, CancellationToken token)
{
Assertion.Assert(pda.AcceptanceCondition.IsFinalState(), "the pda has not final state as acceptance condition");
var pdaWithEmptyStack = PDATransformer <A, char> .ToPDAWithEmptyStack(pda);
var path = RunSimulationWithCFGForEmptyStack(pdaWithEmptyStack, word, token);
return(ConvertEmptyStackSimulationPathBackToFinalState(path, pda));
}
internal PDARunnerWithCFG(PDA <A, S> pda, CancellationToken token)
{
if (pda.AcceptanceCondition.IsEmptyStack())
{
AddCFGOfPDA(pda, AcceptanceCondition.EmptyStack.GetId(), token);
}
if (pda.AcceptanceCondition.IsFinalState())
{
AddCFGOfPDA(PDATransformer <A, S> .ToPDAWithEmptyStack(pda), AcceptanceCondition.FinalState.GetId(), token);
}
}
public void ToDPDAWithAddedAlphabetSymbolTest()
{
var dpda = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), true, 'Z', false, "ZYX");
dpda.AddState(1, false);
dpda.AddState(2, false);
dpda.AddTransition().From(0).To(0).Read('a').Pop('Z').Push("XZ");
dpda.AddTransition().From(0).To(0).Read('a').Pop('X').Push("XX");
dpda.AddTransition().From(0).To(0).Read('a').Pop('Y').Push("XY");
dpda.AddTransition().From(0).To(0).Read('b').Pop('Z').Push("YZ");
dpda.AddTransition().From(0).To(0).Read('b').Pop('X').Push("YX");
dpda.AddTransition().From(0).To(0).Read('b').Pop('Y').Push("YY");
dpda.AddTransition().From(0).To(1).Read('x').Pop('Z').Push("Z");
dpda.AddTransition().From(0).To(1).Read('x').Pop('X').Push("X");
dpda.AddTransition().From(0).To(1).Read('x').Pop('Y').Push("Y");
dpda.AddTransition().From(1).To(1).Read('a').Pop('X').Push("");
dpda.AddTransition().From(1).To(1).Read('b').Pop('Y').Push("");
dpda.AddTransition().From(1).To(2).Read().Pop('Z').Push();
var act = PDATransformer <char, char> .ToDPDAWithAddedAlphabetSymbol(dpda, '$');
act.CreateRunner();
Assert.IsFalse(act.AcceptsWord("").Accepts());
Assert.IsFalse(act.AcceptsWord("ax").Accepts());
Assert.IsFalse(act.AcceptsWord("aaxa").Accepts());
Assert.IsFalse(act.AcceptsWord("xa").Accepts());
Assert.IsFalse(act.AcceptsWord("axaa").Accepts());
Assert.IsFalse(act.AcceptsWord("ax$").Accepts());
Assert.IsFalse(act.AcceptsWord("aaxa$").Accepts());
Assert.IsFalse(act.AcceptsWord("xa$").Accepts());
Assert.IsFalse(act.AcceptsWord("axaa$").Accepts());
Assert.IsFalse(act.AcceptsWord("$").Accepts());
Assert.IsTrue(act.AcceptsWord("x$").Accepts());
Assert.IsTrue(act.AcceptsWord("axa$").Accepts());
Assert.IsTrue(act.AcceptsWord("aaxaa$").Accepts());
Assert.IsTrue(act.AcceptsWord("aaaxaaa$").Accepts());
}
public void ToDPDAWithEmptyStackTest()
{
var dpda = new PDA <char, char>(new AcceptanceCondition.FinalState(), true, 'Z', false, "ZYX", 'B');
dpda.AddState(1, false);
dpda.AddState(2, true);
dpda.AddTransition().From(0).To(0).Read('a').Pop('Z').Push("XZ");
dpda.AddTransition().From(0).To(0).Read('a').Pop('X').Push("XX");
dpda.AddTransition().From(0).To(0).Read('a').Pop('Y').Push("XY");
dpda.AddTransition().From(0).To(0).Read('b').Pop('Z').Push("YZ");
dpda.AddTransition().From(0).To(0).Read('b').Pop('X').Push("YX");
dpda.AddTransition().From(0).To(0).Read('b').Pop('Y').Push("YY");
dpda.AddTransition().From(0).To(1).Read('x').Pop('Z').Push("Z");
dpda.AddTransition().From(0).To(1).Read('x').Pop('X').Push("X");
dpda.AddTransition().From(0).To(1).Read('x').Pop('Y').Push("Y");
dpda.AddTransition().From(1).To(1).Read('a').Pop('X').Push("");
dpda.AddTransition().From(1).To(1).Read('b').Pop('Y').Push("");
dpda.AddTransition().From(1).To(2).Read().Pop('Z').Push("Z");
var exp = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), true, 'B', false, "BZYX");
exp.AddState(1, false);
exp.AddState(2, false);
exp.AddState(3, false);
exp.AddState(4, false);
exp.AddTransition().From(0).To(1).Read().Pop('B').Push("ZB");
exp.AddTransition().From(1).To(1).Read('a').Pop('Z').Push("XZ");
exp.AddTransition().From(1).To(1).Read('a').Pop('X').Push("XX");
exp.AddTransition().From(1).To(1).Read('a').Pop('Y').Push("XY");
exp.AddTransition().From(1).To(1).Read('b').Pop('Z').Push("YZ");
exp.AddTransition().From(1).To(1).Read('b').Pop('X').Push("YX");
exp.AddTransition().From(1).To(1).Read('b').Pop('Y').Push("YY");
exp.AddTransition().From(1).To(2).Read('x').Pop('Z').Push("Z");
exp.AddTransition().From(1).To(2).Read('x').Pop('X').Push("X");
exp.AddTransition().From(1).To(2).Read('x').Pop('Y').Push("Y");
exp.AddTransition().From(2).To(2).Read('a').Pop('X').Push("");
exp.AddTransition().From(2).To(2).Read('b').Pop('Y').Push("");
exp.AddTransition().From(2).To(3).Read().Pop('Z').Push("Z");
exp.AddTransition().From(3).To(4).Read('$').Pop('Z').Push();
exp.AddTransition().From(3).To(4).Read('$').Pop('X').Push();
exp.AddTransition().From(3).To(4).Read('$').Pop('Y').Push();
exp.AddTransition().From(3).To(4).Read('$').Pop('B').Push();
exp.AddTransition().From(4).To(4).Read().Pop('Y').Push();
exp.AddTransition().From(4).To(4).Read().Pop('X').Push();
exp.AddTransition().From(4).To(4).Read().Pop('Z').Push();
exp.AddTransition().From(4).To(4).Read().Pop('B').Push();
var act = PDATransformer <char, char> .ToDPDAWithEmptyStack(dpda, '$');
Assert.IsTrue(act.Equals(exp));
act.CreateRunner();
Assert.IsFalse(act.AcceptsWord("").Accepts());
Assert.IsFalse(act.AcceptsWord("ax").Accepts());
Assert.IsFalse(act.AcceptsWord("aaxa").Accepts());
Assert.IsFalse(act.AcceptsWord("xa").Accepts());
Assert.IsFalse(act.AcceptsWord("axaa").Accepts());
Assert.IsFalse(act.AcceptsWord("ax$").Accepts());
Assert.IsFalse(act.AcceptsWord("aaxa$").Accepts());
Assert.IsFalse(act.AcceptsWord("xa$").Accepts());
Assert.IsFalse(act.AcceptsWord("axaa$").Accepts());
Assert.IsFalse(act.AcceptsWord("$").Accepts());
Assert.IsTrue(act.AcceptsWord("x$").Accepts());
Assert.IsTrue(act.AcceptsWord("axa$").Accepts());
Assert.IsTrue(act.AcceptsWord("aaxaa$").Accepts());
Assert.IsTrue(act.AcceptsWord("aaaxaaa$").Accepts());
}
