public void TestRealDPDAToNormalForm()
        {
            var dpda = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), true, 'Z', false, "ZYX", 'A');

            dpda.AddState(1, 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(1).Read().Pop('Z').Push();

            var dpdaInNormalForm = DPDAToNormalFormConverter <char, char> .ToNormalForm(dpda);

            dpda.CreateRunner();
            dpdaInNormalForm.CreateRunner();

            var equalityResult = new PDAEqualityResult <char, StackSymbolSequence <char> >(dpda, dpdaInNormalForm, "abx", 10, 600000, 3000);

            Assert.IsTrue(equalityResult.AreEqual);
        }
        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);
        }
예제 #3
0
        public void TestMaximumNumberOfWords()
        {
            var pda1 = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), false, 'Z', false, "ZXY");

            pda1.AddState(1, false);
            pda1.AddTransition().From(0).To(0).Read('a').Pop('Z').Push("XZ");
            pda1.AddTransition().From(0).To(0).Read('a').Pop('X').Push("XX");
            pda1.AddTransition().From(0).To(0).Read('a').Pop('Y').Push("XY");
            pda1.AddTransition().From(0).To(0).Read('b').Pop('Z').Push("YZ");
            pda1.AddTransition().From(0).To(0).Read('b').Pop('X').Push("YX");
            pda1.AddTransition().From(0).To(0).Read('b').Pop('Y').Push("YY");

            pda1.AddTransition().From(0).To(1).Read().Pop('Z').Push("Z");
            pda1.AddTransition().From(0).To(1).Read().Pop('X').Push("X");
            pda1.AddTransition().From(0).To(1).Read().Pop('Y').Push("Y");

            pda1.AddTransition().From(1).To(1).Read('c').Pop('X').Push();
            pda1.AddTransition().From(1).To(1).Read('d').Pop('Y').Push();
            pda1.AddTransition().From(1).To(1).Read().Pop('Z').Push();

            var pda2 = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), false, 'Z', false, "ZXY");

            pda2.AddState(1, false);
            pda2.AddTransition().From(0).To(0).Read('a').Pop('Z').Push("XZ");
            pda2.AddTransition().From(0).To(0).Read('a').Pop('X').Push("XX");
            pda2.AddTransition().From(0).To(0).Read('a').Pop('Y').Push("XY");
            pda2.AddTransition().From(0).To(0).Read('b').Pop('Z').Push("YZ");
            pda2.AddTransition().From(0).To(0).Read('b').Pop('X').Push("YX");
            pda2.AddTransition().From(0).To(0).Read('b').Pop('Y').Push("YY");

            pda2.AddTransition().From(0).To(1).Read().Pop('Z').Push("Z");
            pda2.AddTransition().From(0).To(1).Read().Pop('X').Push("X");
            pda2.AddTransition().From(0).To(1).Read().Pop('Y').Push("Y");

            pda2.AddTransition().From(1).To(1).Read('c').Pop('X').Push();
            pda2.AddTransition().From(1).To(1).Read('d').Pop('Y').Push();
            pda2.AddTransition().From(1).To(1).Read('a').Pop('Z').Push();

            pda1.CreateRunner();
            pda2.CreateRunner();

            var watch = new Stopwatch();

            watch.Start();
            var res = new PDAEqualityResult <char, char>(pda1, pda2, "abcd", 10, 400000, 60000);

            watch.Stop();

            Console.WriteLine(watch.ElapsedMilliseconds);

            Assert.IsFalse(res.AreEqual);
        }
        public void ToSDAInNormalFormTest()
        {
            var dpda = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), true, 'Z', false, "ZA");

            dpda.AddState(1, false);

            dpda.HasNormalForm();

            dpda.AddTransition().From(0).To(0).Read('a').Pop('Z').Push("AZ");
            dpda.AddTransition().From(0).To(0).Read('a').Pop('A').Push("AA");
            dpda.AddTransition().From(0).To(1).Read('b').Pop('A').Push("A");
            dpda.AddTransition().From(1).To(1).Read('c').Pop('A').Push();
            dpda.AddTransition().From(1).To(1).Read().Pop('Z').Push();

            var symbols = new Dictionary <string, TripleStackSymbol <char> >()
            {
                { "0A1", new TripleStackSymbol <char>(0, 'A', 1) },
                { "0Z1", new TripleStackSymbol <char>(0, 'Z', 1) },
                { "1A1", new TripleStackSymbol <char>(1, 'A', 1) }
            };

            var exp = new SDA <char, TripleStackSymbol <char> >(symbols.Values);

            exp.AddTransition('a', symbols["0Z1"], new TripleStackSymbol <char>[] { symbols["0A1"] });
            exp.AddTransition('a', symbols["0A1"], new TripleStackSymbol <char>[] { symbols["0A1"], symbols["1A1"] });
            exp.AddTransition('b', symbols["0A1"], new TripleStackSymbol <char>[] { symbols["1A1"] });
            exp.AddTransition('c', symbols["1A1"]);

            var act = DPDAInNormalFormToSDAConverter <char, char> .ToSDAInNormalForm(dpda).sda;

            Assert.IsTrue(exp.Equals(act));

            var actPDA = act.ToPDA(symbols["0Z1"]);

            actPDA.CreateRunner();
            dpda.CreateRunner();

            var equalityResult = new PDAEqualityResult <char, TripleStackSymbol <char> >(dpda, actPDA, "abc", 7, 300000, 3000);

            Assert.IsTrue(equalityResult.AreEqual);

            var actDeterminisedSDA = DeterminisedSDA <char, TripleStackSymbol <char> > .FromSDAInNormalForm(act);

            actDeterminisedSDA.CalculateShortestWordsOfStackSymbols();

            Assert.IsTrue(actDeterminisedSDA.ShortestWordsOfStackSymbols[symbols["1A1"]].SequenceEqual("c"));
            Assert.IsTrue(actDeterminisedSDA.ShortestWordsOfStackSymbols[symbols["0A1"]].SequenceEqual("bc"));
            Assert.IsTrue(actDeterminisedSDA.ShortestWordsOfStackSymbols[symbols["0Z1"]].SequenceEqual("abc"));
        }
예제 #5
0
        public void TestMethod()
        {
            var pdaMirrored = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), false, 'Z', false, "ZAB");

            pdaMirrored.AddState(1, false);

            pdaMirrored.AddTransition().From(0).To(0).Read('a').Pop('Z').Push("AZ");
            pdaMirrored.AddTransition().From(0).To(0).Read('a').Pop('A').Push("AA");
            pdaMirrored.AddTransition().From(0).To(0).Read('a').Pop('B').Push("AB");
            pdaMirrored.AddTransition().From(0).To(0).Read('b').Pop('Z').Push("BZ");
            pdaMirrored.AddTransition().From(0).To(0).Read('b').Pop('A').Push("BA");
            pdaMirrored.AddTransition().From(0).To(0).Read('b').Pop('B').Push("BB");

            pdaMirrored.AddTransition().From(0).To(1).Read().Pop('Z').Push("Z");
            pdaMirrored.AddTransition().From(0).To(1).Read().Pop('A').Push("A");
            pdaMirrored.AddTransition().From(0).To(1).Read().Pop('B').Push("B");
            pdaMirrored.AddTransition().From(0).To(1).Read('a').Pop('Z').Push("Z");
            pdaMirrored.AddTransition().From(0).To(1).Read('a').Pop('A').Push("A");
            pdaMirrored.AddTransition().From(0).To(1).Read('a').Pop('B').Push("B");
            pdaMirrored.AddTransition().From(0).To(1).Read('b').Pop('Z').Push("Z");
            pdaMirrored.AddTransition().From(0).To(1).Read('b').Pop('A').Push("A");
            pdaMirrored.AddTransition().From(0).To(1).Read('b').Pop('B').Push("B");

            pdaMirrored.AddTransition().From(1).To(1).Read('a').Pop('A').Push();
            pdaMirrored.AddTransition().From(1).To(1).Read('b').Pop('B').Push();
            pdaMirrored.AddTransition().From(1).To(1).Read().Pop('Z').Push();

            pdaMirrored.CreateRunner();


            var pdaMirroredEven = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), false, 'Z', false, "ZAB");

            pdaMirroredEven.AddState(1, false);

            pdaMirroredEven.AddTransition().From(0).To(0).Read('a').Pop('Z').Push("AZ");
            pdaMirroredEven.AddTransition().From(0).To(0).Read('a').Pop('A').Push("AA");
            pdaMirroredEven.AddTransition().From(0).To(0).Read('a').Pop('B').Push("AB");
            pdaMirroredEven.AddTransition().From(0).To(0).Read('b').Pop('Z').Push("BZ");
            pdaMirroredEven.AddTransition().From(0).To(0).Read('b').Pop('A').Push("BA");
            pdaMirroredEven.AddTransition().From(0).To(0).Read('b').Pop('B').Push("BB");

            pdaMirroredEven.AddTransition().From(0).To(1).Read().Pop('Z').Push("Z");
            pdaMirroredEven.AddTransition().From(0).To(1).Read().Pop('A').Push("A");
            pdaMirroredEven.AddTransition().From(0).To(1).Read().Pop('B').Push("B");
            pdaMirroredEven.AddTransition().From(0).To(1).Read('a').Pop('Z').Push("Z");
            pdaMirroredEven.AddTransition().From(0).To(1).Read('a').Pop('A').Push("A");
            pdaMirroredEven.AddTransition().From(0).To(1).Read('a').Pop('B').Push("B");
            pdaMirroredEven.AddTransition().From(0).To(1).Read('b').Pop('Z').Push("Z");
            pdaMirroredEven.AddTransition().From(0).To(1).Read('b').Pop('A').Push("A");

            pdaMirroredEven.AddTransition().From(1).To(1).Read('a').Pop('A').Push();
            pdaMirroredEven.AddTransition().From(1).To(1).Read('b').Pop('B').Push();
            pdaMirroredEven.AddTransition().From(1).To(1).Read().Pop('Z').Push();
            pdaMirroredEven.AddTransition().From(1).To(1).Read('a').Pop('Z').Push();

            pdaMirroredEven.CreateRunner();

            var s       = new Stopwatch();
            var results = new Dictionary <int, List <Tuple <bool, TimeSpan> > >();

            for (int i = 1; i <= 15; i++)
            {
                results[i] = new List <Tuple <bool, TimeSpan> >();
            }

            for (int j = 0; j < 1; j++) //TODO: count until 10 for a good average
            {
                for (int i = 1; i <= 15; i++)
                {
                    s.Restart();
                    var eq = new PDAEqualityResult <char, char>(pdaMirrored, pdaMirroredEven, "ab", i, 65535, 20000);
                    s.Stop();
                    results[i].Add(new Tuple <bool, TimeSpan>(eq.AreEqual, s.Elapsed));
                }
            }

            foreach (var t in results)
            {
                var equal = t.Value.All(v => v.Item1);
                var time  = t.Value.Average(v => v.Item2.TotalMilliseconds);
                Console.WriteLine(string.Format("Maximum word length: {0}; Equal: {1}; Time: {2}", t.Key, equal, time));
            }
        }
        public void TestDPDAToNormalForm()
        {
            var dpda = new PDA <char, char>(new AcceptanceCondition.EmptyStack(), true, 'A', false, "ABC", 'Z');

            dpda.AddState(1, false);
            dpda.AddState(2, false);
            dpda.AddState(3, false);
            dpda.AddState(4, false);
            dpda.AddState(5, false);
            dpda.AddState(6, false);
            dpda.AddState(7, false);

            dpda.AddTransition().From(0).To(1).Read().Pop('A').Push("AAA");
            dpda.AddTransition().From(1).To(2).Read('a').Pop('A').Push();
            dpda.AddTransition().From(2).To(3).Read('a').Pop('A').Push();
            dpda.AddTransition().From(3).To(4).Read().Pop('A').Push("BBCC");
            dpda.AddTransition().From(4).To(4).Read('b').Pop('B').Push();
            dpda.AddTransition().From(4).To(4).Read('c').Pop('C').Push();

            dpda.AddTransition().From(1).To(5).Read().Pop('B').Push();
            dpda.AddTransition().From(2).To(6).Read().Pop('B').Push("B");
            dpda.AddTransition().From(6).To(7).Read().Pop('B').Push("B");
            dpda.AddTransition().From(7).To(6).Read().Pop('B').Push("B");


            var allStackSymbols = new List <StackSymbolSequence <char> >()
            {
                new StackSymbolSequence <char>("A"),
                new StackSymbolSequence <char>("B"),
                new StackSymbolSequence <char>("C"),
                new StackSymbolSequence <char>("AA"),
                new StackSymbolSequence <char>("AAA"),
                new StackSymbolSequence <char>("BBCC"),
                new StackSymbolSequence <char>("BCC"),
                new StackSymbolSequence <char>("CC"),
            };
            var exp = new PDA <char, StackSymbolSequence <char> >(new AcceptanceCondition.EmptyStack(), true, new StackSymbolSequence <char>('A'), false, allStackSymbols);

            exp.AddState(1, false);
            exp.AddState(2, false);
            exp.AddState(3, false);
            exp.AddState(4, false);
            exp.AddState(5, false);
            exp.AddState(6, false);
            exp.AddState(7, false);

            exp.AddTransition().From(0).To(2).Read('a').Pop(new StackSymbolSequence <char>("A")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("AA") });
            exp.AddTransition().From(0).To(2).Read('a').Pop(new StackSymbolSequence <char>("AA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("AA"), new StackSymbolSequence <char>("A") });
            exp.AddTransition().From(0).To(2).Read('a').Pop(new StackSymbolSequence <char>("AAA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("AA"), new StackSymbolSequence <char>("AA") });
            exp.AddTransition().From(1).To(5).Read().Pop(new StackSymbolSequence <char>("B")).Push();

            exp.AddTransition().From(1).To(2).Read('a').Pop(new StackSymbolSequence <char>("A")).Push();
            exp.AddTransition().From(1).To(2).Read('a').Pop(new StackSymbolSequence <char>("AA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("A") });
            exp.AddTransition().From(1).To(2).Read('a').Pop(new StackSymbolSequence <char>("AAA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("AA") });

            exp.AddTransition().From(2).To(3).Read('a').Pop(new StackSymbolSequence <char>("A")).Push();
            exp.AddTransition().From(2).To(3).Read('a').Pop(new StackSymbolSequence <char>("AA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("A") });
            exp.AddTransition().From(2).To(3).Read('a').Pop(new StackSymbolSequence <char>("AAA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("AA") });

            exp.AddTransition().From(3).To(4).Read('b').Pop(new StackSymbolSequence <char>("A")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("BCC") });
            exp.AddTransition().From(3).To(4).Read('b').Pop(new StackSymbolSequence <char>("AA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("BCC"), new StackSymbolSequence <char>("A") });
            exp.AddTransition().From(3).To(4).Read('b').Pop(new StackSymbolSequence <char>("AAA")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("BCC"), new StackSymbolSequence <char>("AA") });

            exp.AddTransition().From(4).To(4).Read('b').Pop(new StackSymbolSequence <char>("B")).Push();
            exp.AddTransition().From(4).To(4).Read('b').Pop(new StackSymbolSequence <char>("BCC")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("CC") });
            exp.AddTransition().From(4).To(4).Read('b').Pop(new StackSymbolSequence <char>("BBCC")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("BCC") });
            exp.AddTransition().From(4).To(4).Read('c').Pop(new StackSymbolSequence <char>("C")).Push();
            exp.AddTransition().From(4).To(4).Read('c').Pop(new StackSymbolSequence <char>("CC")).Push(new StackSymbolSequence <char>[] { new StackSymbolSequence <char>("C") });


            var act = DPDAToNormalFormConverter <char, char> .ToNormalForm(dpda);

            Assert.IsTrue(exp.Equals(act));

            dpda.CreateRunner();
            exp.CreateRunner();
            act.CreateRunner();

            var equalityResult1 = new PDAEqualityResult <StackSymbolSequence <char>, StackSymbolSequence <char> >(exp, act, "abc", 7, 300000, 3000);

            Assert.IsTrue(equalityResult1.AreEqual);

            var equalityResult2 = new PDAEqualityResult <char, StackSymbolSequence <char> >(dpda, act, "abc", 10, 600000, 3000);

            Assert.IsTrue(equalityResult2.AreEqual);

            //this is actually unnecessary
            Assert.IsTrue(act.AcceptsWord("aabbcc").Accepts());
            Assert.IsTrue(!act.AcceptsWord("aabbc").Accepts());
            Assert.IsTrue(!act.AcceptsWord("aabcc").Accepts());
            Assert.IsTrue(!act.AcceptsWord("abbcc").Accepts());
            Assert.IsTrue(!act.AcceptsWord("").Accepts());
        }
예제 #7
0
        private static XElement TryToGradeConstructionProblem(XElement xmlPdaCorrect, XElement xmlPdaAttempt, XElement xmlGiveStackAlphabet, XElement xmlMaxGrade, CancellationToken token)
        {
            var pdaCorrect = PDA <char, char> .FromXml(xmlPdaCorrect);

            pdaCorrect.CreateRunner(token);
            var pdaAttempt = PDA <char, char> .FromXml(xmlPdaAttempt);

            pdaAttempt.CreateRunner(token);
            var giveStackAlphabet = bool.Parse(xmlGiveStackAlphabet.Value);
            var maxGrade          = int.Parse(xmlMaxGrade.Value);

            var alphabet = PDAXmlParser.ParseAlphabetFromXmlPDA(xmlPdaCorrect);

            Assertion.Assert(Enumerable.SequenceEqual(alphabet, PDAXmlParser.ParseAlphabetFromXmlPDA(xmlPdaAttempt)), "the alphabets of the given PDAs are not the same");

            var stackAlphabetCorrect = PDAXmlParser.ParseStackAlphabetFromXmlPDA(xmlPdaCorrect);
            var stackAlphabetAttempt = PDAXmlParser.ParseStackAlphabetFromXmlPDA(xmlPdaAttempt);

            Assertion.Assert(!giveStackAlphabet || Enumerable.SequenceEqual(stackAlphabetCorrect, stackAlphabetAttempt), "if the stack-alphabet is given for the solver, the attempt pda has to have the same stack-alphabet");

            int statesDiff = pdaAttempt.States.Count - pdaCorrect.States.Count;
            int stackDiff  = stackAlphabetAttempt.Count - stackAlphabetCorrect.Count;
            PDAEqualityResult <char, char> pdaEqualityResult;

            pdaEqualityResult = new PDAEqualityResult <char, char>(pdaCorrect, pdaAttempt, alphabet, maximumWordLengthTested, maximumNumberOfWords, maximumMilliSeconds);
            if (pdaEqualityResult.PdaCorrectIsinconsistent)
            {
                return(Grader.CreateXmlFeedback(maxGrade, new List <string>()
                {
                    "Oops! Seems like your tutor created an inconsistent pda...therefore, you get the full grade ;)"
                }));
            }

            int    joinSize   = pdaEqualityResult.NumberOfWordsAcceptedByAtLeastOne;
            double proportion = joinSize == 0 ? 1 : (double)pdaEqualityResult.NumberOfWordsAcceptedByBoth / joinSize;
            int    grade      = (int)(maxGrade * proportion);

            var feedback = new List <string>();

            if (!pdaEqualityResult.AreEqual)
            {
                if (pdaEqualityResult.WordsInPdaCorrectButNotInPdaAttempt.Count() == 0 && pdaEqualityResult.WordsInPdaAttemptButNotInPdaCorrect.Count() > 0)
                {
                    feedback.Add(string.Format(HintSuperset));
                }
                else if (pdaEqualityResult.WordsInPdaAttemptButNotInPdaCorrect.Count() == 0 && pdaEqualityResult.WordsInPdaCorrectButNotInPdaAttempt.Count() > 0)
                {
                    feedback.Add(string.Format(HintSubset));
                }

                if (pdaEqualityResult.WordsInPdaCorrectButNotInPdaAttempt.Count() > 0)
                {
                    feedback.Add(string.Format(ErrorWordFalselyExcluded, FindWordWithMinimumLength(pdaEqualityResult.WordsInPdaCorrectButNotInPdaAttempt)));
                }

                if (pdaEqualityResult.WordsInPdaAttemptButNotInPdaCorrect.Count() > 0)
                {
                    feedback.Add(string.Format(ErrorWordFalselyIncluded, FindWordWithMinimumLength(pdaEqualityResult.WordsInPdaAttemptButNotInPdaCorrect)));
                }
            }

            if (pdaEqualityResult.InconsistentWordsInPdaAttempt.Count() > 0)
            {
                grade = Math.Max(grade - 1, 0);
                var tuple = FindElementWithMinimumProperty(pdaEqualityResult.InconsistentWordsInPdaAttempt, t => t.Item1.Length);
                feedback.Add(string.Format(ErrorInconsistentAcceptanceCondition, tuple.Item1, tuple.Item2, !tuple.Item2));
            }

            if (statesDiff > 0 || stackDiff > 0)
            {
                grade = Math.Max(0, grade - 1);

                if (statesDiff > 0)
                {
                    feedback.Add(string.Format(ErrorToManyStates, pdaAttempt.States.Count, pdaCorrect.States.Count));
                }
                if (stackDiff > 0)
                {
                    feedback.Add(string.Format(ErrorToManyStackSymbols, stackAlphabetAttempt.Count, stackAlphabetCorrect.Count));
                }
            }

            if (grade == maxGrade)
            {
                feedback.Add("Perfect!");
            }
            else if (pdaEqualityResult.AreEqual && pdaEqualityResult.InconsistentWordsInPdaAttempt.Count() == 0)
            {
                feedback.Add("Correct (but not perfect)!");
            }

            return(Grader.CreateXmlFeedback(grade, feedback));
        }