// Match only if both symbols are same
private static IEnumerable <Match> matchSymbolSymbol(SymbolicString s1, SymbolicString s2)
{
if (s2.atomic_symbol == s1.atomic_symbol)
{
yield return(Match.FullMatch(LogicalExpression.True()));
}
}
public static string NonRegularCheckWord(ArithmeticLanguage lang, int n, string word)
{
if (word.Length < n)
{
return("<false>Word is too short.</false>");
}
foreach (char c in word)
{
if (!lang.alphabet.Contains(c + ""))
{
return("<false>Word contains illegal letters.</false>");
}
}
if (lang.symbolic_string.isFlat())
{
SymbolicString wordSS = Parser.parseSymbolicString(word, lang.alphabet.ToList());
if (ProofChecker.checkContainment(wordSS, lang, LogicalExpression.True()))
{
return("<true></true>");
}
else
{
return("<false>Word is not in the language.</false>");
}
}
else
{
throw new PumpingLemmaException("Arithmetic Language must be flat!");
}
}
public static Tuple <string, string, string> NonRegularGetPumpableSplit(ArithmeticLanguage language, string word, int n)
{
foreach (var split in possibleSplits(word, n))
{
SymbolicString str = splitToSymbStr(language.alphabet.ToList(), split.Item1, split.Item2, split.Item3);
if (ProofChecker.checkContainment(str, language, LogicalExpression.True()))
{
return(split);
}
}
return(null);
}
public static bool NonRegularCheckI(ArithmeticLanguage language, string start, string mid, string end, int i)
{
string fullWord = pumpMid(start, mid, end, i);
if (language.symbolic_string.isFlat())
{
SymbolicString wordSS = Parser.parseSymbolicString(fullWord.ToString(), language.alphabet.ToList());
return(ProofChecker.checkContainment(wordSS, language, LogicalExpression.True()));
}
else
{
throw new PumpingLemmaException("Arithmetic Language must be flat!");
}
}
private static IEnumerable <Match> matchConcatConcat(SymbolicString s1, SymbolicString s2)
{
if (s1.isEpsilon() || s2.isEpsilon())
{
yield return(Match.MakeMatch(LogicalExpression.True(), s1, s2));
yield break;
}
// Quick match prefix symbols
int i;
for (i = 0; i < s1.sub_strings.Count && i < s2.sub_strings.Count; i++)
{
if (s1.sub_strings[i].expression_type != SymbolicString.SymbolicStringType.Symbol ||
s2.sub_strings[i].expression_type != SymbolicString.SymbolicStringType.Symbol)
{
break;
}
if (s1.sub_strings[i].atomic_symbol != s2.sub_strings[i].atomic_symbol)
{
yield break;
}
}
var sub1 = s1.sub_strings.Skip(i);
var sub2 = s2.sub_strings.Skip(i);
// If we have consumed something fully, just return the remaining bits
if (i == s1.sub_strings.Count || i == s2.sub_strings.Count)
{
yield return(Match.MakeMatch(
LogicalExpression.True(),
SymbolicString.Concat(sub1),
SymbolicString.Concat(sub2)));
yield break;
}
var rest1 = SymbolicString.Concat(sub1.Skip(1));
var rest2 = SymbolicString.Concat(sub2.Skip(1));
foreach (var m in match(sub1.First(), sub2.First()))
{
foreach (var mp in m.continueMatch(rest1, rest2))
{
yield return(mp);
}
}
}
public static string NonRegularGetUnpumpableWord(ArithmeticLanguage language, SymbolicString unpumpableWord, int n)
{
Dictionary <VariableType, int> assignment = new Dictionary <VariableType, int>();
assignment.Add(VariableType.Variable("n"), n);
string word = pumpedWord(unpumpableWord, assignment);
SymbolicString ss = SymbolicString.FromTextDescription(language.alphabet.ToList(), word);
while (!ProofChecker.checkContainment(ss, language, LogicalExpression.True()))
{
assignment[VariableType.Variable("n")]++;
word = pumpedWord(unpumpableWord, assignment);
ss = SymbolicString.FromTextDescription(language.alphabet.ToList(), word);
}
return(word);
}
private static IEnumerable <Match> matchSymbolConcat(SymbolicString s1, SymbolicString s2)
{
if (s2.isEpsilon())
{
yield return(Match.PartialFirst(LogicalExpression.True(), s1));
yield break;
}
var rest = SymbolicString.Concat(s2.sub_strings.Skip(1));
foreach (var m in match(s1, s2.sub_strings.First()))
{
foreach (var mp in m.continueMatch(SymbolicString.Epsilon(), rest))
{
yield return(mp);
}
}
}
public Match forceFinish()
{
BooleanExpression additionalConstraint = LogicalExpression.True();
if (FirstRemaining)
{
additionalConstraint = LogicalExpression.And(
additionalConstraint,
ComparisonExpression.Equal(remaining1.length(), 0)
);
}
if (SecondRemaining)
{
additionalConstraint = LogicalExpression.And(
additionalConstraint,
ComparisonExpression.Equal(remaining2.length(), 0)
);
}
return(FullMatch(LogicalExpression.And(this.constraint, additionalConstraint)));
}
public static int NonRegularGetI(ArithmeticLanguage language, string start, string mid, string end)
{
SymbolicString matchingString = splitToSymbStr(language.alphabet.ToList(), start, mid, end);
if (ProofChecker.checkContainment(matchingString, language, LogicalExpression.True()))
{
return(1); // AI surrenders
}
else
{
int i = 0;
do
{
string word = pumpMid(start, mid, end, i);
SymbolicString ss = SymbolicString.FromTextDescription(language.alphabet.ToList(), word);
if (!ProofChecker.checkContainment(ss, language, LogicalExpression.True()))
{
return(i);
}
i++;
} while (i < 99); //for debugging purposes
return(-1);
}
}
public static ArithmeticLanguage FromTextDescriptions(List <String> alphabet, string symbolicStringText, string constraintText)
{
var symbolPattern = new Regex(@"^[a-zA-Z0-9]$");
var illegalSymbols = alphabet.FindAll(s => !symbolPattern.IsMatch(s));
if (illegalSymbols.Count > 0)
{
var message = string.Format(
"Found illegal symbols {0} in alphabet. Symbols should match [a-zA-Z0-9]",
string.Join(", ", illegalSymbols)
);
throw new PumpingLemmaException(message);
}
// Parse the language
var ss = PumpingLemma.Parser.parseSymbolicString(symbolicStringText, alphabet);
if (ss == null)
{
throw new PumpingLemmaException("Unable to parse language");
}
// Parse the constraintDesc
var constraint = PumpingLemma.Parser.parseCondition(constraintText);
if (constraint == null)
{
throw new PumpingLemmaException("Unable to parse constraint");
}
// Make sure all the variables are bound
var boundVariables = ss.GetIntegerVariables();
var constraintVariables = constraint.GetVariables();
// Console.WriteLine("Bound variables: " + String.Join(", ", boundVariables));
// Console.WriteLine("Constriant variables: " + String.Join(", ", constraintVariables));
foreach (var consVar in constraintVariables)
{
if (!boundVariables.Contains(consVar))
{
throw new PumpingLemmaException(
string.Format("Constraint variable {0} not bound", consVar));
}
}
// Add constraints saying that all variables are >= 0
BooleanExpression defaultConstraint = LogicalExpression.True();
foreach (var consVar in constraintVariables)
{
defaultConstraint = LogicalExpression.And(
defaultConstraint,
ComparisonExpression.GreaterThanOrEqual(
LinearIntegerExpression.SingleTerm(1, consVar),
LinearIntegerExpression.Constant(0)
)
);
}
return(new ArithmeticLanguage(alphabet, ss, constraint));
}
// Generate TwoSplit's where either one may be empty
// Generates the splits in order, i.e., by length of the prefix
// So, for s being symbol and concat, first one will always be (\epsilon, s) and last one always (s, \epsilon)
// So, for s being repeat (abc)^n, first will be ((abc)^i,(abc)^j) and last one always ((abc)^i ab, c(abc)^j)
// Requires a flat symbolic string
public IEnumerable <TwoSplit> TwoSplits()
{
SymbolicString prefix, suffix;
// Contract.Requires(this.isFlat());
switch (this.expression_type)
{
case SymbolicStringType.Symbol:
yield return(TwoSplit.MakeSplit(SymbolicString.Epsilon(), this, LogicalExpression.True()));
yield return(TwoSplit.MakeSplit(this, SymbolicString.Epsilon(), LogicalExpression.True()));
break;
case SymbolicStringType.Concat:
yield return(TwoSplit.MakeSplit(SymbolicString.Epsilon(), this, LogicalExpression.True()));
for (int i = 0; i < this.sub_strings.Count; i++)
{
prefix = SymbolicString.Concat(this.sub_strings.Take(i).ToList());
suffix = SymbolicString.Concat(this.sub_strings.Skip(i + 1).ToList());
foreach (var split in this.sub_strings[i].TwoSplits())
{
if (!split.start.isEpsilon())
{
yield return(split.extend(prefix, suffix));
}
}
}
break;
case SymbolicStringType.Repeat:
var v1 = LinearIntegerExpression.FreshVariable();
var v2 = LinearIntegerExpression.FreshVariable();
var sanityConstraint = LogicalExpression.And(
ComparisonExpression.GreaterThanOrEqual(v1, 0),
ComparisonExpression.GreaterThanOrEqual(v2, 0)
);
prefix = SymbolicString.Repeat(this.root, v1);
suffix = SymbolicString.Repeat(this.root, v2);
yield return(TwoSplit.MakeSplit(
prefix,
suffix,
LogicalExpression.And(sanityConstraint, ComparisonExpression.Equal(v1 + v2, this.repeat))
));
if (this.root.expression_type != SymbolicStringType.Concat)
{
break;
}
for (int i = 1; i < this.root.sub_strings.Count; i++)
{
var split = TwoSplit.MakeSplit(
SymbolicString.Concat(this.root.sub_strings.Take(i)),
SymbolicString.Concat(this.root.sub_strings.Skip(i)),
LogicalExpression.And(
ComparisonExpression.Equal(v1 + v2 + 1, this.repeat),
sanityConstraint
)
);
yield return(split.extend(prefix, suffix));
}
break;
default:
throw new ArgumentOutOfRangeException();
}
}
// Generates splits where all three parts may be empty
public IEnumerable <Split> Splits()
{
// Contract.Requires<ArgumentException>(this.isFlat());
switch (this.expression_type)
{
case SymbolicStringType.Symbol:
yield return(Split.MakeSplit(this, SymbolicString.Epsilon(), SymbolicString.Epsilon(), LogicalExpression.True()));
yield return(Split.MakeSplit(SymbolicString.Epsilon(), this, SymbolicString.Epsilon(), LogicalExpression.True()));
yield return(Split.MakeSplit(SymbolicString.Epsilon(), SymbolicString.Epsilon(), this, LogicalExpression.True()));
break;
case SymbolicStringType.Repeat:
var v1 = LinearIntegerExpression.FreshVariable();
var v2 = LinearIntegerExpression.FreshVariable();
var v3 = LinearIntegerExpression.FreshVariable();
var sanityConstraint = LogicalExpression.And(
ComparisonExpression.GreaterThanOrEqual(v1, 0),
ComparisonExpression.GreaterThanOrEqual(v2, 0),
ComparisonExpression.GreaterThanOrEqual(v3, 0)
);
// Suppose the word w = a_0 a_1 \ldots a_{n-1}
// All splits are of the form
// BEG: (a_0 \ldots a_{n-1})^i (a_0 \ldots a_p) = w^i . w_1
// MID: (a_{p+1} \ldots a_{n-1} a_0 \ldots a_p)^j (a_{p+1} \ldots a_q) = (w_2 w_1)^j w_3
// END: (a_{q+1} \ldots a_{n-1}) (a_0 \ldots a_{n-1})^k = w_4 w^k
var w = this.root.wordSymbols();
var ww = w.Concat(w);
int n = w.Count();
for (int w1len = 0; w1len < n; w1len++)
{
var w_1 = w.Take(w1len);
var w_2 = w.Skip(w1len);
var beg = SymbolicString.Concat(
SymbolicString.Repeat(this.root, v1),
SymbolicString.Concat(w_1));
var mid_root = SymbolicString.Concat(
SymbolicString.Concat(w_2),
SymbolicString.Concat(w_1));
var mid_beg = SymbolicString.Repeat(mid_root, v2);
for (int w3len = 0; w3len < n; w3len++)
{
var w_3 = ww.Skip(w1len).Take(w3len);
var mid = SymbolicString.Concat(mid_beg, SymbolicString.Concat(w_3.ToList()));
IEnumerable <SymbolicString> w_4;
if (w1len + w3len == 0)
{
w_4 = new List <SymbolicString>();
}
else if (w1len + w3len <= n)
{
w_4 = w.Skip(w1len).Skip(w3len);
}
else
{
w_4 = ww.Skip(w1len).Skip(w3len);
}
var end = SymbolicString.Concat(
SymbolicString.Concat(w_4.ToList()),
SymbolicString.Repeat(this.root, v3)
);
var consumed = (w_1.Count() + w_3.Count() + w_4.Count()) / w.Count();
yield return(Split.MakeSplit(
beg,
mid,
end,
LogicalExpression.And(
ComparisonExpression.Equal(v1 + v2 + v3 + consumed, this.repeat),
sanityConstraint
)
));
}
}
break;
case SymbolicStringType.Concat:
foreach (var beg_midend in this.TwoSplits())
{
foreach (var mid_end in beg_midend.end.TwoSplits())
{
yield return(Split.MakeSplit(
beg_midend.start,
mid_end.start,
mid_end.end,
LogicalExpression.And(beg_midend.constraints, mid_end.constraints)));
}
}
break;
default:
throw new ArgumentOutOfRangeException();
}
}
public static BooleanExpression And(IEnumerable <BooleanExpression> ops)
{
return(ops.Aggregate(LogicalExpression.True() as BooleanExpression, (x, y) => And(x, y)));
}
public static BooleanExpression And(params BooleanExpression[] ops)
{
return(ops.Aggregate(LogicalExpression.True() as BooleanExpression, (x, y) => And(x, y)));
}
