// Returns only those matches where s1 is consumed fully
private static IEnumerable <Match> allLeftMatches(SymbolicString s1, SymbolicString s2)
{
// First empty
yield return(Match.PartialSecond(
LogicalExpression.And(
ComparisonExpression.Equal(s1.length(), 0),
ComparisonExpression.GreaterThan(s2.length(), 0)
),
s2
));
// First non-empty
if (!omegaEqual(s1.root, s2.root))
{ // They will mismatch at some point. So, just get small matches up to that point
int firstMismatch = getFirstMismatch(s1.root, s2.root);
foreach (var m in shortLeftMatches(s1, s2, firstMismatch))
{
yield return(m.withAdditionalConstraint(ComparisonExpression.GreaterThan(s1.length(), 0)));
}
}
else
{ // They will never mismatch. So, split s2 into two parts where s1 = first part
foreach (var m in longLeftMatches(s1, s2))
{
yield return(m.withAdditionalConstraint(ComparisonExpression.GreaterThan(s1.length(), 0)));
}
}
}
private static IEnumerable <Match> matchRepeatRepeat(SymbolicString s1, SymbolicString s2)
{
Debug.Assert(s1.root.isWord());
Debug.Assert(s2.root.isWord());
// Assume s1 is fully consumed
foreach (var m in allLeftMatches(s1, s2))
{
yield return(m);
}
// Assume s2 is fully consumed
foreach (var m in allLeftMatches(s2, s1))
{
yield return(m.reverse());
}
// Assume both are fully consumed
if (omegaEqual(s1.root, s2.root))
{
yield return(Match.FullMatch(ComparisonExpression.Equal(
LinearIntegerExpression.Times(s1.root.wordLength(), s1.repeat),
LinearIntegerExpression.Times(s2.root.wordLength(), s2.repeat)
)));
}
else
{
yield return(Match.FullMatch(LogicalExpression.And(
ComparisonExpression.Equal(s2.length(), 0),
ComparisonExpression.Equal(s1.length(), 0)
)));
}
}
public static string NonRegularGetRandomWord(ArithmeticLanguage language, int n)
{
HashSet <Dictionary <VariableType, int> > usedAssigments = new HashSet <Dictionary <VariableType, int> >();
HashSet <VariableType> vars = language.constraint.GetVariables();
for (int i = 0; i < Math.Pow(n, vars.Count); i++)
{
Dictionary <VariableType, int> newAssigment = new Dictionary <VariableType, int>();
foreach (VariableType v in vars)
{
newAssigment.Add(v, randInt(0, n));
}
if (usedAssigments.Contains(newAssigment))
{
i--;
}
else
{
usedAssigments.Add(newAssigment);
//check sat
HashSet <BooleanExpression> ops = new HashSet <BooleanExpression>();
ops.Add(language.constraint);
foreach (var entry in newAssigment)
{
ops.Add(ComparisonExpression.Equal(LinearIntegerExpression.Variable(entry.Key.ToString()), entry.Value));
}
BooleanExpression expr = LogicalExpression.And(ops);
if (expr.isSatisfiable())
{
return(pumpedWord(language.symbolic_string, newAssigment));
}
}
}
return(wordError());
}
private static IEnumerable <Match> longLeftMatches(SymbolicString s1, SymbolicString s2)
{
var l1 = s1.root.wordLength();
var l2 = s2.root.wordLength();
var g = gcd(l1, l2);
var v_beg = LinearIntegerExpression.FreshVariable();
var v_end = LinearIntegerExpression.FreshVariable();
// Split exactly at s2 root border
yield return(Match.PartialSecond(
LogicalExpression.And(
// the beginning matches the s1
ComparisonExpression.Equal(
LinearIntegerExpression.Times(l2, v_beg),
LinearIntegerExpression.Times(l1, s1.repeat)
),
// left over right bit is nonempty
ComparisonExpression.GreaterThan(
LinearIntegerExpression.Times(l2, v_end),
0
),
// beginning and end match s2
ComparisonExpression.Equal(v_beg + v_end, s2.repeat),
ComparisonExpression.GreaterThanOrEqual(v_beg, 0),
ComparisonExpression.GreaterThanOrEqual(v_end, 0)
),
SymbolicString.Repeat(s2.root, v_end)
));
// Split in the middle of s2 root
if (l2 != 1)
{
for (int i = g; i < l2; i += g)
{
var suffix = SymbolicString.Concat(s2.root.sub_strings.Skip(i));
yield return(Match.PartialSecond(
LogicalExpression.And(
ComparisonExpression.Equal(
LinearIntegerExpression.Times(l2, v_beg) + g,
LinearIntegerExpression.Times(l1, s1.repeat)
),
ComparisonExpression.GreaterThan(
LinearIntegerExpression.Times(l2, v_beg) + suffix.length(),
0
),
ComparisonExpression.Equal(v_beg + v_end + 1, s2.repeat),
ComparisonExpression.GreaterThanOrEqual(v_beg, 0),
ComparisonExpression.GreaterThanOrEqual(v_end, 0)
),
SymbolicString.Concat(suffix, SymbolicString.Repeat(s2.root, v_end))
));
}
}
}
public static bool check(ArithmeticLanguage language, SymbolicString pumpingString)
{
if (pumpingString.GetIntegerVariables().Count() != 1)
{
return(false);
}
var pumpingLength = pumpingString.GetIntegerVariables().First();
var pumpingLengthVariable = PumpingLemma.LinearIntegerExpression
.SingleTerm(1, pumpingLength);
var additionalConstraint = LogicalExpression.And(
PumpingLemma.ComparisonExpression.GreaterThan(pumpingLengthVariable, 0),
LogicalExpression.And(pumpingString.repeats().Select(x => ComparisonExpression.GreaterThanOrEqual(x, 0)))
);
// 0. Need to check if pumping string grows unboundedly with p
var pumpingStringLength = pumpingString.length();
if (pumpingStringLength.isConstant() || pumpingStringLength.coefficients[pumpingLength] < 0)
{
return(false);
}
foreach (var r in pumpingString.repeats())
{
if (r.coefficients[pumpingLength] < 0)
{
return(false);
}
}
// 1. Check that the pumping string is in the language for all p
if (!checkContainment(pumpingString, language, additionalConstraint))
{
return(false);
}
Console.WriteLine("Language is non-regular if all the following splits are good:");
int i = 0;
// 2. Check that each split of the pumping string has an valid pumping length
foreach (var split in pumpingString.ValidSplits(pumpingLengthVariable, additionalConstraint))
{
Console.WriteLine("\t" + (i++) + ": " + split + " when " + additionalConstraint);
if (!splitGood(split, language, additionalConstraint))
{
return(false);
}
}
return(true);
}
// Either consume symbol with first symbol of repeat and say repeat is positive
// Or don't consume symbol and say repeat is zero
private static IEnumerable <Match> matchSymbolRepeat(SymbolicString s1, SymbolicString s2)
{
Debug.Assert(s2.isFlat());
// When repeat is 0
yield return(Match.PartialFirst(ComparisonExpression.Equal(s2.repeat, 0), s1));
// When repeat is non-zero
foreach (var m in match(s1, s2.root))
{
// Because the root is a word, we immediately know if the symbol matches or not
// and get an m if and only if the symbol matches
Debug.Assert(!m.FirstRemaining);
yield return(Match.PartialSecond(
LogicalExpression.And(m.constraint, ComparisonExpression.GreaterThan(s2.repeat, 0)),
SymbolicString.Concat(m.remaining2, SymbolicString.Repeat(s2.root, s2.repeat - 1))
));
}
}
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)));
}
private static IEnumerable <Match> shortLeftMatches(SymbolicString s1, SymbolicString s2, int firstMismatch)
{
int l1 = s1.root.wordLength();
for (int i = 1; l1 *i <= firstMismatch; i++)
{
var s1r = SymbolicString.Concat(Enumerable.Repeat(s1.root, i));
foreach (var m in match(s1r, s2))
{
if (m.FirstRemaining)
{
continue;
}
yield return(m.withAdditionalConstraint(LogicalExpression.And(
ComparisonExpression.Equal(s1.length(), s1r.length()),
ComparisonExpression.GreaterThan(m.remaining2.length(), 0)
)));
}
}
}
private static IEnumerable <Match> matchRepeatConcat(SymbolicString s1, SymbolicString s2)
{
if (s2.isEpsilon())
{
yield return(Match.FullMatch(ComparisonExpression.Equal(s1.length(), 0)));
yield return(Match.PartialFirst(ComparisonExpression.GreaterThan(s1.length(), 0), s1));
yield break;
}
var first = s2.sub_strings.First();
var rest = SymbolicString.Concat(s2.sub_strings.Skip(1));
foreach (var m in match(s1, first))
{
foreach (var mp in m.continueMatch(SymbolicString.Epsilon(), rest))
{
yield return(mp);
}
}
}
// Generates splits (x, y, z) such that |y| > 0 and |xy| < p
public IEnumerable <Split> ValidSplits(
LinearIntegerExpression pumpingLengthVariable,
BooleanExpression additionalConstraints)
{
foreach (var split in this.Splits())
{
if (split.mid.isEpsilon())
{
continue;
}
var cond1 = ComparisonExpression.GreaterThan(split.mid.length(), LinearIntegerExpression.Constant(0));
var cond2 = ComparisonExpression.LessThan(split.start.length() + split.mid.length(), pumpingLengthVariable);
var condition = LogicalExpression.And(additionalConstraints, cond1, cond2);
if (condition.isMaybeSatisfiable())
{
split.AddConstraint(condition);
yield return(split);
}
}
}
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));
}
public Dictionary <VariableType, UnaryComparison> getReducedUnaryConstraints()
{
if (!getComparisonExpressions(constraint).All(expr => expr.isUnary()))
{
throw new PumpingLemmaException("The Language doesn't contain only unary constraints.");
}
if (!constraint.isSatisfiable())
{
throw new PumpingLemmaException("The Language constraint is not satisfiable.");
}
Dictionary <VariableType, UnaryComparison> comparisonsToReturn = new Dictionary <VariableType, UnaryComparison>();
IEnumerable <ComparisonExpression> allExpr = getComparisonExpressions(constraint);
//delete non-constraints
allExpr = allExpr.Except(allExpr.Where(e => e.arithmetic_operand1.isConstant() && e.arithmetic_operand2.isConstant()));
//put variable on left side
//divide, so that coefficient = 1
HashSet <ComparisonExpression> ToDelete = new HashSet <ComparisonExpression>();
var exprToAdd = new HashSet <ComparisonExpression>();
foreach (ComparisonExpression expr in allExpr)
{
if (expr.arithmetic_operand1.isConstant())
{
switch (expr.comparison_operator)
{
case ComparisonExpression.ComparisonOperator.GEQ:
exprToAdd.Add(ComparisonExpression.LessThanOrEqual(expr.arithmetic_operand2, expr.arithmetic_operand1));
break;
case ComparisonExpression.ComparisonOperator.GT:
exprToAdd.Add(ComparisonExpression.LessThan(expr.arithmetic_operand2, expr.arithmetic_operand1));
break;
case ComparisonExpression.ComparisonOperator.LEQ:
exprToAdd.Add(ComparisonExpression.GreaterThanOrEqual(expr.arithmetic_operand2, expr.arithmetic_operand1));
break;
case ComparisonExpression.ComparisonOperator.LT:
exprToAdd.Add(ComparisonExpression.GreaterThan(expr.arithmetic_operand2, expr.arithmetic_operand1));
break;
default:
break;
}
}
}
ToDelete = new HashSet <ComparisonExpression>(allExpr.Where(e => e.arithmetic_operand1.isConstant()));
allExpr = allExpr.Except(ToDelete);
allExpr = allExpr.Union(exprToAdd);
ToDelete = new HashSet <ComparisonExpression>();
exprToAdd = new HashSet <ComparisonExpression>();
foreach (var expr in allExpr)
{
foreach (VariableType variable in expr.GetVariables())
{
int coefficient = expr.arithmetic_operand1.coefficients[variable];
int constant = expr.arithmetic_operand2.constant;
double divided = (double)constant / (double)coefficient;
switch (expr.comparison_operator)
{
case ComparisonExpression.ComparisonOperator.EQ:
case ComparisonExpression.ComparisonOperator.NEQ:
if (!isInt(divided))
{
ToDelete.Add(expr);
}
else
{
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(divided));
}
break;
case ComparisonExpression.ComparisonOperator.GEQ:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Ceiling(divided)));
break;
case ComparisonExpression.ComparisonOperator.GT:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Floor(divided)));
break;
case ComparisonExpression.ComparisonOperator.LEQ:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Floor(divided)));
break;
case ComparisonExpression.ComparisonOperator.LT:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Ceiling(divided)));
break;
default:
throw new ArgumentException();
}
}
}
allExpr = allExpr.Except(ToDelete);
allExpr = allExpr.Union(exprToAdd);
ToDelete = new HashSet <ComparisonExpression>();
exprToAdd = new HashSet <ComparisonExpression>();
//reduce if equal constraint is found
HashSet <string> varsToDelete = new HashSet <string>();
foreach (ComparisonExpression expr in allExpr)
{
if (expr.comparison_operator == ComparisonExpression.ComparisonOperator.EQ)
{
VariableType variable = expr.arithmetic_operand1.GetVariables().First();
int coefficient = expr.arithmetic_operand1.coefficients[variable];
int constant = expr.arithmetic_operand2.constant;
int divided = divideConstant(constant, coefficient);
comparisonsToReturn.Add(variable, UnaryComparison.equal(variable, divided));
varsToDelete.Add(variable.ToString());
}
}
IEnumerable <ComparisonExpression> exprToDelete = allExpr.Where(e => varsToDelete.Contains(e.arithmetic_operand1.GetVariables().First().ToString()));
allExpr = allExpr.Except(exprToDelete);
//GEQ -> GT, LEQ -> LT
exprToDelete = new HashSet <ComparisonExpression>();
exprToAdd = new HashSet <ComparisonExpression>();
foreach (ComparisonExpression expr in allExpr)
{
if (expr.comparison_operator == ComparisonExpression.ComparisonOperator.GEQ)
{
ComparisonExpression newExpr = ComparisonExpression.GreaterThan(expr.arithmetic_operand1, expr.arithmetic_operand2.constant - 1);
exprToAdd.Add(newExpr);
}
if (expr.comparison_operator == ComparisonExpression.ComparisonOperator.LEQ)
{
ComparisonExpression newExpr = ComparisonExpression.LessThan(expr.arithmetic_operand1, expr.arithmetic_operand2.constant + 1);
exprToAdd.Add(newExpr);
}
}
exprToDelete = allExpr.Where(e => e.comparison_operator == ComparisonExpression.ComparisonOperator.LEQ ||
e.comparison_operator == ComparisonExpression.ComparisonOperator.GEQ);
allExpr = allExpr.Except(exprToDelete);
allExpr = allExpr.Union(exprToAdd);
HashSet <VariableType> allVars = new HashSet <VariableType>();
foreach (ComparisonExpression expr in allExpr)
{
allVars.Add(expr.arithmetic_operand1.GetVariables().First());
}
foreach (VariableType variable in allVars)
{
IEnumerable <ComparisonExpression> varExpr = allExpr.Where(e => variable.ToString().Equals(e.GetVariables().First().ToString()));
//reduce to single constraints
IEnumerable <ComparisonExpression> gtExpr = varExpr.Where(e => e.comparison_operator == ComparisonExpression.ComparisonOperator.GT);
int gthan = -1;
foreach (ComparisonExpression expr in gtExpr)
{
int coefficient = expr.arithmetic_operand1.coefficients[variable];
int constant = expr.arithmetic_operand2.constant;
//floor
int divided = constant / coefficient;
if (constant > gthan)
{
gthan = constant;
}
}
IEnumerable <ComparisonExpression> ltExpr = varExpr.Where(e => e.comparison_operator == ComparisonExpression.ComparisonOperator.LT);
int lthan = Int32.MaxValue;
foreach (ComparisonExpression expr in ltExpr)
{
int coefficient = expr.arithmetic_operand1.coefficients[variable];
int constant = expr.arithmetic_operand2.constant;
if (constant < lthan)
{
lthan = constant;
}
}
varExpr = varExpr.Except(gtExpr);
varExpr = varExpr.Except(ltExpr);
//rest should be NEQ
HashSet <int> neqInts = new HashSet <int>();
foreach (ComparisonExpression expr in varExpr)
{
if (expr.comparison_operator != ComparisonExpression.ComparisonOperator.NEQ)
{
throw new PumpingLemmaException("The programmer is stupid.");
}
int coefficient = expr.arithmetic_operand1.coefficients[variable];
int constant = expr.arithmetic_operand2.constant;
double divided = (double)constant / coefficient;
//if not int, discard
if (Math.Abs(divided % 1) <= (Double.Epsilon * 100))
{
int divided_int = (int)divided;
neqInts.Add(divided_int);
}
}
if (gthan > -1 && lthan < Int32.MaxValue)
{
comparisonsToReturn.Add(variable, UnaryComparison.between(variable, gthan, lthan, neqInts));
}
else if (gthan > -1 && lthan == Int32.MaxValue)
{
comparisonsToReturn.Add(variable, UnaryComparison.greater(variable, gthan, neqInts));
}
else if (gthan == -1 && lthan < Int32.MaxValue)
{
comparisonsToReturn.Add(variable, UnaryComparison.between(variable, -1, lthan, neqInts));
}
else
{
comparisonsToReturn.Add(variable, UnaryComparison.greater(variable, -1, neqInts));
}
}
return(comparisonsToReturn);
}
// 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();
}
}
// Generates XML for the
public XElement SplitDisplayXML(
VariableType pumpingLength,
BooleanExpression additionalConstraints)
{
Contract.Assert(additionalConstraints.GetVariables().Count() <= 1);
if (additionalConstraints.GetVariables().Count == 1)
{
Contract.Assert(additionalConstraints.GetVariables().First().Equals(pumpingLength));
}
var pumpingLengthVariable = LinearIntegerExpression.SingleTerm(1, pumpingLength);
var repeatLengths = repeats();
// For great and inexplicable reasons. Trust me, it looks better this way.
var displayConstraints = LogicalExpression.And(repeatLengths.Select(x =>
ComparisonExpression.GreaterThanOrEqual(x, LinearIntegerExpression.Constant(5))
));
XElement symbstrings = new XElement("symbstrings");
foreach (var split in this.ValidSplits(pumpingLengthVariable, additionalConstraints))
{
var splitRepeatLengths = split.start.repeats();
splitRepeatLengths.AddRange(split.mid.repeats());
splitRepeatLengths.AddRange(split.end.repeats());
// Get models that don't look terrible
var splitDisplayConstraints = LogicalExpression.And(splitRepeatLengths.Select(x =>
ComparisonExpression.GreaterThanOrEqual(x, LinearIntegerExpression.Constant(1))
));
var constraint = LogicalExpression.And(displayConstraints, split.constraints, splitDisplayConstraints);
if (!constraint.isSatisfiable())
{
continue;
}
var splitModel = constraint.getModel();
var symbstr = new XElement("symbstr");
var strings = new XElement("strings");
var splits = new XElement("splits");
var constrs = new XElement("constraints");
Func <string, Tuple <int, int, SymbolicString>, XElement> handleSegment = (parentTagName, segment) => {
var parent = new XElement(parentTagName);
var from = new XElement("from"); from.Value = segment.Item1.ToString();
var to = new XElement("to"); to.Value = segment.Item2.ToString();
var label = new XElement("label"); label.Add(segment.Item3.ToDisplayXML());
parent.Add(from);
parent.Add(to);
parent.Add(label);
return(parent);
};
int strIndex = 0;
foreach (var segment in getSegments(splitModel, ref strIndex))
{
strings.Add(handleSegment("string", segment));
}
int splitIndex = 0;
foreach (var segment in new[] { split.start, split.mid, split.end })
{
splits.Add(handleSegment("split", segment.makeSegment(splitModel, ref splitIndex)));
}
var constr = new XElement("constraint");
constr.Add(split.constraints.ToDisplayXML());
constrs.Add(constr);
symbstr.Add(strings);
symbstr.Add(splits);
symbstr.Add(constrs);
symbstrings.Add(symbstr);
}
return(symbstrings);
}
private static UnaryComparison compExprToUnaryComp(ComparisonExpression expr)
{
if (!expr.isUnary())
{
return(null);
}
if (expr.arithmetic_operand1.isConstant())
{
LinearIntegerExpression tmp = expr.arithmetic_operand1;
expr.arithmetic_operand1 = expr.arithmetic_operand2;
expr.arithmetic_operand2 = tmp;
switch (expr.comparison_operator)
{
case ComparisonExpression.ComparisonOperator.GEQ:
expr.comparison_operator = ComparisonExpression.ComparisonOperator.LEQ;
break;
case ComparisonExpression.ComparisonOperator.GT:
expr.comparison_operator = ComparisonExpression.ComparisonOperator.LT;
break;
case ComparisonExpression.ComparisonOperator.LEQ:
expr.comparison_operator = ComparisonExpression.ComparisonOperator.GEQ;
break;
case ComparisonExpression.ComparisonOperator.LT:
expr.comparison_operator = ComparisonExpression.ComparisonOperator.GT;
break;
default:
break;
}
}
VariableType variable = expr.GetVariables().First();
int coefficient = expr.arithmetic_operand1.coefficients[variable];
int constant = expr.arithmetic_operand2.constant;
double divided = (double)constant / (double)coefficient;
switch (expr.comparison_operator)
{
case ComparisonExpression.ComparisonOperator.EQ:
case ComparisonExpression.ComparisonOperator.NEQ:
if (!isInt(divided))
{
return(null);
}
else
{
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(divided));
}
break;
case ComparisonExpression.ComparisonOperator.GEQ:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Ceiling(divided)));
break;
case ComparisonExpression.ComparisonOperator.GT:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Floor(divided)));
break;
case ComparisonExpression.ComparisonOperator.LEQ:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Floor(divided)));
break;
case ComparisonExpression.ComparisonOperator.LT:
expr.arithmetic_operand2 = LinearIntegerExpression.Constant(Convert.ToInt32(Math.Ceiling(divided)));
break;
default:
throw new ArgumentException();
}
if (expr.comparison_operator == ComparisonExpression.ComparisonOperator.GEQ)
{
expr.comparison_operator = ComparisonExpression.ComparisonOperator.GT;
expr.arithmetic_operand2.constant--;
}
if (expr.comparison_operator == ComparisonExpression.ComparisonOperator.LEQ)
{
expr.comparison_operator = ComparisonExpression.ComparisonOperator.LT;
expr.arithmetic_operand2.constant++;
}
switch (expr.comparison_operator)
{
case ComparisonExpression.ComparisonOperator.EQ:
return(UnaryComparison.equal(variable, expr.arithmetic_operand2.constant));
case ComparisonExpression.ComparisonOperator.GT:
return(UnaryComparison.greater(variable, expr.arithmetic_operand2.constant, new HashSet <int>()));
case ComparisonExpression.ComparisonOperator.LT:
return(UnaryComparison.between(variable, -1, expr.arithmetic_operand2.constant, new HashSet <int>()));
default:
return(null);
}
}
