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 SymbolicString splitToSymbStr(List <string> alphabet, string start, string mid, string end)
{
VariableType freshVar = VariableType.FreshVariable();
List <SymbolicString> strings = new List <SymbolicString>();
if (!start.Equals(""))
{
strings.Add(SymbolicString.FromTextDescription(alphabet, start));
}
SymbolicString pumpedMid = SymbolicString.Repeat(SymbolicString.FromTextDescription(alphabet, mid), LinearIntegerExpression.Variable(freshVar.ToString()));
strings.Add(pumpedMid);
if (!end.Equals(""))
{
strings.Add(SymbolicString.FromTextDescription(alphabet, end));
}
SymbolicString matchingString = SymbolicString.Concat(strings);
return(matchingString);
}
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);
}
}