//For random strategy:
/// <summary>
/// Used during game:
/// 2. Step Condition Check of the Duplicator: Fp(alpha(x)) smaller Fp(alpha(y)) </summary>
/// <param name="predicate"> the move of spoiler p_1</param>
/// <param name="t1"> Fp(alpha(x))</param>
/// <param name="t2"> Fp(alpha(y))</param>
public bool getRandomPredicate_HelperMethod(List <int> predicate_1, List <int> predicate_2, List <List <int> > t1, List <List <int> > t2)
{
List <List <int> > Fp1_t1 = ReturnFp(predicate_1)(t1);
List <List <int> > Fp2_t2 = ReturnFp(predicate_2)(t2);
if (Fp1_t1.Count == 0 && Fp2_t2.Count == 0)
{
return(false);
}
int alphabets = Fp2_t2.Count;
bool ret = false;
if (Fp1_t1.Count == 0 && Fp2_t2.Count == 0)
{
return(false);
}
else
{
// has to satisfy this for all alphabets:
for (int i = 0; i < alphabets; i++)
{
if (Fp2_t2[i].Contains(1) && Fp1_t1[i].Count != 0)
{
ret = true; //{0,1} <= {1}
}
if ((Fp1_t1[i].Contains(0) && Fp1_t1[i].Count == 1) && (Fp2_t2[i].Count != 0))
{
ret = true; //{0} <= {0,1} and {0} <= {1}
}
}
}
return(ret);
}
public string Fpalpha_xToString(int state, List <int> predicate, Matrix <List <List <int> >, int> ts)
{
string ret = "{";
List <List <int> > t = ReturnAlpha_X(state, ts.columns(), ts, ts.Alphabet);
List <List <int> > Fp_t = ReturnFp(predicate)(t);
int alphabets = Fp_t.Count;
// has to satisfy this for all alphabets:
for (int i = 0; i < alphabets; i++)
{
if (i != 0 && !ret.Substring(ret.Length - 1).Equals("{"))
{
if (Fp_t[i].Contains(0) && Fp_t[i].Contains(1))
{
ret = ret + ",(" + ts.Alphabet[i].ToString() + ",0)" + "," + "(" + ts.Alphabet[i].ToString() + ",1)";
}
if (Fp_t[i].Contains(0) && !Fp_t[i].Contains(1))
{
ret = ret + ",(" + ts.Alphabet[i].ToString() + ",0)";
}
if (Fp_t[i].Contains(1) && !Fp_t[i].Contains(0))
{
ret = ret + ",(" + ts.Alphabet[i].ToString() + ",1)";
}
}
else
{
if (Fp_t[i].Contains(0) && Fp_t[i].Contains(1))
{
ret = ret + "(" + ts.Alphabet[i].ToString() + ",0)" + "," + "(" + ts.Alphabet[i].ToString() + ",1)";
}
if (Fp_t[i].Contains(0) && !Fp_t[i].Contains(1))
{
ret = ret + "(" + ts.Alphabet[i].ToString() + ",0)";
}
if (Fp_t[i].Contains(1) && !Fp_t[i].Contains(0))
{
ret = ret + "(" + ts.Alphabet[i].ToString() + ",1)";
}
}
}
ret = ret + "}";
return(ret);
}