public override MSOFormula ToMSO(FreshGen fg, string V)
{
int c = fg.get();
string x = "_x_" + c.ToString();
string y = "_y_" + c.ToString();
string X = "_X_" + c.ToString();
int i = str.Length - 1;
string z_i, z_im;
MSOFormula phi = null;
phi = new MSOLabel("z0", str[0]);
while (i > 0)
{
z_i = "z" + i.ToString();
z_im = "z" + (i - 1).ToString();
phi = new MSOExistsFO(z_i, new MSOAnd(new MSOSucc(z_im, z_i),
new MSOAnd(new MSOLabel(z_i, str[i]), phi)));
i--;
}
return(new MSOForallFO("z0", new MSOIff(new MSOBelong("z0", V), phi)));
}
public override MSOFormula ToMSO(FreshGen fg, string v)
{
switch (op)
{
case PDLStringPosOperator.FirstOcc:
{
int i = str.Length - 1;
string z_i, z_im;
MSOFormula phi = null; //new MSOForallFO("x", new MSOEqual("x", "x"));
//TODO make sure input string is non empty that is i/=0
phi = new MSOLabel("z0", str[0]);
while (i > 0)
{
z_i = "z" + i.ToString();
z_im = "z" + (i - 1).ToString();
phi = new MSOExistsFO(z_i, new MSOAnd(new MSOSucc(z_im, z_i),
new MSOAnd(new MSOLabel(z_i, str[i]), phi)));
i--;
}
return(new MSOAnd(new MSOForallFO("z0", new MSOIf(phi, new MSOLessEq(v, "z0"))),
new MSOExistsFO("z0", new MSOAnd(phi, new MSOEqual(v, "z0")))));
}
case PDLStringPosOperator.LastOcc:
{
int i = str.Length - 1;
string z_i, z_im;
MSOFormula phi = null; //new MSOForallFO("x", new MSOEqual("x", "x"));
//TODO make sure input string is non empty that is i/=0
phi = new MSOLabel("z0", str[0]);
while (i > 0)
{
z_i = "z" + i.ToString();
z_im = "z" + (i - 1).ToString();
phi = new MSOExistsFO(z_i, new MSOAnd(new MSOSucc(z_im, z_i),
new MSOAnd(new MSOLabel(z_i, str[i]), phi)));
i--;
}
return(new MSOAnd(new MSOForallFO("z0", new MSOIf(phi, new MSOLessEq("z0", v))),
new MSOExistsFO("z0", new MSOAnd(phi, new MSOEqual(v, "z0")))));
}
default: throw new PDLException("undefined operator");
}
}