public static PDLPos posMinusN(PDLPos position, int n)
{
if (n == 0)
{
return(position);
}
else
{
return(posMinusN(new PDLPredecessor(position), n - 1));
}
}
public static Testcase createTestcase4()
{
PDLPos lastMinusFour = posMinusN(new PDLLast(), 4);
PDLPred xLeqLastMinusFour = new PDLPosLeq(new PDLPosVar("x"), lastMinusFour);
PDLPred xLeqY = new PDLPosLeq(new PDLPosVar("x"), new PDLPosVar("y"));
PDLPred xLeqZ = new PDLPosLeq(new PDLPosVar("x"), new PDLPosVar("z"));
PDLPred yLeqXPlusFour = new PDLPosLeq(new PDLPosVar("y"), posPlusN(new PDLPosVar("x"), 4));
PDLPred zLeqXPlusFour = new PDLPosLeq(new PDLPosVar("z"), posPlusN(new PDLPosVar("x"), 4));
PDLPred yNeqZ = new PDLNot(new PDLPosEq(new PDLPosVar("y"), new PDLPosVar("z")));
PDLPred zeroAtY = new PDLAtPos('0', new PDLPosVar("y"));
PDLPred zeroAtZ = new PDLAtPos('0', new PDLPosVar("z"));
PDLPred consequence = new PDLAnd(xLeqY, new PDLAnd(xLeqZ, new PDLAnd(yLeqXPlusFour, new PDLAnd(zLeqXPlusFour, new PDLAnd(yNeqZ, new PDLAnd(zeroAtY, zeroAtZ))))));
PDLPred quantConsequence = new PDLExistsFO("y", new PDLExistsFO("z", consequence));
PDLPred language = new PDLForallFO("x", new PDLIf(xLeqLastMinusFour, quantConsequence));
return(new Testcase(4, oneZeroAlphabet, language));
}
public static PDLPos posMinusN(PDLPos position, int n)
{
if (n == 0)
{
return position;
}
else
{
return posMinusN(new PDLPredecessor(position), n - 1);
}
}
private static bool IsNumericalFromFirstLastOcc(PDLPos phi, out int size)
{
if (phi is PDLLastOcc || phi is PDLFirstOcc)
{
size = 1;
return true;
}
var v1 = phi as PDLPredecessor;
if (v1 != null)
{
int s = 0;
if (IsNumericalFromFirstLastOcc(v1.pos, out s))
{
size = s + 1;
return true;
}
}
var v2 = phi as PDLSuccessor;
if (v2 != null)
{
int s = 0;
if (IsNumericalFromFirstLastOcc(v2.pos, out s))
{
size = s + 1;
return true;
}
}
size = 0;
return false;
}
private static bool IsNumericalFromFirst(PDLPos phi, out int size)
{
if (phi is PDLFirst)
{
size = 1;
return true;
}
var v = phi as PDLSuccessor;
if (v != null)
{
int s = 0;
if (IsNumericalFromFirst(v.pos, out s))
{
size = s + 1;
return true;
}
}
size = 0;
return false;
}
internal static bool SyntacticDisequivIsFalse(PDLPos p1, PDLPos p2)
{
if (p1 is PDLSuccessor)
{
var p11 = p1 as PDLSuccessor;
return SyntacticDisequivIsFalse(p11.pos, p2);
}
if (p2 is PDLPredecessor)
{
var p21 = p2 as PDLPredecessor;
return SyntacticDisequivIsFalse(p1, p21.pos);
}
return p1.CompareTo(p2) == 0;
}
//return true if two positions are trivially different
internal static bool SyntacticDisequivIsTrivial(PDLPos p1, PDLPos p2)
{
return SyntacticDisequivIsTrue(p1, p2) || SyntacticDisequivIsFalse(p1, p2);
}
private PDLPos NthSuccessor(int n, PDLPos operand)
{
PDLPos returnValue = operand;
for (int i = 0; i < n; ++i)
{
returnValue = new PDLSuccessor(returnValue);
}
return returnValue;
}
