/// <summary>
/// Initializes a new instance of the <see cref="T:ShefferMultioperationRank4.ArrSet4"/> class.
/// Creates an algebra with nullary multioperations (tetha, epsilon, pi) and op
/// </summary>
/// <param name="op">Multioperation op</param>
public ArrSet4(Multioperation4 op)
{
Add(Multioperation4.Zero);
Add(Multioperation4.E);
Add(Multioperation4.All);
Add(op);
}
public static bool IsFourthType(Multioperation4 op)
{
var first = op & Multioperation4.E;
if (first != Multioperation4.E)
{
return(false);
}
var second = (!op) & op;
if (second != Multioperation4.E)
{
return(false);
}
var third1 = op * (!op);
var third2 = (!op) * op;
if (third1 != Multioperation4.All || third2 != Multioperation4.All)
{
return(false);
}
var fourth = op * op;
if (fourth != Multioperation4.All)
{
return(false);
}
return(true);
}
public static bool IsSecondType(Multioperation4 op)
{
var set = new ArrSet4(op);
if (set.Count <= 3 || set.Count > 4)
{
return(false);
}
var first = op & Multioperation4.E;
if (first != Multioperation4.E)
{
return(false);
}
var mu = !op;
if (mu != op)
{
return(false);
}
var op2 = op * op;
if (op2 != Multioperation4.All)
{
return(false);
}
return(true);
}
public int Add(Multioperation4 op)
{
var prev = Interlocked.CompareExchange(ref opFlags[op.Value], 1, 0);
if (prev != 0)
{
return(prev);
}
opList[_count] = op;
Interlocked.Add(ref _count, 1 - prev);
return(prev);
}
public static bool IsFifthType(Multioperation4 op)
{
var first = op & Multioperation4.E;
if (first != Multioperation4.Zero)
{
return(false);
}
if (!op != op)
{
return(false);
}
var third = op * op;
if (third != Multioperation4.All)
{
return(false);
}
return(true);
}
/// <summary>
/// Generate the whole algebra
/// </summary>
/// <returns>Number of multioperations in algebra</returns>
/// <param name="op">Multioperation generator</param>
public static int CheckOp4Arr(Multioperation4 op)
{
var set = new ArrSet4(op);
if (set.Count <= 3)
{
return(set.Count);
}
var prevCount = 0;
// generate new multioperation while it is possible
while (set.Count < 65536 && prevCount != set.Count)
{
prevCount = set.Count;
// add mu(f) multioperations
for (int i = 0; i < set.Count; i++)
{
set.Add(!set[i]);
}
for (int i = 0; i < set.Count; i++)
{
var op1 = set[i];
// For multioperation tetha: (tetha * x)(x) = (tetha)
// and (tetha intersection f)(x) = (tetha)
// so we could skip this step
if (op1 == Multioperation4.Zero)
{
continue;
}
for (int j = 0; j < set.Count; j++)
{
var op2 = set[j];
// For multioperation tetha: (f * tetha)(x) = (tetha)
// and (f intersection tetha)(x) = (tetha)
// so we could skip this step too
if (op2 == Multioperation4.Zero)
{
continue;
}
// (f * g)(x)
var opSup = op1 * op2;
// (f intersection g)(x)
var opUn = op1 & op2;
set.Add(opSup);
set.Add(opUn);
if (op1 == op2)
{
continue;
}
// (g * f)(x)
opSup = op2 * op1;
set.Add(opSup);
}
}
}
return(set.Count);
}
public bool Contains(Multioperation4 op)
{
return(opFlags[op.Value] == 1);
}
