public TertiaryOpExpression(BooleanFunction f, BooleanExpression first, BooleanExpression second, BooleanExpression third)
{
F = f;
First = first;
Second = second;
Third = third;
}
public static bool CheckMonotony(BooleanFunction f, bool verbose = false)
{
for (int i = 0; i < 8; i++)
{
for (int j = 0; j < 8; j++)
{
if (!AreAdjacent(i, j) || !IsLessThan(i, j))
{
continue;
}
if (f.EvalAt(i) > f.EvalAt(j))
{
if (verbose)
{
Console.WriteLine("F ∉ T_<=, т.к. F({0}) > F({1})", PointAsString(i), PointAsString(j));
}
return(false);
}
}
}
if (verbose)
{
Console.WriteLine("F ∈ T_<=, т.к. я на всех наборах проверял, честно!");
}
return(true);
}
public BooleanFunction DirectionalDeriv(params BooleanVariable[] variables)
{
Dictionary <BooleanVariable, bool> values;
int res = 0;
for (int i = 0; i < 8; i++)
{
res *= 2;
values = new Dictionary <BooleanVariable, bool> {
{ BooleanVariable.A, i / 4 == 1 },
{ BooleanVariable.B, i / 2 % 2 == 1 },
{ BooleanVariable.C, i % 2 == 1 },
};
BooleanFunction leftOp = this;
BooleanFunction rightOp = this;
foreach (var variable in variables)
{
leftOp = leftOp.FixVar(variable, values[variable] ? 1 : 0);
rightOp = rightOp.FixVar(variable, values[variable] ? 0 : 1);
}
res += leftOp.EvalAt(i) ^ rightOp.EvalAt(i);
}
return(new BooleanFunction((byte)res));
}
public static void PrintMaclauren0EqOr(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
Console.WriteLine("F(A,B,C) = " + f.GetTailorStringEq(7));
Console.WriteLine();
}
static void PrintJustTruthTable(BooleanFunction f)
{
Console.WriteLine((new BooleanFunction(0x0F)).ToString("A"));
Console.WriteLine((new BooleanFunction(0x33)).ToString("B"));
Console.WriteLine((new BooleanFunction(0x55)).ToString("C"));
Console.WriteLine(f.ToString("F"));
}
public static void PrintExpressionFor3DirDerivative(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
Console.WriteLine(DirDerivStrings[6] + " = " + BooleanExpression.FindMininalExpressionInBasis(
f.DirectionalDeriv(VarLists[6]).Eval(), AvdoshinBases[0], AvdoshinVars[0]).ToString());
Console.WriteLine();
}
public static void Print3DirectionalDerivative(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
PrintJustTruthTable(f);
Console.WriteLine(f.DirectionalDeriv(VarLists[6]).ToString(DirDerivStrings[6]));
Console.WriteLine();
}
public BooleanFunction Deriv(params BooleanVariable[] variables)
{
BooleanFunction res = this;
foreach (var variable in variables)
{
res = new BooleanFunction((byte)(res.FixVar(variable, 0).Eval() ^ res.FixVar(variable, 1).Eval()));
}
return(res);
}
public static void PrintTailor0EqOr(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
for (int i = 0; i < 8; i++)
{
Console.WriteLine(ReprStrings[i] + ": F(A,B,C) = " + f.GetTailorStringEq(i));
}
Console.WriteLine();
}
public static void PrintExpressionsFor2DirDerivatives(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
for (int i = 3; i <= 5; i++)
{
Console.WriteLine(DirDerivStrings[i] + " = " + BooleanExpression.FindMininalExpressionInBasis(
f.DirectionalDeriv(VarLists[i]).Eval(), AvdoshinBases[0], AvdoshinVars[0]).ToString());
}
Console.WriteLine();
}
public static void Print2DirectionalDerivatives(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
PrintJustTruthTable(f);
for (int i = 3; i <= 5; i++)
{
Console.WriteLine(f.DirectionalDeriv(VarLists[i]).ToString(DirDerivStrings[i]));
}
Console.WriteLine();
}
public static void PrintClosedClasses(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
PostClosedClasses.CheckConservationZero(f, true);
PostClosedClasses.CheckConservationOne(f, true);
PostClosedClasses.CheckSelfDuality(f, true);
PostClosedClasses.CheckMonotony(f, true);
PostClosedClasses.CheckLinearity(f, true);
Console.WriteLine();
}
static public IEnumerable <TertiaryOpExpression> CombineTertiary(BooleanFunction f,
BooleanExpression firstExpression, BooleanExpression anotherExpression, BooleanExpression thirdExpression)
{
yield return(new TertiaryOpExpression(f, firstExpression.Clone(), anotherExpression.Clone(),
thirdExpression.Clone()));
yield return(new TertiaryOpExpression(f, firstExpression.Clone(), thirdExpression.Clone(),
anotherExpression.Clone()));
yield return(new TertiaryOpExpression(f, anotherExpression.Clone(), firstExpression.Clone(),
thirdExpression.Clone()));
yield return(new TertiaryOpExpression(f, thirdExpression.Clone(), firstExpression.Clone(),
anotherExpression.Clone()));
yield return(new TertiaryOpExpression(f, anotherExpression.Clone(), thirdExpression.Clone(),
firstExpression.Clone()));
yield return(new TertiaryOpExpression(f, thirdExpression.Clone(), anotherExpression.Clone(),
firstExpression.Clone()));
}
public static bool CheckConservationZero(BooleanFunction f, bool verbose = false)
{
if (f.EvalAt(0) == 0)
{
if (verbose)
{
Console.WriteLine("F ∈ T_0, т.к. F(0,0,0) = 0");
}
return(true);
}
else
{
if (verbose)
{
Console.WriteLine("F ∉ T_0, т.к. F(0,0,0) = 1");
}
return(false);
}
}
public static bool CheckConservationOne(BooleanFunction f, bool verbose = false)
{
if (f.EvalAt(7) == 1)
{
if (verbose)
{
Console.WriteLine("F ∈ T_1, т.к. F(1,1,1) = 1");
}
return(true);
}
else
{
if (verbose)
{
Console.WriteLine("F ∉ T_1, т.к. F(1,1,1) = 0");
}
return(false);
}
}
public static bool CheckSelfDuality(BooleanFunction f, bool verbose = false)
{
for (int i = 0; i < 8; i++)
{
if (f.EvalAt(i) == f.EvalAt(7 - i))
{
if (verbose)
{
Console.WriteLine("F ∉ T_*, т.к. F({0}) = F({1}) = {2}", PointAsString(i), PointAsString(7 - i), f.EvalAt(i));
}
return(false);
}
}
if (verbose)
{
Console.WriteLine("F ∈ T_*, т.к. я на всех наборах проверял, честно!");
}
return(true);
}
public static bool CheckLinearity(BooleanFunction f, bool verbose = false)
{
string zhegalkinRep = f.GetTailorStringXor(0);
foreach (string s in new string[] { "AB", "BC", "AC", "ABC", })
{
if (zhegalkinRep.Contains(s))
{
if (verbose)
{
Console.WriteLine("F ∉ T_L, т.к. F(A,B,C) = " + zhegalkinRep);
}
return(false);
}
}
if (verbose)
{
Console.WriteLine("F ∈ T_L, т.к. F(A,B,C) = " + zhegalkinRep);
}
return(true);
}
static void PrintJustTruthTable(BooleanFunction f)
{
Console.WriteLine((new BooleanFunction(0x0F)).ToString("A"));
Console.WriteLine((new BooleanFunction(0x33)).ToString("B"));
Console.WriteLine((new BooleanFunction(0x55)).ToString("C"));
Console.WriteLine(f.ToString("F"));
}
public static bool CheckConservationOne(BooleanFunction f, bool verbose = false)
{
if(f.EvalAt(7) == 1) {
if(verbose)
Console.WriteLine("F ∈ T_1, т.к. F(1,1,1) = 1");
return true;
}
else {
if(verbose)
Console.WriteLine("F ∉ T_1, т.к. F(1,1,1) = 0");
return false;
}
}
public BooleanFunction Deriv(params BooleanVariable[] variables)
{
BooleanFunction res = this;
foreach(var variable in variables) {
res = new BooleanFunction((byte)(res.FixVar(variable, 0).Eval() ^ res.FixVar(variable, 1).Eval()));
}
return res;
}
public static BooleanExpression FindMininalExpressionForBinary(BooleanExpression targetBinary, BooleanFunction f,
List <BooleanExpression> availableExpressions)
{
var queue = new ImprovisedPriorityQueue <BooleanExpression>(20);
var knownTruthTables = new HashSet <byte>();
var knownExpressions = new HashSet <BooleanExpression>();
foreach (var expression in availableExpressions)
{
queue.TryEnqueue(expression, 1);
}
while (queue.Count != 0)
{
var curExperession = queue.Dequeue();
byte truthTable = curExperession.Eval();
if (knownTruthTables.Contains(truthTable))
{
continue;
}
if ((curExperession.Eval() & 0xAA) == (targetBinary.Eval() & 0xAA))
{
return(curExperession);
}
knownExpressions.Add(curExperession);
knownTruthTables.Add(truthTable);
foreach (var anotherExpression in knownExpressions)
{
foreach (var thirdExpression in knownExpressions)
{
foreach (var neighbourExpression in CombineTertiary(f, curExperession, anotherExpression, thirdExpression))
{
queue.TryEnqueue(neighbourExpression, neighbourExpression.CountOps());
}
}
}
}
throw new CouldntFindExpressionException();
}
public static bool[] GetFunctionClasses(BooleanFunction f)
{
return(new bool[] { CheckConservationZero(f), CheckConservationOne(f), CheckSelfDuality(f), CheckMonotony(f), CheckLinearity(f), });
}
public static IEnumerable<TertiaryOpExpression> CombineTertiary(BooleanFunction f,
BooleanExpression firstExpression, BooleanExpression anotherExpression, BooleanExpression thirdExpression)
{
yield return new TertiaryOpExpression(f, firstExpression.Clone(), anotherExpression.Clone(),
thirdExpression.Clone());
yield return new TertiaryOpExpression(f, firstExpression.Clone(), thirdExpression.Clone(),
anotherExpression.Clone());
yield return new TertiaryOpExpression(f, anotherExpression.Clone(), firstExpression.Clone(),
thirdExpression.Clone());
yield return new TertiaryOpExpression(f, thirdExpression.Clone(), firstExpression.Clone(),
anotherExpression.Clone());
yield return new TertiaryOpExpression(f, anotherExpression.Clone(), thirdExpression.Clone(),
firstExpression.Clone());
yield return new TertiaryOpExpression(f, thirdExpression.Clone(), anotherExpression.Clone(),
firstExpression.Clone());
}
public static bool CheckConservationZero(BooleanFunction f, bool verbose = false)
{
if(f.EvalAt(0) == 0) {
if(verbose)
Console.WriteLine("F ∈ T_0, т.к. F(0,0,0) = 0");
return true;
}
else {
if(verbose)
Console.WriteLine("F ∉ T_0, т.к. F(0,0,0) = 1");
return false;
}
}
public static bool CheckMonotony(BooleanFunction f, bool verbose = false)
{
for(int i = 0; i < 8; i++) {
for(int j = 0; j < 8; j++) {
if(!AreAdjacent(i, j) || !IsLessThan(i, j))
continue;
if(f.EvalAt(i) > f.EvalAt(j)) {
if(verbose)
Console.WriteLine("F ∉ T_<=, т.к. F({0}) > F({1})", PointAsString(i), PointAsString(j));
return false;
}
}
}
if(verbose)
Console.WriteLine("F ∈ T_<=, т.к. я на всех наборах проверял, честно!");
return true;
}
public static bool CheckLinearity(BooleanFunction f, bool verbose = false)
{
string zhegalkinRep = f.GetTailorStringXor(0);
foreach(string s in new string[] { "AB", "BC", "AC", "ABC", }) {
if(zhegalkinRep.Contains(s)) {
if(verbose)
Console.WriteLine("F ∉ T_L, т.к. F(A,B,C) = " + zhegalkinRep);
return false;
}
}
if(verbose)
Console.WriteLine("F ∈ T_L, т.к. F(A,B,C) = " + zhegalkinRep);
return true;
}
public static void PrintTailor1XorAnd(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
for(int i = 0; i < 8; i++) {
Console.WriteLine(ReprStrings[i] + ": F(A,B,C) = " + f.GetTailorStringXor(i));
}
Console.WriteLine();
}
public static void PrintDerivatives(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
PrintJustTruthTable(f);
for(int i = 0; i < 7; i++) {
Console.WriteLine(f.Deriv(VarLists[i]).ToString(DerivStrings[i]));
}
Console.WriteLine();
}
public static BooleanExpression FindMininalExpressionForBinary(BooleanExpression targetBinary, BooleanFunction f,
List<BooleanExpression> availableExpressions)
{
var queue = new ImprovisedPriorityQueue<BooleanExpression>(20);
var knownTruthTables = new HashSet<byte>();
var knownExpressions = new HashSet<BooleanExpression>();
foreach(var expression in availableExpressions) {
queue.TryEnqueue(expression, 1);
}
while(queue.Count != 0) {
var curExperession = queue.Dequeue();
byte truthTable = curExperession.Eval();
if(knownTruthTables.Contains(truthTable)) {
continue;
}
if((curExperession.Eval() & 0xAA) == (targetBinary.Eval() & 0xAA)) {
return curExperession;
}
knownExpressions.Add(curExperession);
knownTruthTables.Add(truthTable);
foreach(var anotherExpression in knownExpressions) {
foreach(var thirdExpression in knownExpressions) {
foreach(var neighbourExpression in CombineTertiary(f, curExperession, anotherExpression, thirdExpression)) {
queue.TryEnqueue(neighbourExpression, neighbourExpression.CountOps());
}
}
}
}
throw new CouldntFindExpressionException();
}
public static void PrintExpressionsForDerivatives(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
for(int i = 0; i < 7; i++) {
Console.WriteLine(DerivStrings[i] + " = " + BooleanExpression.FindMininalExpressionInBasis(
f.Deriv(VarLists[i]).Eval(), AvdoshinBases[0], AvdoshinVars[0]).ToString());
}
Console.WriteLine();
}
public static bool CheckSelfDuality(BooleanFunction f, bool verbose = false)
{
for(int i = 0; i < 8; i++) {
if(f.EvalAt(i) == f.EvalAt(7 - i)) {
if(verbose)
Console.WriteLine("F ∉ T_*, т.к. F({0}) = F({1}) = {2}", PointAsString(i), PointAsString(7 - i), f.EvalAt(i));
return false;
}
}
if(verbose)
Console.WriteLine("F ∈ T_*, т.к. я на всех наборах проверял, честно!");
return true;
}
public static void Print3DirectionalDerivative(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
PrintJustTruthTable(f);
Console.WriteLine(f.DirectionalDeriv(VarLists[6]).ToString(DirDerivStrings[6]));
Console.WriteLine();
}
public static void PrintClosedClasses(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
PostClosedClasses.CheckConservationZero(f, true);
PostClosedClasses.CheckConservationOne(f, true);
PostClosedClasses.CheckSelfDuality(f, true);
PostClosedClasses.CheckMonotony(f, true);
PostClosedClasses.CheckLinearity(f, true);
Console.WriteLine();
}
public static void PrintExpressionFor3DirDerivative(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
Console.WriteLine(DirDerivStrings[6] + " = " + BooleanExpression.FindMininalExpressionInBasis(
f.DirectionalDeriv(VarLists[6]).Eval(), AvdoshinBases[0], AvdoshinVars[0]).ToString());
Console.WriteLine();
}
public static bool[] GetFunctionClasses(BooleanFunction f)
{
return new bool[] { CheckConservationZero(f), CheckConservationOne(f), CheckSelfDuality(f), CheckMonotony(f), CheckLinearity(f), };
}
public TertiaryOpExpression(BooleanFunction f, BooleanExpression first, BooleanExpression second, BooleanExpression third)
{
F = f;
First = first;
Second = second;
Third = third;
}
public static void PrintMaclauren1XorAnd(int n)
{
BooleanFunction f = new BooleanFunction((byte)n);
Console.WriteLine("F(A,B,C) = " + f.GetTailorStringXor(0));
Console.WriteLine();
}