/// <summary>
/// x_j = x_i + n, with min(nonempty-set)-semantics
/// </summary>
public static Automaton <BDD> MkSuccN2(int i, int j, int n, IBDDAlgebra alg)
{
var ieq0 = alg.MkBitFalse(i);
var ieq1 = alg.MkBitTrue(i);
var jeq0 = alg.MkBitFalse(j);
var jeq1 = alg.MkBitTrue(j);
var both0 = alg.MkAnd(ieq0, jeq0);
var ieq1_jeq0 = alg.MkAnd(ieq1, jeq0);
//Create moves
var moves = new List <Move <BDD> >();
moves.Add(new Move <BDD>(0, 0, both0));
moves.Add(new Move <BDD>(0, 1, ieq1_jeq0));
for (int k = 1; k < n; k++)
{
moves.Add(new Move <BDD>(k, k + 1, jeq0));
}
moves.Add(new Move <BDD>(n, n + 1, jeq1));
moves.Add(new Move <BDD>(n + 1, n + 1, alg.True));
var aut = Automaton <BDD> .Create(alg, 0, new int[] { n + 1 }, moves, false, false, true);
return(aut);
}
public static Automaton <BDD> MkSuccN(int i1, int i2, int n, IBDDAlgebra bddAlg)
{
var alg = bddAlg;
var ind10 = bddAlg.MkBitFalse(i1);
var ind11 = bddAlg.MkBitTrue(i1);
var ind20 = bddAlg.MkBitFalse(i2);
var ind21 = bddAlg.MkBitTrue(i2);
var both0 = bddAlg.MkAnd(ind10, ind20);
var ind11ind20 = bddAlg.MkAnd(ind11, ind20);
var ind10ind21 = bddAlg.MkAnd(ind10, ind21);
//Create moves
var moves = new List <Move <BDD> >();
moves.Add(new Move <BDD>(0, 0, both0));
moves.Add(new Move <BDD>(0, 1, ind11ind20));
moves.Add(new Move <BDD>(n, n + 1, ind10ind21));
moves.Add(new Move <BDD>(n + 1, n + 1, both0));
for (int i = 1; i < n; i++)
{
moves.Add(new Move <BDD>(i, i + 1, both0));
}
var aut = Automaton <BDD> .Create(bddAlg, 0, new int[] { n + 1 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// X_i = X_j
/// </summary>
public static Automaton <BDD> MkEqualSets(int i, int j, IBDDAlgebra alg)
{
var bit_j_is1 = alg.MkBitTrue(j);
var bit_i_is1 = alg.MkBitTrue(i);
var bit_i_is0 = alg.MkBitFalse(i);
var bit_j_is0 = alg.MkBitFalse(j);
var cond = alg.MkOr(alg.MkAnd(bit_i_is1, bit_j_is1), alg.MkAnd(bit_i_is0, bit_j_is0));
var moves = new Move <BDD>[] { new Move <BDD>(0, 0, cond) };
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 0 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// x_i = x_j, with min(nonempty-set)-semantics for f-o vars
/// </summary>
public static Automaton <BDD> MkEqualPositions2(int i, int j, IBDDAlgebra alg)
{
var bit_j_is1 = alg.MkBitTrue(j);
var bit_i_is1 = alg.MkBitTrue(i);
var bit_i_is0 = alg.MkBitFalse(i);
var bit_j_is0 = alg.MkBitFalse(j);
var both0 = alg.MkAnd(bit_i_is0, bit_j_is0);
var both1 = alg.MkAnd(bit_i_is1, bit_j_is1);
var moves = new Move <BDD>[] { new Move <BDD>(0, 0, both0),
new Move <BDD>(0, 1, both1), new Move <BDD>(1, 1, alg.True) };
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 1 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// x_i = max X_j with min(nonempty-set)-semantics for x_i
/// </summary>
internal static Automaton <BDD> MkMax2(int i, int j, IBDDAlgebra alg)
{
var ieq0 = alg.MkBitFalse(i);
var ieq1 = alg.MkBitTrue(i);
var jeq0 = alg.MkBitFalse(j);
var jeq1 = alg.MkBitTrue(j);
var both1 = alg.MkAnd(jeq1, ieq1);
var moves = new Move <BDD>[] {
new Move <BDD>(0, 0, ieq0),
new Move <BDD>(0, 1, both1),
new Move <BDD>(1, 1, jeq0)
};
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 1 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// x_i < x_j, with singleton-set semantics for f-o vars
/// </summary>
public static Automaton <BDD> MkLt1(int i, int j, IBDDAlgebra alg)
{
var bit_i_is0 = alg.MkBitFalse(i);
var bit_i_is1 = alg.MkBitTrue(i);
var bit_j_is0 = alg.MkBitFalse(j);
var bit_j_is1 = alg.MkBitTrue(j);
var both0 = alg.MkAnd(bit_i_is0, bit_j_is0);
var cond1 = alg.MkAnd(bit_i_is1, bit_j_is0);
var cond2 = alg.MkAnd(bit_j_is1, bit_i_is0);
var moves = new Move <BDD>[] { new Move <BDD>(0, 0, both0),
new Move <BDD>(0, 1, cond1), new Move <BDD>(1, 1, both0),
new Move <BDD>(1, 2, cond2), new Move <BDD>(2, 2, both0) };
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 2 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// all1 x: x in X_i => [psi](x)
/// </summary>
public static Automaton <BDD> MkLabelOfSet(int i, BDD psi, IBDDAlgebra alg)
{
var bit_i_is0 = alg.MkBitFalse(i);
var cond = alg.MkOr(psi, bit_i_is0);
var moves = new Move <BDD>[] { new Move <BDD>(0, 0, cond) };
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 0 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// X_i = {}
/// </summary>
internal static Automaton <BDD> MkIsEmpty(int i, IBDDAlgebra alg)
{
var ieq0 = alg.MkBitFalse(i);
var moves = new Move <BDD>[] {
new Move <BDD>(0, 0, ieq0),
};
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 0 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// X_i sub X_j
/// </summary>
public static Automaton <BDD> MkSubset(int i, int j, IBDDAlgebra alg)
{
var bit_j_is1 = alg.MkBitTrue(j);
var bit_i_is0 = alg.MkBitFalse(i);
var subsetCond = alg.MkOr(bit_j_is1, bit_i_is0);
var moves = new Move <BDD>[] { new Move <BDD>(0, 0, subsetCond) };
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 0 }, moves, false, false, true);
return(aut);
}
public static Automaton <BDD> MkSingleton(int i, IBDDAlgebra alg)
{
var bit_i_is0 = alg.MkBitFalse(i);
var bit_i_is1 = alg.MkBitTrue(i);
var moves = new Move <BDD>[] { new Move <BDD>(0, 0, bit_i_is0),
new Move <BDD>(0, 1, bit_i_is1), new Move <BDD>(1, 1, bit_i_is0) };
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 1 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// [psi](x_i) with min(nonempty-set)-semantics
/// </summary>
/// <returns></returns>
public static Automaton <BDD> MkLabelOfPosition2(int i, BDD psi, IBDDAlgebra alg)
{
var bit_i_is0 = alg.MkBitFalse(i);
var bit_i_is1 = alg.MkBitTrue(i);
var cond = alg.MkAnd(bit_i_is1, psi);
var moves = new Move <BDD>[] {
new Move <BDD>(0, 0, bit_i_is0),
new Move <BDD>(0, 1, cond),
new Move <BDD>(1, 1, alg.True)
};
var aut = Automaton <BDD> .Create(alg, 0, new int[] { 1 }, moves, false, false, true);
return(aut);
}
/// <summary>
/// x_i = n, with min(nonempty-set)-semantics
/// </summary>
internal static Automaton <BDD> MkEqN2(int i, int n, IBDDAlgebra alg)
{
var ieq0 = alg.MkBitFalse(i);
var ieq1 = alg.MkBitTrue(i);
var moves = new List <Move <BDD> >();
for (int k = 0; k < n; k++)
{
moves.Add(new Move <BDD>(k, k + 1, ieq0));
}
moves.Add(new Move <BDD>(n, n + 1, ieq1));
moves.Add(new Move <BDD>(n + 1, n + 1, alg.True));
var aut = Automaton <BDD> .Create(alg, 0, new int[] { n + 1 }, moves, false, false, true);
return(aut);
}