func buildLogEncoding(pred sat.Pred, uId int, cutoff int, depth int, tag string, lits []sat.Literal) (clauses sat.ClauseSet) {
if len(lits) <= cutoff {
trans2 := TranslateAtMostOne(Naive, tag, lits)
clauses.AddClauseSet(trans2.Clauses)
} else {
atom := sat.NewAtomP2(pred, uId, depth)
first := lits[:len(lits)/2]
for _, l := range first {
clauses.AddTaggedClause(tag, sat.Literal{true, atom}, sat.Neg(l))
}
second := lits[len(lits)/2:]
for _, l := range second {
clauses.AddTaggedClause(tag, sat.Literal{false, atom}, sat.Neg(l))
}
depth++
clauses.AddClauseSet(buildLogEncoding(pred, uId, cutoff, depth, tag, first))
clauses.AddClauseSet(buildLogEncoding(pred, uId, cutoff, depth, tag, second))
}
return
}
func TranslateAtMostOne(typ OneTranslationType, tag string, lits []sat.Literal) (trans CardTranslation) {
var clauses sat.ClauseSet
switch typ {
case Naive:
for i, l := range lits {
for j := i + 1; j < len(lits); j++ {
clauses.AddTaggedClause(tag, sat.Neg(l), sat.Neg(lits[j]))
}
}
case Split:
// a constant that should be exposed,
// its the cuttoff for the split method of atMostOne
cutoff := 5
if len(lits) <= cutoff {
return TranslateAtMostOne(Naive, tag, lits)
} else {
aux := sat.NewAtomP1(sat.Pred("split"), newId())
trans.Aux = append(trans.Aux, sat.Literal{true, aux})
for _, l := range lits[:len(lits)/2] {
clauses.AddTaggedClause(tag, sat.Literal{true, aux}, sat.Neg(l))
}
for _, l := range lits[len(lits)/2:] {
clauses.AddTaggedClause(tag, sat.Literal{false, aux}, sat.Neg(l))
}
clauses.AddClauseSet(TranslateAtMostOne(typ, tag, lits[:len(lits)/2]).Clauses)
clauses.AddClauseSet(TranslateAtMostOne(typ, tag, lits[len(lits)/2:]).Clauses)
}
case Count:
pred := sat.Pred("c")
counterId := newId()
auxs := make([]sat.Literal, len(lits))
for i, _ := range auxs {
auxs[i] = sat.Literal{true, sat.NewAtomP2(pred, counterId, i)}
}
trans.Aux = auxs
// S_i -> S_{i-1}
for i := 1; i < len(lits); i++ {
clauses.AddTaggedClause(tag, auxs[i-1], sat.Neg(auxs[i]))
}
// X_i -> S_i
for i := 0; i < len(lits); i++ {
clauses.AddTaggedClause(tag, auxs[i], sat.Neg(lits[i]))
}
// X_i-1 -> -S_i
for i := 1; i < len(lits); i++ {
clauses.AddTaggedClause(tag, sat.Neg(auxs[i]), sat.Neg(lits[i-1]))
}
// (S_i-1 /\ -S_i) -> X_i-1
for i := 1; i <= len(lits); i++ {
if i != len(lits) {
clauses.AddTaggedClause(tag, sat.Neg(auxs[i-1]), auxs[i], lits[i-1])
} else {
clauses.AddTaggedClause(tag, sat.Neg(auxs[i-1]), lits[i-1])
}
}
case Heule:
k := 4 // fixed size for the heule encoding
if len(lits) > k+1 {
aux := sat.NewAtomP1(sat.Pred("heule"), newId())
trans.Aux = append(trans.Aux, sat.Literal{true, aux})
front := make([]sat.Literal, k+1)
copy(front, lits[:k])
front[k] = sat.Literal{true, aux}
trans2 := TranslateAtMostOne(Naive, tag, front)
clauses.AddClauseSet(trans2.Clauses)
back := make([]sat.Literal, len(lits)-k+1)
copy(back, lits[k:])
back[len(lits)-k] = sat.Literal{false, aux}
trans2 = TranslateAtMostOne(typ, tag, back)
trans.Aux = append(trans.Aux, trans2.Aux...)
clauses.AddClauseSet(trans2.Clauses)
} else {
trans2 := TranslateAtMostOne(Naive, tag, lits)
clauses.AddClauseSet(trans2.Clauses)
}
case Log:
cutoff := 5 //will be a parameter of this encoding
clauses = buildLogEncoding(sat.Pred("logE"), newId(), cutoff, 0, tag, lits)
case Sort:
panic("CNF translation for this type not implemented yet")
default:
panic("CNF translation for this type not implemented yet")
}
trans.Typ = typ
trans.Clauses = clauses
return
}
func TranslateExactlyOne(typ OneTranslationType, tag string, lits []sat.Literal) (trans CardTranslation) {
var clauses sat.ClauseSet
switch typ {
case Heule, Log, Naive, Split:
trans2 := TranslateAtMostOne(typ, tag, lits)
trans.Aux = append(trans.Aux, trans2.Aux...)
clauses.AddClauseSet(trans2.Clauses)
clauses.AddTaggedClause(tag, lits...)
case Count:
pred := sat.Pred("cx")
counterId := newId()
auxs := make([]sat.Literal, len(lits))
for i, _ := range auxs {
auxs[i] = sat.Literal{true, sat.NewAtomP2(pred, counterId, i)}
}
trans.Aux = auxs
// S_i -> S_{i-1}
for i := 1; i < len(lits); i++ {
clauses.AddTaggedClause(tag, auxs[i-1], sat.Neg(auxs[i]))
}
// X_i -> S_i
for i := 0; i < len(lits); i++ {
clauses.AddTaggedClause(tag, auxs[i], sat.Neg(lits[i]))
}
// X_i-1 -> -S_i
for i := 1; i < len(lits); i++ {
clauses.AddTaggedClause(tag, sat.Neg(auxs[i]), sat.Neg(lits[i-1]))
}
// (S_i-1 /\ -S_i) -> X_i-1
for i := 1; i <= len(lits); i++ {
if i != len(lits) {
clauses.AddTaggedClause(tag, sat.Neg(auxs[i-1]), auxs[i], lits[i-1])
} else {
clauses.AddTaggedClause(tag, sat.Neg(auxs[i-1]), lits[i-1])
}
}
clauses.AddTaggedClause(tag, auxs[0])
case Sort:
panic("CNF translation for this type not implemented yet")
default:
panic("CNF translation for this type not implemented yet")
}
trans.Typ = typ
trans.Clauses = clauses
return
}
