mirror of
https://github.com/mudler/luet.git
synced 2025-09-12 21:33:31 +00:00
Ettore Di Giacinto
480
vendor/github.com/crillab/gophersat/bf/bf.go
generated
vendored
Normal file
480
vendor/github.com/crillab/gophersat/bf/bf.go
generated
vendored
Normal file
@@ -0,0 +1,480 @@
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package bf
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import (
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"fmt"
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"io"
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"math"
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"sort"
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"strconv"
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"strings"
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"github.com/crillab/gophersat/solver"
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)
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// A Formula is any kind of boolean formula, not necessarily in CNF.
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type Formula interface {
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nnf() Formula
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String() string
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Eval(model map[string]bool) bool
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}
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// Solve solves the given formula.
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// f is first converted as a CNF formula. It is then given to gophersat.
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// The function returns a model associating each variable name with its binding, or nil if the formula was not satisfiable.
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func Solve(f Formula) map[string]bool {
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return asCnf(f).solve()
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}
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// Dimacs writes the DIMACS CNF version of the formula on w.
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// It is useful so as to feed it to any SAT solver.
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// The original names of variables is associated with their DIMACS integer counterparts
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// in comments, between the prolog and the set of clauses.
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// For instance, if the variable "a" is associated with the index 1, there will be a comment line
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// "c a=1".
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func Dimacs(f Formula, w io.Writer) error {
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cnf := asCnf(f)
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nbVars := len(cnf.vars.all)
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nbClauses := len(cnf.clauses)
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prefix := fmt.Sprintf("p cnf %d %d\n", nbVars, nbClauses)
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if _, err := io.WriteString(w, prefix); err != nil {
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return fmt.Errorf("could not write DIMACS output: %v", err)
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}
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var pbVars []string
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for v := range cnf.vars.pb {
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if !v.dummy {
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pbVars = append(pbVars, v.name)
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}
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}
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sort.Sort(sort.StringSlice(pbVars))
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for _, v := range pbVars {
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idx := cnf.vars.pb[pbVar(v)]
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line := fmt.Sprintf("c %s=%d\n", v, idx)
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if _, err := io.WriteString(w, line); err != nil {
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return fmt.Errorf("could not write DIMACS output: %v", err)
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}
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}
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for _, clause := range cnf.clauses {
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strClause := make([]string, len(clause))
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for i, lit := range clause {
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strClause[i] = strconv.Itoa(lit)
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}
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line := fmt.Sprintf("%s 0\n", strings.Join(strClause, " "))
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if _, err := io.WriteString(w, line); err != nil {
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return fmt.Errorf("could not write DIMACS output: %v", err)
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}
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}
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return nil
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}
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// The "true" constant.
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type trueConst struct{}
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// True is the constant denoting a tautology.
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var True Formula = trueConst{}
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func (t trueConst) nnf() Formula { return t }
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func (t trueConst) String() string { return "⊤" }
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func (t trueConst) Eval(model map[string]bool) bool { return true }
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// The "false" constant.
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type falseConst struct{}
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// False is the constant denoting a contradiction.
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var False Formula = falseConst{}
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func (f falseConst) nnf() Formula { return f }
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func (f falseConst) String() string { return "⊥" }
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func (f falseConst) Eval(model map[string]bool) bool { return false }
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// Var generates a named boolean variable in a formula.
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func Var(name string) Formula {
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return pbVar(name)
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}
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func pbVar(name string) variable {
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return variable{name: name, dummy: false}
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}
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func dummyVar(name string) variable {
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return variable{name: name, dummy: true}
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}
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type variable struct {
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name string
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dummy bool
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}
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func (v variable) nnf() Formula {
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return lit{signed: false, v: v}
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}
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func (v variable) String() string {
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return v.name
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}
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func (v variable) Eval(model map[string]bool) bool {
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b, ok := model[v.name]
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if !ok {
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panic(fmt.Errorf("Model lacks binding for variable %s", v.name))
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}
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return b
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}
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type lit struct {
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v variable
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signed bool
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}
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func (l lit) nnf() Formula {
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return l
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}
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func (l lit) String() string {
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if l.signed {
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return "not(" + l.v.name + ")"
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}
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return l.v.name
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}
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func (l lit) Eval(model map[string]bool) bool {
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b := l.v.Eval(model)
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if l.signed {
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return !b
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}
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return b
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}
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// Not represents a negation. It negates the given subformula.
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func Not(f Formula) Formula {
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return not{f}
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}
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type not [1]Formula
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func (n not) nnf() Formula {
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switch f := n[0].(type) {
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case variable:
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l := f.nnf().(lit)
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l.signed = true
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return l
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case lit:
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f.signed = !f.signed
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return f
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case not:
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return f[0].nnf()
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case and:
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subs := make([]Formula, len(f))
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for i, sub := range f {
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subs[i] = not{sub}.nnf()
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}
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return or(subs).nnf()
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case or:
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subs := make([]Formula, len(f))
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for i, sub := range f {
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subs[i] = not{sub}.nnf()
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}
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return and(subs).nnf()
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case trueConst:
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return False
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case falseConst:
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return True
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default:
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panic("invalid formula type")
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}
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}
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func (n not) String() string {
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return "not(" + n[0].String() + ")"
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}
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func (n not) Eval(model map[string]bool) bool {
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return !n[0].Eval(model)
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}
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// And generates a conjunction of subformulas.
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func And(subs ...Formula) Formula {
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return and(subs)
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}
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type and []Formula
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func (a and) nnf() Formula {
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var res and
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for _, s := range a {
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nnf := s.nnf()
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switch nnf := nnf.(type) {
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case and: // Simplify: "and"s in the "and" get to the higher level
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res = append(res, nnf...)
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case trueConst: // True is ignored
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case falseConst:
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return False
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default:
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res = append(res, nnf)
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}
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}
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if len(res) == 1 {
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return res[0]
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}
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if len(res) == 0 {
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return False
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}
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return res
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}
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func (a and) String() string {
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strs := make([]string, len(a))
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for i, f := range a {
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strs[i] = f.String()
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}
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return "and(" + strings.Join(strs, ", ") + ")"
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}
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func (a and) Eval(model map[string]bool) (res bool) {
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for i, s := range a {
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b := s.Eval(model)
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if i == 0 {
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res = b
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} else {
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res = res && b
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}
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}
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return
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}
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// Or generates a disjunction of subformulas.
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func Or(subs ...Formula) Formula {
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return or(subs)
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}
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type or []Formula
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func (o or) nnf() Formula {
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var res or
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for _, s := range o {
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nnf := s.nnf()
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switch nnf := nnf.(type) {
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case or: // Simplify: "or"s in the "or" get to the higher level
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res = append(res, nnf...)
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case falseConst: // False is ignored
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case trueConst:
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return True
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default:
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res = append(res, nnf)
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}
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}
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if len(res) == 1 {
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return res[0]
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}
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if len(res) == 0 {
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return True
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}
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return res
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}
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func (o or) String() string {
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strs := make([]string, len(o))
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for i, f := range o {
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strs[i] = f.String()
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}
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return "or(" + strings.Join(strs, ", ") + ")"
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}
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func (o or) Eval(model map[string]bool) (res bool) {
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for i, s := range o {
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b := s.Eval(model)
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if i == 0 {
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res = b
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} else {
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res = res || b
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}
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}
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return
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}
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// Implies indicates a subformula implies another one.
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func Implies(f1, f2 Formula) Formula {
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return or{not{f1}, f2}
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}
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// Eq indicates a subformula is equivalent to another one.
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func Eq(f1, f2 Formula) Formula {
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return and{or{not{f1}, f2}, or{f1, not{f2}}}
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}
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// Xor indicates exactly one of the two given subformulas is true.
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func Xor(f1, f2 Formula) Formula {
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return and{or{not{f1}, not{f2}}, or{f1, f2}}
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}
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// Unique indicates exactly one of the given variables must be true.
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// It might create dummy variables to reduce the number of generated clauses.
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func Unique(vars ...string) Formula {
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vars2 := make([]variable, len(vars))
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for i, v := range vars {
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vars2[i] = pbVar(v)
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}
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return uniqueRec(vars2...)
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}
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// uniqueSmall generates clauses indicating exactly one of the given variables is true.
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// It is suitable when the number of variables is small (typically, <= 4).
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func uniqueSmall(vars ...variable) Formula {
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res := make([]Formula, 1, 1+(len(vars)*len(vars)-1)/2)
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varsAsForms := make([]Formula, len(vars))
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for i, v := range vars {
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varsAsForms[i] = v
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||||
}
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res[0] = Or(varsAsForms...)
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||||
for i := 0; i < len(vars)-1; i++ {
|
||||
for j := i + 1; j < len(vars); j++ {
|
||||
res = append(res, Or(Not(varsAsForms[i]), Not(varsAsForms[j])))
|
||||
}
|
||||
}
|
||||
return And(res...)
|
||||
}
|
||||
|
||||
func uniqueRec(vars ...variable) Formula {
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||||
nbVars := len(vars)
|
||||
if nbVars <= 4 {
|
||||
return uniqueSmall(vars...)
|
||||
}
|
||||
sqrt := math.Sqrt(float64(nbVars))
|
||||
nbLines := int(sqrt + 0.5)
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||||
lines := make([]variable, nbLines)
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||||
linesF := make([][]Formula, nbLines)
|
||||
allNames := make([]string, len(vars))
|
||||
for i := range vars {
|
||||
allNames[i] = vars[i].name
|
||||
}
|
||||
fullName := strings.Join(allNames, "-")
|
||||
for i := range lines {
|
||||
lines[i] = dummyVar(fmt.Sprintf("line-%d-%s", i, fullName))
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||||
linesF[i] = []Formula{}
|
||||
}
|
||||
nbCols := int(math.Ceil(sqrt))
|
||||
cols := make([]variable, nbCols)
|
||||
colsF := make([][]Formula, nbCols)
|
||||
for i := range cols {
|
||||
cols[i] = dummyVar(fmt.Sprintf("col-%d-%s", i, fullName))
|
||||
colsF[i] = []Formula{}
|
||||
}
|
||||
res := make([]Formula, 0, 2*nbVars+1)
|
||||
for i, v := range vars {
|
||||
linesF[i/nbCols] = append(linesF[i/nbCols], v)
|
||||
colsF[i%nbCols] = append(colsF[i%nbCols], v)
|
||||
}
|
||||
for i := range lines {
|
||||
res = append(res, Eq(lines[i], Or(linesF[i]...)))
|
||||
}
|
||||
for i := range cols {
|
||||
res = append(res, Eq(cols[i], Or(colsF[i]...)))
|
||||
}
|
||||
|
||||
res = append(res, uniqueRec(lines...))
|
||||
res = append(res, uniqueRec(cols...))
|
||||
return And(res...)
|
||||
}
|
||||
|
||||
// vars associate variable names with numeric indices.
|
||||
type vars struct {
|
||||
all map[variable]int // all vars, including those created when converting the formula
|
||||
pb map[variable]int // Only the vars that appeared orinigally in the problem
|
||||
}
|
||||
|
||||
// litValue returns the int value associated with the given problem var.
|
||||
// If the var was not referenced yet, it is created first.
|
||||
func (vars *vars) litValue(l lit) int {
|
||||
val, ok := vars.all[l.v]
|
||||
if !ok {
|
||||
val = len(vars.all) + 1
|
||||
vars.all[l.v] = val
|
||||
vars.pb[l.v] = val
|
||||
}
|
||||
if l.signed {
|
||||
return -val
|
||||
}
|
||||
return val
|
||||
}
|
||||
|
||||
// Dummy creates a dummy variable and returns its associated index.
|
||||
func (vars *vars) dummy() int {
|
||||
val := len(vars.all) + 1
|
||||
vars.all[dummyVar(fmt.Sprintf("dummy-%d", val))] = val
|
||||
return val
|
||||
}
|
||||
|
||||
// A CNF is the representation of a boolean formula as a conjunction of disjunction.
|
||||
// It can be solved by a SAT solver.
|
||||
type cnf struct {
|
||||
vars vars
|
||||
clauses [][]int
|
||||
}
|
||||
|
||||
// solve solves the given formula.
|
||||
// cnf is given to gophersat.
|
||||
// If it is satisfiable, the function returns a model, associating each variable name with its binding.
|
||||
// Else, the function returns nil.
|
||||
func (cnf *cnf) solve() map[string]bool {
|
||||
pb := solver.ParseSlice(cnf.clauses)
|
||||
s := solver.New(pb)
|
||||
if s.Solve() != solver.Sat {
|
||||
return nil
|
||||
}
|
||||
m := s.Model()
|
||||
vars := make(map[string]bool)
|
||||
for v, idx := range cnf.vars.pb {
|
||||
vars[v.name] = m[idx-1]
|
||||
}
|
||||
return vars
|
||||
}
|
||||
|
||||
// asCnf returns a CNF representation of the given formula.
|
||||
func asCnf(f Formula) *cnf {
|
||||
vars := vars{all: make(map[variable]int), pb: make(map[variable]int)}
|
||||
clauses := cnfRec(f.nnf(), &vars)
|
||||
return &cnf{vars: vars, clauses: clauses}
|
||||
}
|
||||
|
||||
// transforms the f NNF formula into a CNF formula.
|
||||
// nbDummies is the current number of dummy variables created.
|
||||
// Note: code should be improved, there are a few useless allocs/deallocs
|
||||
// here and there.
|
||||
func cnfRec(f Formula, vars *vars) [][]int {
|
||||
switch f := f.(type) {
|
||||
case lit:
|
||||
return [][]int{{vars.litValue(f)}}
|
||||
case and:
|
||||
var res [][]int
|
||||
for _, sub := range f {
|
||||
res = append(res, cnfRec(sub, vars)...)
|
||||
}
|
||||
return res
|
||||
case or:
|
||||
var res [][]int
|
||||
var lits []int
|
||||
for _, sub := range f {
|
||||
switch sub := sub.(type) {
|
||||
case lit:
|
||||
lits = append(lits, vars.litValue(sub))
|
||||
case and:
|
||||
d := vars.dummy()
|
||||
lits = append(lits, d)
|
||||
for _, sub2 := range sub {
|
||||
cnf := cnfRec(sub2, vars)
|
||||
cnf[0] = append(cnf[0], -d)
|
||||
res = append(res, cnf...)
|
||||
}
|
||||
default:
|
||||
panic("unexpected or in or")
|
||||
}
|
||||
}
|
||||
res = append(res, lits)
|
||||
return res
|
||||
case trueConst: // True clauses are ignored
|
||||
return [][]int{}
|
||||
case falseConst: // TODO: improve this. This should simply be declared to make the problem UNSAT.
|
||||
return [][]int{{}}
|
||||
default:
|
||||
panic("invalid NNF formula")
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user