Packages

trait Solver extends CNF

Source
Solving.scala
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Inherited
  1. Solver
  2. CNF
  3. PropositionalLogic
  4. AnyRef
  5. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Type Members

  1. trait AbsVar extends AnyRef
    Definition Classes
    PropositionalLogic
  2. final case class And(ops: Set[Prop]) extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  3. final case class AtMostOne(ops: List[Sym]) extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  4. final case class Eq(p: Var, q: Const) extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  5. final case class Not(a: Prop) extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  6. final case class Or(ops: Set[Prop]) extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  7. sealed abstract class Prop extends AnyRef
    Definition Classes
    PropositionalLogic
  8. trait PropMap extends AnyRef
    Definition Classes
    PropositionalLogic
  9. trait PropTraverser extends AnyRef
    Definition Classes
    PropositionalLogic
  10. final case class Solution(model: Model, unassigned: List[Sym]) extends Product with Serializable
    Definition Classes
    PropositionalLogic
  11. final class Sym extends Prop
    Definition Classes
    PropositionalLogic
  12. trait TypeConstExtractor extends AnyRef
    Definition Classes
    PropositionalLogic
  13. trait ValueConstExtractor extends AnyRef
    Definition Classes
    PropositionalLogic
  14. trait VarExtractor extends AnyRef
    Definition Classes
    PropositionalLogic
  15. class AlreadyInCNF extends AnyRef
    Definition Classes
    CNF
  16. trait CnfBuilder extends AnyRef
    Definition Classes
    CNF
  17. trait LitApi extends AnyRef
    Definition Classes
    CNF
  18. trait LitModule extends AnyRef
    Definition Classes
    CNF
  19. final case class Solvable(cnf: Cnf, symbolMapping: SymbolMapping) extends Product with Serializable
    Definition Classes
    CNF
  20. class SymbolMapping extends AnyRef
    Definition Classes
    CNF
  21. class TransformToCnf extends CnfBuilder

    Plaisted transformation: used for conversion of a propositional formula into conjunctive normal form (CNF) (input format for SAT solver).

    Plaisted transformation: used for conversion of a propositional formula into conjunctive normal form (CNF) (input format for SAT solver). A simple conversion into CNF via Shannon expansion would also be possible but it's worst-case complexity is exponential (in the number of variables) and thus even simple problems could become untractable. The Plaisted transformation results in an _equisatisfiable_ CNF-formula (it generates auxiliary variables) but runs with linear complexity. The common known Tseitin transformation uses bi-implication, whereas the Plaisted transformation uses implication only, thus the resulting CNF formula has (on average) only half of the clauses of a Tseitin transformation. The Plaisted transformation uses the polarities of sub-expressions to figure out which part of the bi-implication can be omitted. However, if all sub-expressions have positive polarity (e.g., after transformation into negation normal form) then the conversion is rather simple and the pseudo-normalization via NNF increases chances only one side of the bi-implication is needed.

    Definition Classes
    CNF
  22. type Clause = Set[Lit]
    Definition Classes
    CNF
  23. type Cnf = Array[Clause]

    Conjunctive normal form (of a Boolean formula).

    Conjunctive normal form (of a Boolean formula). A formula in this form is amenable to a SAT solver (i.e., solver that decides satisfiability of a formula).

    Definition Classes
    CNF
  24. abstract type Const
    Definition Classes
    PropositionalLogic
  25. case class Lit(v: Int) extends LitApi with Product with Serializable
  26. type Model = Map[Sym, Boolean]
    Definition Classes
    PropositionalLogic
  27. abstract type Tree
    Definition Classes
    PropositionalLogic
  28. type TseitinModel = collection.immutable.List[Lit]
  29. type TseitinSearch = collection.immutable.List[(Array[Clause], List[Lit])]
  30. abstract type Type
    Definition Classes
    PropositionalLogic
  31. abstract type TypeConst <: Const
    Definition Classes
    PropositionalLogic
  32. abstract type ValueConst <: Const
    Definition Classes
    PropositionalLogic
  33. abstract type Var <: AbsVar
    Definition Classes
    PropositionalLogic

Abstract Value Members

  1. abstract val NullConst: Const
    Definition Classes
    PropositionalLogic
  2. abstract def TypeConst: TypeConstExtractor
    Definition Classes
    PropositionalLogic
  3. abstract def ValueConst: ValueConstExtractor
    Definition Classes
    PropositionalLogic
  4. abstract val Var: VarExtractor
    Definition Classes
    PropositionalLogic
  5. abstract def prepareNewAnalysis(): Unit
    Definition Classes
    PropositionalLogic
  6. abstract def reportWarning(message: String): Unit
    Definition Classes
    PropositionalLogic
  7. abstract def uncheckedWarning(pos: Global.Position, msg: String, site: Global.Symbol): Unit
    Definition Classes
    PropositionalLogic

Concrete Value Members

  1. object AnalysisBudget
    Definition Classes
    PropositionalLogic
  2. object And extends java.io.Serializable
    Definition Classes
    PropositionalLogic
  3. case object False extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  4. object Or extends java.io.Serializable
    Definition Classes
    PropositionalLogic
  5. object Sym
    Definition Classes
    PropositionalLogic
  6. case object True extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  7. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  8. final def ##: Int
    Definition Classes
    AnyRef → Any
  9. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Solver toany2stringadd[Solver] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  10. def ->[B](y: B): (Solver, B)
    Implicit
    This member is added by an implicit conversion from Solver toArrowAssoc[Solver] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  11. def /\(props: Iterable[Prop]): Prop
    Definition Classes
    PropositionalLogic
  12. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  13. val ArrayOfFalse: Array[Clause]
    Definition Classes
    CNF
  14. val EmptyModel: Map[Sym, Boolean]
    Definition Classes
    SolverPropositionalLogic
  15. val NoClauses: Array[Clause]
    Definition Classes
    CNF
  16. val NoModel: Model
    Definition Classes
    SolverPropositionalLogic
  17. val NoTseitinModel: TseitinModel
  18. def \/(props: Iterable[Prop]): Prop
    Definition Classes
    PropositionalLogic
  19. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  20. def clause(ls: IterableOnce[Lit]): Clause
    Definition Classes
    CNF
  21. def clause(l: Lit, l2: Lit, ls: Lit*): Clause
    Definition Classes
    CNF
  22. def clause(l: Lit, l2: Lit): Clause
    Definition Classes
    CNF
  23. def clause(l: Lit): Clause
    Definition Classes
    CNF
  24. def clause(): Clause
    Definition Classes
    CNF
  25. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  26. def cnfString(f: Array[Clause]): String
    Definition Classes
    SolverCNF
  27. def ensuring(cond: (Solver) => Boolean, msg: => Any): Solver
    Implicit
    This member is added by an implicit conversion from Solver toEnsuring[Solver] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  28. def ensuring(cond: (Solver) => Boolean): Solver
    Implicit
    This member is added by an implicit conversion from Solver toEnsuring[Solver] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  29. def ensuring(cond: Boolean, msg: => Any): Solver
    Implicit
    This member is added by an implicit conversion from Solver toEnsuring[Solver] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  30. def ensuring(cond: Boolean): Solver
    Implicit
    This member is added by an implicit conversion from Solver toEnsuring[Solver] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  31. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  32. def eqFreePropToSolvable(p: Prop): Solvable
    Definition Classes
    CNFPropositionalLogic
  33. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  34. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable])
  35. def findAllModelsFor(solvable: Solvable, owner: Global.Symbol): List[Solution]
    Definition Classes
    SolverPropositionalLogic
  36. def findTseitinModelFor(clauses: Array[Clause]): TseitinModel
  37. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Solver toStringFormat[Solver] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  38. def gatherSymbols(p: Prop): Set[Sym]
    Definition Classes
    PropositionalLogic
  39. def gatherVariables(p: Prop): Set[Var]
    Definition Classes
    PropositionalLogic
  40. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  41. def hasModel(solvable: Solvable): Boolean
    Definition Classes
    SolverPropositionalLogic
  42. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  43. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  44. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  45. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  46. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  47. def propToSolvable(p: Prop): Solvable
    Definition Classes
    PropositionalLogic
  48. def removeVarEq(props: List[Prop], modelNull: Boolean = false): (Prop, List[Prop])
    Definition Classes
    PropositionalLogic
  49. def simplify(f: Prop): Prop

    Simplifies propositional formula according to the following rules: - eliminate double negation (avoids unnecessary Tseitin variables) - flatten trees of same connectives (avoids unnecessary Tseitin variables) - removes constants and connectives that are in fact constant because of their operands - eliminates duplicate operands - convert formula into NNF: all sub-expressions have a positive polarity which makes them amenable for the subsequent Plaisted transformation and increases chances to figure out that the formula is already in CNF

    Simplifies propositional formula according to the following rules: - eliminate double negation (avoids unnecessary Tseitin variables) - flatten trees of same connectives (avoids unnecessary Tseitin variables) - removes constants and connectives that are in fact constant because of their operands - eliminates duplicate operands - convert formula into NNF: all sub-expressions have a positive polarity which makes them amenable for the subsequent Plaisted transformation and increases chances to figure out that the formula is already in CNF

    Complexity: DFS over formula tree

    See https://www.decision-procedures.org/slides/propositional_logic-2x3.pdf

    Definition Classes
    PropositionalLogic
  50. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  51. def toString(): String
    Definition Classes
    AnyRef → Any
  52. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  53. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  54. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  55. object Lit extends LitModule with java.io.Serializable
    Definition Classes
    SolverCNF

Deprecated Value Members

  1. def [B](y: B): (Solver, B)
    Implicit
    This member is added by an implicit conversion from Solver toArrowAssoc[Solver] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from CNF

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromSolver to any2stringadd[Solver]

Inherited by implicit conversion StringFormat fromSolver to StringFormat[Solver]

Inherited by implicit conversion Ensuring fromSolver to Ensuring[Solver]

Inherited by implicit conversion ArrowAssoc fromSolver to ArrowAssoc[Solver]

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