Packages

trait CNF extends PropositionalLogic

Source
Solving.scala
Linear Supertypes
Solving.PropositionalLogic, AnyRef, Any
Known Subclasses
OptimizingMatchTranslator, Solver
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Inherited
  1. CNF
  2. PropositionalLogic
  3. AnyRef
  4. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. All

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. 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
  16. type Clause = Set[Lit]
  17. 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).

  18. trait CnfBuilder extends AnyRef
  19. abstract type Const
    Definition Classes
    PropositionalLogic
  20. type Model = Map[Sym, Boolean]
    Definition Classes
    PropositionalLogic
  21. final case class Solvable(cnf: Cnf, symbolMapping: SymbolMapping) extends Product with Serializable
  22. class SymbolMapping extends AnyRef
  23. 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.

  24. abstract type Tree
    Definition Classes
    PropositionalLogic
  25. abstract type Type
    Definition Classes
    PropositionalLogic
  26. abstract type TypeConst <: Const
    Definition Classes
    PropositionalLogic
  27. abstract type ValueConst <: Const
    Definition Classes
    PropositionalLogic
  28. abstract type Var <: AbsVar
    Definition Classes
    PropositionalLogic

Abstract Value Members

  1. abstract val EmptyModel: Model
    Definition Classes
    PropositionalLogic
  2. abstract val NoModel: Model
    Definition Classes
    PropositionalLogic
  3. abstract val NullConst: Const
    Definition Classes
    PropositionalLogic
  4. abstract def TypeConst: TypeConstExtractor
    Definition Classes
    PropositionalLogic
  5. abstract def ValueConst: ValueConstExtractor
    Definition Classes
    PropositionalLogic
  6. abstract val Var: VarExtractor
    Definition Classes
    PropositionalLogic
  7. abstract def cnfString(f: Array[Clause]): String
  8. abstract def findAllModelsFor(solvable: Solvable, pos: Position = NoPosition): List[Solution]
    Definition Classes
    PropositionalLogic
  9. abstract def findModelFor(solvable: Solvable): Model
    Definition Classes
    PropositionalLogic
  10. abstract def prepareNewAnalysis(): Unit
    Definition Classes
    PropositionalLogic
  11. abstract def reportWarning(message: String): Unit
    Definition Classes
    PropositionalLogic
  12. abstract def uncheckedWarning(pos: Position, msg: String): Unit
    Definition Classes
    PropositionalLogic

Concrete Value Members

  1. object AnalysisBudget
    Definition Classes
    PropositionalLogic
  2. object And extends Serializable
    Definition Classes
    PropositionalLogic
  3. object False extends Prop with Product with Serializable
    Definition Classes
    PropositionalLogic
  4. object Or extends Serializable
    Definition Classes
    PropositionalLogic
  5. object Sym
    Definition Classes
    PropositionalLogic
  6. 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 CNF to any2stringadd[CNF] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  10. def ->[B](y: B): (CNF, B)
    Implicit
    This member is added by an implicit conversion from CNF to ArrowAssoc[CNF] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  11. def /\(props: Iterable[Prop]): Product with Serializable with Prop
    Definition Classes
    PropositionalLogic
  12. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  13. def \/(props: Iterable[Prop]): Product with Serializable with Prop
    Definition Classes
    PropositionalLogic
  14. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  15. val budgetProp: sys.Prop[String]
    Definition Classes
    PropositionalLogic
  16. def clause(l: Lit*): Clause
  17. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  18. def ensuring(cond: (CNF) ⇒ Boolean, msg: ⇒ Any): CNF
    Implicit
    This member is added by an implicit conversion from CNF to Ensuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: (CNF) ⇒ Boolean): CNF
    Implicit
    This member is added by an implicit conversion from CNF to Ensuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean, msg: ⇒ Any): CNF
    Implicit
    This member is added by an implicit conversion from CNF to Ensuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean): CNF
    Implicit
    This member is added by an implicit conversion from CNF to Ensuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  23. def eqFreePropToSolvable(p: Prop): Solvable
    Definition Classes
    CNF → PropositionalLogic
  24. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  25. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  26. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from CNF to StringFormat[CNF] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  27. def gatherSymbols(p: Prop): Set[Sym]
    Definition Classes
    PropositionalLogic
  28. def gatherVariables(p: Prop): Set[Var]
    Definition Classes
    PropositionalLogic
  29. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  30. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  31. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  32. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  33. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  34. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  35. def propToSolvable(p: Prop): Solvable
    Definition Classes
    PropositionalLogic
  36. def removeVarEq(props: List[Prop], modelNull: Boolean = false): (Prop, List[Prop])
    Definition Classes
    PropositionalLogic
  37. 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 http://www.decision-procedures.org/slides/propositional_logic-2x3.pdf

    Definition Classes
    PropositionalLogic
  38. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  39. def toString(): String
    Definition Classes
    AnyRef → Any
  40. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  41. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  42. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  43. def →[B](y: B): (CNF, B)
    Implicit
    This member is added by an implicit conversion from CNF to ArrowAssoc[CNF] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Solving.PropositionalLogic

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from CNF to any2stringadd[CNF]

Inherited by implicit conversion StringFormat from CNF to StringFormat[CNF]

Inherited by implicit conversion Ensuring from CNF to Ensuring[CNF]

Inherited by implicit conversion ArrowAssoc from CNF to ArrowAssoc[CNF]

Ungrouped