Packages

trait Solver extends CNF

Source
Solving.scala
Linear Supertypes
CNF, Solving.PropositionalLogic, AnyRef, Any
Known Subclasses
OptimizingMatchTranslator
Type Hierarchy
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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. 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. final case class Solvable(cnf: Cnf, symbolMapping: SymbolMapping) extends Product with Serializable
    Definition Classes
    CNF
  18. class SymbolMapping extends AnyRef
    Definition Classes
    CNF
  19. 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
  20. type Clause = Set[Lit]
    Definition Classes
    CNF
  21. 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
  22. abstract type Const
    Definition Classes
    PropositionalLogic
  23. type Model = Map[Sym, Boolean]
    Definition Classes
    PropositionalLogic
  24. abstract type Tree
    Definition Classes
    PropositionalLogic
  25. type TseitinModel = Set[Lit]
  26. abstract type Type
    Definition Classes
    PropositionalLogic
  27. abstract type TypeConst <: Const
    Definition Classes
    PropositionalLogic
  28. abstract type ValueConst <: Const
    Definition Classes
    PropositionalLogic
  29. 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: 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. def /\(props: Iterable[Prop]): Product with Serializable with Prop
    Definition Classes
    PropositionalLogic
  8. val EmptyModel: Map[Sym, Boolean]
    Definition Classes
    Solver → PropositionalLogic
  9. val EmptyTseitinModel: Set[Lit]
  10. val NoModel: Model
    Definition Classes
    Solver → PropositionalLogic
  11. val NoTseitinModel: TseitinModel
  12. def \/(props: Iterable[Prop]): Product with Serializable with Prop
    Definition Classes
    PropositionalLogic
  13. val budgetProp: sys.Prop[String]
    Definition Classes
    PropositionalLogic
  14. def clause(l: Lit*): Clause
    Definition Classes
    CNF
  15. def cnfString(f: Array[Clause]): String
    Definition Classes
    Solver → CNF
  16. def eqFreePropToSolvable(p: Prop): Solvable
    Definition Classes
    CNF → PropositionalLogic
  17. def findAllModelsFor(solvable: Solvable, pos: Position): List[Solution]
    Definition Classes
    Solver → PropositionalLogic
  18. def findModelFor(solvable: Solvable): Model
    Definition Classes
    Solver → PropositionalLogic
  19. def findTseitinModelFor(clauses: Array[Clause]): TseitinModel
  20. def gatherSymbols(p: Prop): Set[Sym]
    Definition Classes
    PropositionalLogic
  21. def gatherVariables(p: Prop): Set[Var]
    Definition Classes
    PropositionalLogic
  22. def propToSolvable(p: Prop): Solvable
    Definition Classes
    PropositionalLogic
  23. def removeVarEq(props: List[Prop], modelNull: Boolean = false): (Prop, List[Prop])
    Definition Classes
    PropositionalLogic
  24. 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