trait Solver extends CNF
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- trait AbsVar extends AnyRef
- Definition Classes
- PropositionalLogic
- final case class And(ops: Set[Prop]) extends Prop with Product with Serializable
- Definition Classes
- PropositionalLogic
- final case class AtMostOne(ops: List[Sym]) extends Prop with Product with Serializable
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- PropositionalLogic
- final case class Eq(p: Var, q: Const) extends Prop with Product with Serializable
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- PropositionalLogic
- final case class Not(a: Prop) extends Prop with Product with Serializable
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- PropositionalLogic
- final case class Or(ops: Set[Prop]) extends Prop with Product with Serializable
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- sealed abstract class Prop extends AnyRef
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- PropositionalLogic
- trait PropMap extends AnyRef
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- PropositionalLogic
- trait PropTraverser extends AnyRef
- Definition Classes
- PropositionalLogic
- final case class Solution(model: Model, unassigned: List[Sym]) extends Product with Serializable
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- PropositionalLogic
- final class Sym extends Prop
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- PropositionalLogic
- trait TypeConstExtractor extends AnyRef
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- PropositionalLogic
- trait ValueConstExtractor extends AnyRef
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- PropositionalLogic
- trait VarExtractor extends AnyRef
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- PropositionalLogic
- class AlreadyInCNF extends AnyRef
- Definition Classes
- CNF
- trait CnfBuilder extends AnyRef
- Definition Classes
- CNF
- trait LitApi extends AnyRef
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- CNF
- trait LitModule extends AnyRef
- Definition Classes
- CNF
- final case class Solvable(cnf: Cnf, symbolMapping: SymbolMapping) extends Product with Serializable
- Definition Classes
- CNF
- class SymbolMapping extends AnyRef
- Definition Classes
- CNF
- 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
- type Clause = Set[Lit]
- Definition Classes
- CNF
- 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
- abstract type Const
- Definition Classes
- PropositionalLogic
- case class Lit(v: Int) extends LitApi with Product with Serializable
- type Model = Map[Sym, Boolean]
- Definition Classes
- PropositionalLogic
- abstract type Tree
- Definition Classes
- PropositionalLogic
- type TseitinModel = collection.immutable.List[Lit]
- type TseitinSearch = collection.immutable.List[(Array[Clause], List[Lit])]
- abstract type Type
- Definition Classes
- PropositionalLogic
- abstract type TypeConst <: Const
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- abstract type ValueConst <: Const
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- abstract type Var <: AbsVar
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- PropositionalLogic
Abstract Value Members
- abstract val NullConst: Const
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- PropositionalLogic
- abstract def TypeConst: TypeConstExtractor
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- PropositionalLogic
- abstract def ValueConst: ValueConstExtractor
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- PropositionalLogic
- abstract val Var: VarExtractor
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- PropositionalLogic
- abstract def prepareNewAnalysis(): Unit
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- PropositionalLogic
- abstract def reportWarning(message: String): Unit
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- PropositionalLogic
- abstract def uncheckedWarning(pos: Global.Position, msg: String, site: Global.Symbol): Unit
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- PropositionalLogic
Concrete Value Members
- object AnalysisBudget
- Definition Classes
- PropositionalLogic
- object And extends java.io.Serializable
- Definition Classes
- PropositionalLogic
- case object False extends Prop with Product with Serializable
- Definition Classes
- PropositionalLogic
- object Or extends java.io.Serializable
- Definition Classes
- PropositionalLogic
- object Sym
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- PropositionalLogic
- case object True extends Prop with Product with Serializable
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- PropositionalLogic
- final def !=(arg0: Any): Boolean
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- AnyRef → Any
- final def ##: Int
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- AnyRef → Any
- def +(other: String): String
- def ->[B](y: B): (Solver, B)
- def /\(props: Iterable[Prop]): Prop
- Definition Classes
- PropositionalLogic
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- val ArrayOfFalse: Array[Clause]
- Definition Classes
- CNF
- val EmptyModel: Map[Sym, Boolean]
- Definition Classes
- Solver → PropositionalLogic
- val NoClauses: Array[Clause]
- Definition Classes
- CNF
- val NoModel: Model
- Definition Classes
- Solver → PropositionalLogic
- val NoTseitinModel: TseitinModel
- def \/(props: Iterable[Prop]): Prop
- Definition Classes
- PropositionalLogic
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def clause(ls: IterableOnce[Lit]): Clause
- Definition Classes
- CNF
- def clause(l: Lit, l2: Lit, ls: Lit*): Clause
- Definition Classes
- CNF
- def clause(l: Lit, l2: Lit): Clause
- Definition Classes
- CNF
- def clause(l: Lit): Clause
- Definition Classes
- CNF
- def clause(): Clause
- Definition Classes
- CNF
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native()
- def cnfString(f: Array[Clause]): String
- def ensuring(cond: (Solver) => Boolean, msg: => Any): Solver
- def ensuring(cond: (Solver) => Boolean): Solver
- def ensuring(cond: Boolean, msg: => Any): Solver
- def ensuring(cond: Boolean): Solver
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def eqFreePropToSolvable(p: Prop): Solvable
- Definition Classes
- CNF → PropositionalLogic
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- def finalize(): Unit
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- protected[lang]
- Definition Classes
- AnyRef
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- @throws(classOf[java.lang.Throwable])
- def findAllModelsFor(solvable: Solvable, owner: Global.Symbol): List[Solution]
- Definition Classes
- Solver → PropositionalLogic
- def findTseitinModelFor(clauses: Array[Clause]): TseitinModel
- def formatted(fmtstr: String): String
- def gatherSymbols(p: Prop): Set[Sym]
- Definition Classes
- PropositionalLogic
- def gatherVariables(p: Prop): Set[Var]
- Definition Classes
- PropositionalLogic
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- def hasModel(solvable: Solvable): Boolean
- Definition Classes
- Solver → PropositionalLogic
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- final def ne(arg0: AnyRef): Boolean
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- final def notify(): Unit
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- @native()
- final def notifyAll(): Unit
- Definition Classes
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- @native()
- def propToSolvable(p: Prop): Solvable
- Definition Classes
- PropositionalLogic
- def removeVarEq(props: List[Prop], modelNull: Boolean = false): (Prop, List[Prop])
- Definition Classes
- PropositionalLogic
- 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
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def toString(): String
- Definition Classes
- AnyRef → Any
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- object Lit extends LitModule with java.io.Serializable
Deprecated Value Members
- 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.
The Scala compiler and reflection APIs.