trait CNF extends PropositionalLogic
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- trait AbsVar extends AnyRef
- Definition Classes
- PropositionalLogic
- final case class And(ops: Set[Prop]) extends Prop with Product with Serializable
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- 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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- class Prop extends AnyRef
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- trait PropMap extends AnyRef
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- PropositionalLogic
- trait PropTraverser extends AnyRef
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- 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
- type Clause = Set[Lit]
- 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).
- trait CnfBuilder extends AnyRef
- abstract type Const
- Definition Classes
- PropositionalLogic
- type Model = Map[Sym, Boolean]
- Definition Classes
- PropositionalLogic
- final case class Solvable(cnf: Cnf, symbolMapping: SymbolMapping) extends Product with Serializable
- class SymbolMapping extends AnyRef
- 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.
- abstract type Tree
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- PropositionalLogic
- abstract type Type
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- abstract type TypeConst <: Const
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- abstract type ValueConst <: Const
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- abstract type Var <: AbsVar
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Abstract Value Members
- abstract val EmptyModel: Model
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- PropositionalLogic
- abstract val NoModel: Model
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- abstract val NullConst: Const
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- abstract def TypeConst: TypeConstExtractor
- Definition Classes
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- abstract def ValueConst: ValueConstExtractor
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- abstract val Var: VarExtractor
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- PropositionalLogic
- abstract def cnfString(f: Array[Clause]): String
- abstract def findAllModelsFor(solvable: Solvable, pos: Position = NoPosition): List[Solution]
- Definition Classes
- PropositionalLogic
- abstract def findModelFor(solvable: Solvable): Model
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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: Position, msg: String): Unit
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- PropositionalLogic
Concrete Value Members
- object AnalysisBudget
- Definition Classes
- PropositionalLogic
- object And extends java.io.Serializable
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- PropositionalLogic
- object False extends Prop with Product with Serializable
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- object Or extends java.io.Serializable
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- object Sym
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- PropositionalLogic
- 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): (CNF, B)
- def /\(props: Iterable[Prop]): Product with Prop with java.io.Serializable
- Definition Classes
- PropositionalLogic
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- val ArrayOfFalse: Array[Clause]
- val NoClauses: Array[Clause]
- def \/(props: Iterable[Prop]): Product with Prop with java.io.Serializable
- Definition Classes
- PropositionalLogic
- final def asInstanceOf[T0]: T0
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- Any
- def clause(ls: IterableOnce[Lit]): Clause
- def clause(l: Lit, l2: Lit, ls: Lit*): Clause
- def clause(l: Lit, l2: Lit): Clause
- def clause(l: Lit): Clause
- def clause(): Clause
- def clone(): AnyRef
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- protected[lang]
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- @throws(classOf[java.lang.CloneNotSupportedException]) @native()
- def ensuring(cond: (CNF) => Boolean, msg: => Any): CNF
- def ensuring(cond: (CNF) => Boolean): CNF
- def ensuring(cond: Boolean, msg: => Any): CNF
- def ensuring(cond: Boolean): CNF
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def eqFreePropToSolvable(p: Prop): Solvable
- Definition Classes
- CNF → PropositionalLogic
- def equals(arg0: AnyRef): Boolean
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- AnyRef → Any
- def finalize(): Unit
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- protected[lang]
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- @throws(classOf[java.lang.Throwable])
- def formatted(fmtstr: String): String
- def gatherSymbols(p: Prop): Set[Sym]
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- PropositionalLogic
- def gatherVariables(p: Prop): Set[Var]
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- PropositionalLogic
- final def getClass(): Class[_ <: AnyRef]
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- @native()
- def hashCode(): Int
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- final def isInstanceOf[T0]: Boolean
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- final def ne(arg0: AnyRef): Boolean
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- final def notify(): Unit
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- final def notifyAll(): Unit
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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 http://www.decision-procedures.org/slides/propositional_logic-2x3.pdf
- Definition Classes
- PropositionalLogic
- final def synchronized[T0](arg0: => T0): T0
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- def toString(): String
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- AnyRef → Any
- final def wait(): Unit
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- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long, arg1: Int): Unit
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- final def wait(arg0: Long): Unit
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- @throws(classOf[java.lang.InterruptedException]) @native()
Deprecated Value Members
- def →[B](y: B): (CNF, B)
- Implicit
- This member is added by an implicit conversion from CNF toArrowAssoc[CNF] performed by method ArrowAssoc in scala.Predef.
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- ArrowAssoc
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- @deprecated
- Deprecated
(Since version 2.13.0) Use
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