| Copyright | (c) 2022-2024 Dakotah Lambert |
|---|---|
| License | MIT |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
LTK.Decide.Multitier
Description
The Boolean closure of tier-based locally V is a subclass of the Meification of V. For instance, multiple-tier-based definite is a proper subclass of the L-trivial languages. This module includes decision algorithms for some classes of multiple-tier-based languages.
The equations given here are adapted from Almeida's (1995) "Finite Semigroups and Universal Algebra" https://doi.org/10.1142/2481 as they are simpler than the equivalent ones I had found independently.
Since: 1.1
Synopsis
- isMTF :: (Ord n, Ord e) => FSA n e -> Bool
- isMTDef :: (Ord n, Ord e) => FSA n e -> Bool
- isMTRDef :: (Ord n, Ord e) => FSA n e -> Bool
- isMTGD :: (Ord n, Ord e) => FSA n e -> Bool
- isMTFM :: (Ord n, Ord e) => SynMon n e -> Bool
- isMTDefM :: (Ord n, Ord e) => SynMon n e -> Bool
- isMTRDefM :: (Ord n, Ord e) => SynMon n e -> Bool
- isMTGDM :: (Ord n, Ord e) => SynMon n e -> Bool
- isMTFs :: FiniteSemigroupRep s => s -> Bool
- isMTDefs :: FiniteSemigroupRep s => s -> Bool
- isMTRDefs :: FiniteSemigroupRep s => s -> Bool
- isMTGDs :: FiniteSemigroupRep s => s -> Bool
Documentation
isMTF :: (Ord n, Ord e) => FSA n e -> Bool Source #
True iff the given language is multiple-tier-based (co)finite.
isMTDef :: (Ord n, Ord e) => FSA n e -> Bool Source #
True iff the given language is multiple-tier-based definite.
isMTRDef :: (Ord n, Ord e) => FSA n e -> Bool Source #
True iff the given language is multiple-tier-based reverse-definite.
isMTGD :: (Ord n, Ord e) => FSA n e -> Bool Source #
True iff the given language is multiple-tier-based generalized-definite.
isMTFM :: (Ord n, Ord e) => SynMon n e -> Bool Source #
True iff the monoid is aperiodic and satisfies \(x^{\omega}y=yx^{\omega}\).
isMTDefM :: (Ord n, Ord e) => SynMon n e -> Bool Source #
True iff the monoid satisfies \(xyx^{\omega}=yx^{\omega}\).
isMTRDefM :: (Ord n, Ord e) => SynMon n e -> Bool Source #
True iff the monoid satisfies \(x^{\omega}yx=x^{\omega}y\).
isMTFs :: FiniteSemigroupRep s => s -> Bool Source #
True iff the semigroup is aperiodic and satisfies \(x^{\omega}y=yx^{\omega}\).
Since: 1.2
isMTDefs :: FiniteSemigroupRep s => s -> Bool Source #
True iff the semigroup satisifes \(xyx^{\omega}=yx^{\omega}\).
Since: 1.2
isMTRDefs :: FiniteSemigroupRep s => s -> Bool Source #
True iff the semigroup satisifes \(x^{\omega}yx=x^{\omega}y\).
Since: 1.2
isMTGDs :: FiniteSemigroupRep s => s -> Bool Source #
True iff the semigroup satisfies \(x^{\omega}uxvx^{\omega}=x^{\omega}uvx^{\omega}\) and \(x^{\omega}uxzvz^{\omega}=x^{\omega}uzxvz^{\omega}\). Thanks to Almeida (1995) for the simplification.
Since: 1.2