> {-# OPTIONS_HADDOCK show-extensions #-}
> {-|
> Module    : LTK.Decide.TLTT
> Copyright : (c) 2019,2021-2024 Dakotah Lambert
> License   : MIT

> This module implements an algorithm to decide whether a given FSA
> is Tier-Based Locally Threshold Testable (TLTT) by my own algorithm.
>
> @since 0.2
> -}
> module LTK.Decide.TLTT (isTLTT, isTLTTM, isTLTTs) where

> import Data.Representation.FiniteSemigroup

> import LTK.Decide.LTT (isLTT, isLTTM, isLTTs)
> import LTK.FSA (FSA)
> import LTK.Tiers (project)
> import LTK.Algebra (SynMon)

> -- |True iff the automaton recognizes a TLTT stringset.
> isTLTT :: (Ord n, Ord e) => FSA n e -> Bool
> isTLTT :: forall n e. (Ord n, Ord e) => FSA n e -> Bool
isTLTT = FSA n e -> Bool
forall n e. (Ord n, Ord e) => FSA n e -> Bool
isLTT (FSA n e -> Bool) -> (FSA n e -> FSA n e) -> FSA n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FSA n e -> FSA n e
forall n e. (Ord n, Ord e) => FSA n e -> FSA n e
project

> -- |True iff the monoid recognizes a TLTT stringset.
> --
> -- @since 1.0
> isTLTTM :: (Ord n, Ord e) => SynMon n e -> Bool
> isTLTTM :: forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isTLTTM = SynMon n e -> Bool
forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isLTTM (SynMon n e -> Bool)
-> (SynMon n e -> SynMon n e) -> SynMon n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. SynMon n e -> SynMon n e
forall n e. (Ord n, Ord e) => FSA n e -> FSA n e
project

> -- |True iff the semigroup recognizes a TLTT stringset.
> --
> -- @since 1.2
> isTLTTs :: FiniteSemigroupRep s => s -> Bool
> isTLTTs :: forall s. FiniteSemigroupRep s => s -> Bool
isTLTTs = FSMult -> Bool
forall s. FiniteSemigroupRep s => s -> Bool
isLTTs (FSMult -> Bool) -> (s -> FSMult) -> s -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. s -> FSMult
forall s. FiniteSemigroupRep s => s -> FSMult
projectedSubsemigroup