Deterministic finite automaton. Accepts regular languages. More...

#include <DFA.h>

Inheritance diagram for automaton::DFA< SymbolTypeT, StateTypeT >:

Collaboration diagram for automaton::DFA< SymbolTypeT, StateTypeT >:

Public Types
typedef SymbolTypeT	SymbolType

typedef StateTypeT	StateType

Public Member Functions
	DFA (StateType initialState)
	Creates a new instance of the automaton with a concrete initial state. More...

	DFA (ext::set< StateType > states, ext::set< SymbolType > inputAlphabet, StateType initialState, ext::set< StateType > finalStates)
	Creates a new instance of the automaton with a concrete set of states, input alphabet, initial state, and a set of final states. More...

const StateType &	getInitialState () const &

StateType &&	getInitialState () &&

bool	setInitialState (StateType state)

const ext::set< StateType > &	getStates () const &

ext::set< StateType > &&	getStates () &&

bool	addState (StateType state)

void	setStates (ext::set< StateType > states)

void	removeState (const StateType &state)

const ext::set< StateType > &	getFinalStates () const &

ext::set< StateType > &&	getFinalStates () &&

bool	addFinalState (StateType state)

void	setFinalStates (ext::set< StateType > states)

void	removeFinalState (const StateType &state)

const ext::set< SymbolType > &	getInputAlphabet () const &

ext::set< SymbolType > &&	getInputAlphabet () &&

bool	addInputSymbol (SymbolType symbol)

void	addInputSymbols (ext::set< SymbolType > symbols)

void	setInputAlphabet (ext::set< SymbolType > symbols)

void	removeInputSymbol (const SymbolType &symbol)

bool	addTransition (StateType from, SymbolType input, StateType to)
	Add a transition to the automaton. More...

bool	removeTransition (const StateType &from, const SymbolType &input, const StateType &to)
	Removes a transition from the automaton. More...

const ext::map< ext::pair< StateType, SymbolType >, StateType > &	getTransitions () const &

ext::map< ext::pair< StateType, SymbolType >, StateType > &&	getTransitions () &&

ext::iterator_range< typename ext::map< ext::pair< StateType, SymbolType >, StateType >::const_iterator >	getTransitionsFromState (const StateType &from) const

ext::map< ext::pair< StateType, SymbolType >, StateType >	getTransitionsToState (const StateType &to) const

bool	isTotal () const
	Determines whether the automaton is total. More...

auto	operator<=> (const DFA &other) const

bool	operator== (const DFA &other) const

Public Member Functions inherited from core::Components< DFA< DefaultSymbolType, DefaultStateType >, ext::set< DefaultSymbolType >, component::Set, InputAlphabet, ext::set< DefaultStateType >, component::Set, std::tuple< States, FinalStates >, DefaultStateType, component::Value, InitialState >
void	accessComponent ()

Friends
ext::ostream &	operator<< (ext::ostream &out, const DFA &instance)

Additional Inherited Members
Static Public Member Functions inherited from core::Components< DFA< DefaultSymbolType, DefaultStateType >, ext::set< DefaultSymbolType >, component::Set, InputAlphabet, ext::set< DefaultStateType >, component::Set, std::tuple< States, FinalStates >, DefaultStateType, component::Value, InitialState >
static void	registerComponent ()

static void	unregisterComponent ()

Detailed Description

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>
class automaton::DFA< SymbolTypeT, StateTypeT >

Deterministic finite automaton. Accepts regular languages.

Definition is classical definition of finite automata. A = (Q, T, I, \delta, F), Q (States) = nonempty finite set of states, T (TerminalAlphabet) = finite set of terminal symbols - having this empty won't let automaton do much though, I (InitialState) = initial state, \delta = transition function of the form A \times a -> B, where A, B \in Q and a \in T, F (FinalStates) = set of final states

Note that target state of a transition is required. This class is used to store minimal, total, ... variants of deterministic finite automata.

Template Parameters

SymbolTypeT	used for the terminal alphabet
StateTypeT	used to the states, and the initial state of the automaton.

Member Typedef Documentation

◆ StateType

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

typedef StateTypeT automaton::DFA< SymbolTypeT, StateTypeT >::StateType

◆ SymbolType

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

typedef SymbolTypeT automaton::DFA< SymbolTypeT, StateTypeT >::SymbolType

Constructor & Destructor Documentation

◆ DFA() [1/2]

template<class SymbolType , class StateType >

automaton::DFA< SymbolType, StateType >::DFA ( StateType initialState )

explicit

Creates a new instance of the automaton with a concrete initial state.

Parameters

initialState the initial state of the automaton

◆ DFA() [2/2]

template<class SymbolType , class StateType >

automaton::DFA< SymbolType, StateType >::DFA	(	ext::set< StateType >	states,
		ext::set< SymbolType >	inputAlphabet,
		StateType	initialState,
		ext::set< StateType >	finalStates
	)

explicit

Creates a new instance of the automaton with a concrete set of states, input alphabet, initial state, and a set of final states.

Parameters

states	the initial set of states of the automaton
inputAlphabet	the initial input alphabet
initialState	the initial state of the automaton
finalStates	the initial set of final states of the automaton

Member Function Documentation

◆ addFinalState()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

bool automaton::DFA< SymbolTypeT, StateTypeT >::addFinalState ( StateType state )

inline

Adder of a final state.

Parameters

state the new state to be added to a set of final states

Returns: true if the state was indeed added

Here is the caller graph for this function:

◆ addInputSymbol()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

bool automaton::DFA< SymbolTypeT, StateTypeT >::addInputSymbol ( SymbolType symbol )

inline

Adder of a input symbol.

Parameters

symbol the new symbol to be added to an input alphabet

Returns: true if the symbol was indeed added

Here is the caller graph for this function:

◆ addInputSymbols()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

void automaton::DFA< SymbolTypeT, StateTypeT >::addInputSymbols ( ext::set< SymbolType > symbols )

inline

Adder of input symbols.

Parameters

symbols new symbols to be added to an input alphabet

◆ addState()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

bool automaton::DFA< SymbolTypeT, StateTypeT >::addState ( StateType state )

inline

Adder of a state.

Parameters

state the new state to be added to a set of states

Returns: true if the state was indeed added

Here is the caller graph for this function:

◆ addTransition()

template<class SymbolType , class StateType >

bool automaton::DFA< SymbolType, StateType >::addTransition	(	StateType	from,
		SymbolType	input,
		StateType	to
	)

Add a transition to the automaton.

The transition is in a form A \times a -> B, where A, B \in Q and a \in T

Parameters

current	the source state (A)
input	the input symbol (a)
next	the target state (B)

Exceptions

AutomatonException when transition contains state or symbol not present in the automaton components

Returns: true if the transition was indeed added

Here is the call graph for this function:

Here is the caller graph for this function:

◆ getFinalStates() [1/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

ext::set< StateType > && automaton::DFA< SymbolTypeT, StateTypeT >::getFinalStates ( ) &&

inline

Getter of final states.

Returns: the final states of the automaton

Here is the call graph for this function:

◆ getFinalStates() [2/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

const ext::set< StateType > & automaton::DFA< SymbolTypeT, StateTypeT >::getFinalStates ( ) const &

inline

Getter of final states.

Returns: the final states of the automaton

Here is the caller graph for this function:

◆ getInitialState() [1/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

StateType && automaton::DFA< SymbolTypeT, StateTypeT >::getInitialState ( ) &&

inline

Getter of the initial state.

Returns: the initial state of the automaton

Here is the call graph for this function:

◆ getInitialState() [2/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

const StateType & automaton::DFA< SymbolTypeT, StateTypeT >::getInitialState ( ) const &

inline

Getter of the initial state.

Returns: the initial state of the automaton

Here is the caller graph for this function:

◆ getInputAlphabet() [1/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

ext::set< SymbolType > && automaton::DFA< SymbolTypeT, StateTypeT >::getInputAlphabet ( ) &&

inline

Getter of the input alphabet.

Returns: the input alphabet of the automaton

Here is the call graph for this function:

◆ getInputAlphabet() [2/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

const ext::set< SymbolType > & automaton::DFA< SymbolTypeT, StateTypeT >::getInputAlphabet ( ) const &

inline

Getter of the input alphabet.

Returns: the input alphabet of the automaton

Here is the caller graph for this function:

◆ getStates() [1/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

ext::set< StateType > && automaton::DFA< SymbolTypeT, StateTypeT >::getStates ( ) &&

inline

Getter of states.

Returns: the states of the automaton

Here is the call graph for this function:

◆ getStates() [2/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

const ext::set< StateType > & automaton::DFA< SymbolTypeT, StateTypeT >::getStates ( ) const &

inline

Getter of states.

Returns: the states of the automaton

Here is the caller graph for this function:

◆ getTransitions() [1/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

ext::map< ext::pair< StateType, SymbolType >, StateType > && automaton::DFA< SymbolType, StateType >::getTransitions ( ) &&

Get the transition function of the automaton in its natural form.

Returns: transition function of the automaton

◆ getTransitions() [2/2]

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

const ext::map< ext::pair< StateType, SymbolType >, StateType > & automaton::DFA< SymbolType, StateType >::getTransitions ( ) const &

Get the transition function of the automaton in its natural form.

Returns: transition function of the automaton

Here is the caller graph for this function:

◆ getTransitionsFromState()

template<class SymbolType , class StateType >

ext::iterator_range< typename ext::map< ext::pair< StateType, SymbolType >, StateType >::const_iterator > automaton::DFA< SymbolType, StateType >::getTransitionsFromState ( const StateType & from ) const

Get a subset of the transition function of the automaton, with the source state fixed as a view to the internal representation.

Parameters

from	filter the transition function based on this state as a source state

Returns: a subset of the transition function of the automaton with the source state fixed

Here is the call graph for this function:

Here is the caller graph for this function:

◆ getTransitionsToState()

template<class SymbolType , class StateType >

ext::map< ext::pair< StateType, SymbolType >, StateType > automaton::DFA< SymbolType, StateType >::getTransitionsToState ( const StateType & to ) const

Get the transition function of the automaton, with the target state fixed in the transitions natural representation.

Parameters

to	filter the transition function based on this state as a source state

Returns: a subset of the transition function of the automaton with the target state fixed

Here is the call graph for this function:

Here is the caller graph for this function:

◆ isTotal()

template<class SymbolType , class StateType >

bool automaton::DFA< SymbolType, StateType >::isTotal

Determines whether the automaton is total.

The automaton is total if and only if:

size of transition function \forall states \times input symbols = 1

Returns: true if the automaton is total, false otherwise

Here is the caller graph for this function:

◆ operator<=>()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

auto automaton::DFA< SymbolTypeT, StateTypeT >::operator<=> ( const DFA< SymbolTypeT, StateTypeT > & other ) const

inline

The three way comparison implementation

Parameters

other the other instance

Returns: the ordering between this object and the other.

Here is the call graph for this function:

◆ operator==()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

bool automaton::DFA< SymbolTypeT, StateTypeT >::operator== ( const DFA< SymbolTypeT, StateTypeT > & other ) const

inline

The equality comparison implementation.

Parameters

other the other object to compare with.

Returns: true if this and other objects are equal, false othervise

Here is the call graph for this function:

◆ removeFinalState()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

void automaton::DFA< SymbolTypeT, StateTypeT >::removeFinalState ( const StateType & state )

inline

Remover of a final state.

Parameters

state a state to be removed from a set of final states

Returns: true if the state was indeed removed

◆ removeInputSymbol()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

void automaton::DFA< SymbolTypeT, StateTypeT >::removeInputSymbol ( const SymbolType & symbol )

inline

Remover of an input symbol.

Parameters

symbol a symbol to be removed from an input alphabet

Returns: true if the symbol was indeed removed

◆ removeState()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

void automaton::DFA< SymbolTypeT, StateTypeT >::removeState ( const StateType & state )

inline

Remover of a state.

Parameters

state a state to be removed from a set of states

Returns: true if the state was indeed removed

◆ removeTransition()

template<class SymbolType , class StateType >

bool automaton::DFA< SymbolType, StateType >::removeTransition	(	const StateType &	from,
		const SymbolType &	input,
		const StateType &	to
	)

Removes a transition from the automaton.

The transition is in a form A \times a -> B, where A, B \in Q and a \in T

Parameters

current	the source state (A)
input	the input symbol (a)
next	the target state (B)

Returns: true if the transition was indeed removed

Here is the call graph for this function:

◆ setFinalStates()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

void automaton::DFA< SymbolTypeT, StateTypeT >::setFinalStates ( ext::set< StateType > states )

inline

Setter of final states.

Parameters

states completely new set of final states

◆ setInitialState()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

bool automaton::DFA< SymbolTypeT, StateTypeT >::setInitialState ( StateType state )

inline

Setter of the initial state.

Parameters

state new initial state of the automaton

Returns: true if the initial state was indeed changed

◆ setInputAlphabet()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

void automaton::DFA< SymbolTypeT, StateTypeT >::setInputAlphabet ( ext::set< SymbolType > symbols )

inline

Setter of input alphabet.

Parameters

symbols completely new input alphabet

Here is the caller graph for this function:

◆ setStates()

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

void automaton::DFA< SymbolTypeT, StateTypeT >::setStates ( ext::set< StateType > states )

inline

Setter of states.

Parameters

states completely new set of states

Friends And Related Function Documentation

◆ operator<<

template<class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType>

ext::ostream & operator<<	(	ext::ostream &	out,
		const DFA< SymbolTypeT, StateTypeT > &	instance
	)

friend

Print this object as raw representation to ostream.

Parameters

out	ostream where to print
instance	object to print

Returns: modified output stream

The documentation for this class was generated from the following file:

alib2data/src/automaton/FSM/DFA.h

Public Types

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ StateType

◆ SymbolType

Constructor & Destructor Documentation

◆ DFA() [1/2]

◆ DFA() [2/2]

Member Function Documentation

◆ addFinalState()

◆ addInputSymbol()

◆ addInputSymbols()

◆ addState()

◆ addTransition()

◆ getFinalStates() [1/2]

◆ getFinalStates() [2/2]

◆ getInitialState() [1/2]

◆ getInitialState() [2/2]

◆ getInputAlphabet() [1/2]

◆ getInputAlphabet() [2/2]

◆ getStates() [1/2]

◆ getStates() [2/2]

◆ getTransitions() [1/2]

◆ getTransitions() [2/2]

◆ getTransitionsFromState()

◆ getTransitionsToState()

◆ isTotal()

◆ operator<=>()

◆ operator==()

◆ removeFinalState()

◆ removeInputSymbol()

◆ removeState()

◆ removeTransition()

◆ setFinalStates()

◆ setInitialState()

◆ setInputAlphabet()

◆ setStates()

Friends And Related Function Documentation

◆ operator<<