Obviously infinite

This page collects the documentation for the functionality in libsemigroups for checking if a finitely presented semigroup or monoid is obviously infinite.

Classes
class	IsObviouslyInfinite
	Class for checking if a finitely presented semigroup or monoid is obviously infinite. More...

Functions
template<typename Word>
bool	is_obviously_infinite (Congruence< Word > &c)
	Function for checking if a congruence obviously has infinite many classes.
template<typename Rewriter, typename ReductionOrder>
bool	is_obviously_infinite (detail::KnuthBendixImpl< Rewriter, ReductionOrder > &kb)
	Function for checking if the quotient of a finitely presented semigroup or monoid defined by a KnuthBendix object is obviously infinite or not.
bool	is_obviously_infinite (detail::ToddCoxeterImpl const &tc)
	Function for checking if the quotient of a finitely presented semigroup or monoid defined by a ToddCoxeterImpl object is obviously infinite or not.
template<typename Word>
bool	is_obviously_infinite (Kambites< Word > &k)
	Function for checking if the finitely presented semigroup or monoid defined by a Kambites object obviously has infinite many classes.
template<>
bool	is_obviously_infinite (Presentation< std::string > const &p)
	Function for checking if the finitely presented semigroup or monoid defined by a Presentation object is obviously infinite or not.
template<typename Word>
bool	is_obviously_infinite (Presentation< Word > const &p)
	Function for checking if the finitely presented semigroup or monoid defined by a Presentation object is obviously infinite or not.

Function Documentation

is_obviously_infinite() [1/6]

template<typename Word>

bool is_obviously_infinite

(

Congruence< Word > &

c

)

This function returns true if the quotient of the finitely presented semigroup or monoid defined by the Congruence object c is obviously infinite; false is returned if it is not.

This function exists to make it simpler to call an IsObviouslyInfinite object a single time, and uses some information from the (possible incomplete) Congruence object to assist in this determination.

Parameters

c	the Congruence instance.

Returns

Whether or not the congruence obviously has infinitely many classes.

Note

If this function returns false, it is still possible that the congruence has infinitely many classes.

is_obviously_infinite() [2/6]

template<typename Rewriter, typename ReductionOrder>

bool is_obviously_infinite

(

detail::KnuthBendixImpl< Rewriter, ReductionOrder > &

kb

)

This function returns true if the quotient of the finitely presented semigroup or monoid defined by the KnuthBendix object kb is obviously infinite; false is returned if it is not.

This function exists to make it simpler to call an IsObviouslyInfinite object a single time, and uses some information from the (possible incomplete) KnuthBendix object to assist in this determination.

Parameters

kb	the KnuthBendix instance.

Returns

Whether or not the quotient defined by a KnuthBendix instance is obviously infinite.

Note

If this function returns false, it is still possible that the quotient defined by the KnuthBendix object kb is infinite.

is_obviously_infinite() [3/6]

bool is_obviously_infinite

(

detail::ToddCoxeterImpl const &

tc

)

This function returns true if the quotient of the finitely presented semigroup or monoid defined by the ToddCoxeterImpl object tc is obviously infinite; false is returned if it is not.

This function exists to make it simpler to call an IsObviouslyInfinite object a single time, and uses some information from the (possible incomplete) ToddCoxeterImpl object to assist in this determination.

Parameters

tc	the ToddCoxeterImpl instance.

Returns

Whether or not the quotient defined by a ToddCoxeterImpl instance is obviously infinite.

Note

If this function returns false, it is still possible that the quotient defined by the ToddCoxeterImpl object tc is infinite.

is_obviously_infinite() [4/6]

template<typename Word>

bool is_obviously_infinite

(

Kambites< Word > &

k

)

This function returns true if the finitely presented semigroup or monoid defined by a Kambites object is obviously infinite; false is returned if it is not.

This function exists to make it simpler to call an IsObviouslyInfinite object a single time, and uses some information from the (possible incomplete) Kambites object to assist in this determination.

Parameters

k	the Kambites instance.

Returns

Whether or not the finitely presented semigroup or monoid defined by a Kambites object is obviously infinite.

Note

If this function returns false, it is still possible that the finitely presented semigroup or monoid defined by k is infinite.

is_obviously_infinite() [5/6]

template<>

bool is_obviously_infinite

(

Presentation< std::string > const &

p

)

This function returns true if the finitely presented semigroup or monoid defined by the Presentation object p is obviously infinite. This function exists to make it simpler to call an IsObviouslyInfinite object a single time.

Parameters

p	the presentation.

Returns

Whether or not the presentation defines an obviously infinite semigroup or monoid.

Exceptions

LibsemigroupsException

If the presentation p is not valid.

Note

If this function returns false, it is still possible that the finitely presented semigroup or monoid defined by p is infinite.

is_obviously_infinite() [6/6]

template<typename Word>

bool is_obviously_infinite

(

Presentation< Word > const &

p

)

This function returns true if the finitely presented semigroup or monoid defined by the Presentation object p is obviously infinite. This function exists to make it simpler to call an IsObviouslyInfinite object a single time.

Template Parameters

Word	the type of the words in the presentation p.

Parameters

p	the presentation.

Returns

Whether or not the presentation defines an obviously infinite semigroup or monoid.

Exceptions

LibsemigroupsException

If the presentation p is not valid.

Note

If this function returns false, it is still possible that semigroup or monoid defined by p is infinite.