Pure virtual member functions

This page contains information about the pure virtual member functions of the FpSemigroupInterface class.

virtual bool libsemigroups::FpSemigroupInterface::equal_to(std::string const &u, std::string const &v) = 0

Check if two strings represent the same element.

See also

equal_to(word_type const&, word_type const&).

Complexity

See warning.

Warning

The problem of determining the return value of this function is undecidable in general, and this function may never terminate.

Parameters

  • u – a string over the alphabet of the finitely presented semigroup.

  • v – a string over the alphabet of the finitely presented semigroup.

Throws
Returns

true if the strings u and v represent the same element of the finitely presented semigroup, and false otherwise.

virtual std::string libsemigroups::FpSemigroupInterface::normal_form(std::string const &w) = 0

Returns a normal form for a string.

If u and v represent the same element of the finitely presented semigroup represented by this, then normal_form(u) is guaranteed to equal normal_form(v). No further guarantees are given, the return value of normal_form() depends on the implementation and may vary between finitely presented semigroups defined in precisely the same way.

See also

normal_form(word_type const&).

Complexity

See warning.

Warning

The function for finding the structure of a finitely presented semigroup may be non-deterministic, or since the problem is undecidable in general, this function may never return a result.

Parameters

w – the word whose normal form we want to find. The parameter w must be a std::string consisting of letters in alphabet().

Throws

LibsemigroupsException – if w contains a letter that is not in alphabet(), or the object has not been fully initialised.

Returns

The normal form of the parameter w, a value of type std::string.

virtual uint64_t libsemigroups::FpSemigroupInterface::size() = 0

Returns the size of the finitely presented semigroup.

Complexity

See warning.

Parameters

(None)

Warning

The problem of determining the return value of this function is undecidable in general, and this function may never terminate.

Throws

(None) – This function guarantees not to throw a LibsemigroupsException.

Returns

A uint64_t, the value of which equals the size of this if this number is finite, or POSITIVE_INFINITY in some cases if this number is not finite.