Knuth-Bendix

This page contains links to the documentation related to the implementation of the Knuth-Bendix algorithm in libsemigroups.

The purpose of this algorithm is to find a locally confluent presentation for a semigroup or monoid, with respect to some alphabet order and reduction ordering.

Topics
	KnuthBendix class
	Class template containing an implementation of the Knuth-Bendix Algorithm.
	Knuth-Bendix helper functions
	Helper functions for the KnuthBendix class.
	to<KnuthBendix>
	Convert to KnuthBendix instance.

Functions
template<typename Word, typename Rewriter, typename ReductionOrder>
std::ostream &	operator<< (std::ostream &os, KnuthBendix< Word, Rewriter, ReductionOrder > const &kb)
	Insert into std::ostream.
template<typename Word, typename Rewriter, typename ReductionOrder>
std::string	to_human_readable_repr (KnuthBendix< Word, Rewriter, ReductionOrder > &kb)
	Return a string representation of a KnuthBendix instance.

Function Documentation

operator<<()

template<typename Word, typename Rewriter, typename ReductionOrder>

std::ostream & operator<<	(	std::ostream &	os,
		KnuthBendix< Word, Rewriter, ReductionOrder > const &	kb )

Defined in knuth-bendix.hpp.

This function allows a KnuthBendix object to be left shifted into a std::ostream, such as std::cout. The currently active rules of the system are represented in the output.

Parameters

os	the output stream to insert into.
kb	the KnuthBendix object.

Returns

A reference to the first argument.

to_human_readable_repr()

template<typename Word, typename Rewriter, typename ReductionOrder>

std::string to_human_readable_repr

(

KnuthBendix< Word, Rewriter, ReductionOrder > &

kb

)

Defined in knuth-bendix.hpp.

This function returns a string representation of a KnuthBendix instance, specifying the size of the underlying alphabet and the number of active rules.

Template Parameters

Rewriter	the first template parameter for KnuthBendix.
ReductionOrder	the second template parameter for KnuthBendix.

Parameters

kb	the KnuthBendix instance.

Returns

The representation, a value of type std::string.