libsemigroups implements serveral algorithms for computing a congruence of a semigroup or monoid. The main algorithms implemented are Todd-Coxeter, Knuth-Bendix, and brute-force enumeration; see the links below for further details. As a convenience, libsemigroups also has a class Congruence that runs some predetermined variants of Todd-Coxeter, Knuth-Bendix, and the brute-force enumeration in parallel. This class is, at present, not very customisable, and lacks some of the fine grained control offered by the classes implementing individual algorithms, such as congruence::ToddCoxeter and congruence::KnuthBendix.

All of the classes for congruences in libsemigroups can be used “interactively”, in the sense that they can be run for a particular amount of time, or until some condition is met; for further details see, for example, Runner::run_for() and Runner::run_until().

The “handedness” of a congruence is determined by:

enum libsemigroups::congruence_type

The values in this enum can be used to indicate that a congruence should be 2-sided, left, or right.


enumerator left
enumerator right
enumerator twosided

The classes in libsemigroups for congruences are: