Congruences¶
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
libsemigroups::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,
libsemigroups::Runner::run_for()
and
libsemigroups::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.
Values:
-
enumerator
left
= 0¶
-
enumerator
right
= 1¶
-
enumerator
twosided
= 2¶
-
enumerator
The classes in libsemigroups
for congruences are: