Monoids Benchmark

This benchmark solves the "word problem" in a bunch of monoids simultaneously, using Swift concurrency (or really, just Task). It exercises the standard library data structures heavily. You can also run "sh compile.sh" inside the source directory to build a standalone binary separately from the benchmark harness. The standalone binary prints results to standard output.

More specifically, this program enumerates two-generator two-relation monoid presentations up to length 10, and then applies the Knuth-Bendix algorithm to each one:

<a,b|u=v,w=x>  where |u| + |v| + |w| + |x| <= 10

This takes a few seconds to finish and solves all but three instances. The three it cannot solve are:

<a,b|aaa=a,abba=bb>
<a,b|bab=aaa,bbbb=1>
<a,b|aaaa=1,abbba=b>

In addition to Knuth-Bendix completion, there are some other interesting algorithms here as well:

Shortlex order with arbitrary permutation of alphabet
Wreath product order (also known as recursive path order) with arbitrary degree mapping
Enumerating all words, permutations, monoid presentations
Inverse of a permutation
Computing number of irreducible words in complete presentation (= cardinality of presented monoid) with finite state automata

The Knuth-Bendix implementation is pretty fast. It uses a trie to speed up reduction and finding overlaps.

The main "entry point" is func run() in Monoids.swift.

A formal write-up is here: https://factorcode.org/slava/aaaaabbabb.pdf