There are work-alike programs with the same names for all of the main KBMAG programs: kbprog, autgroup, kbprogcos, autcos (amongst others). If the KBMAG versions are replaced by the corresponding MAF programs, the GAP KBMAG package works. Refer to Using MAF from the GAP package for KBMAG for details.
For computations with groups and monoids MAF includes several new utilities which can:
For computations with coset systems MAF can:
All these facilities, together with the new program simplify, make coset systems a much more useful feature than they were in KBMAG. These extra facilities require you to use MAF directly, because the GAP components of KBMAG would be confused otherwise.
MAF can, in principle, compute automatic structures using any supported word-ordering, not just
"shortlex" automatic structures. However, such computations are often significantly more difficult than for
"shortlex". Such structures often do not exist, even when the rewriting system is confluent. In fact, the author has not been able to find any group which has an automatic structure that can be computed using MAF, but which does not have either a
"shortlex" automatic structure (possibly using another set of generators) or else a confluent rewriting system for the choice of generators and ordering in question. So this new facility appears to be of limited use. The author would be very interested to learn of any groups for which it is genuinely useful. Success is very likely with word-orderings that can be recognised by a finite state automaton, or for orderings (such as "wtlex") that can be recognised by an automaton which only needs to keep a very small amount of information about words. Success is much less likely with wreath-product type word-orderings, and even less likely where these assign different levels to a generator and its inverse.
When MAF or KBMAG are asked to perform computations using very difficult presentations it is impossible to know in advance which will succeed faster, or indeed whether either will succeed at all. Though the author hopes that MAF will usually out-perform KBMAG by a wide margin this is by no means always the case. It is always possible that the groups you are interested in might be better suited to KBMAG than to MAF.
MAF succeeds on many examples where KBMAG either fails, or requires a very careful selection of options to succeed. In particular, MAF will usually work better with recursive orderings.
For very difficult rewriting systems, MAF is more likely to succeed more quickly, provided plenty of memory is available. For example the degen4c example (a famous presentation of the trivial group using three relators of length 125) can be solved in about 20 seconds or less on a modern PC. MAF tends also to be much quicker than KBMAG when processing rewriting systems for large finite groups that are otherwise not particularly difficult. For example it can find confluent rewriting systems for groups of orders of a million or so in around two or three minutes even when the confluent rewriting system may have up to a million or so equations. However, MAF has fewer options for limiting its memory use than KBMAG, and uses memory less conservatively in any case. MAF's default strategy may not always work as well as KBMAG's when a presentation has very long axioms (relators), especially when the word-ordering method used by the rewriting system means that it is possible to create very many shorter equations from the shorter axioms. For example, if default settings are used for both programs, KBMAG's kbprog performs much better than MAF's automata on the balanced presentation of SL(2,p). In such cases using a wreath-product word-ordering, or specifying special strategy options will often improve MAF's performance significantly.
For some rewriting systems MAF may take longer to complete automatic structure calculations than KBMAG. This is partly because because it sometimes computes more automata, but mainly because it uses a different kind of criterion to determine when it should stop Knuth-Bendix completion. For example there is one coset system which KBMAG solves almost instantly, but which takes about 40 seconds using MAF, unless you supply a certain command line option, in which case it completes in under 2 seconds. For "difficult" presentations, it may sometimes happen that KBMAG is "lucky" when MAF is not.
Although MAF is highly configurable, most of the time you should not have to give it any special options in order to solve a problem. While the programs that emulate KBMAG programs accept most of their command line and configuration options, many of them are ignored. MAF's "real" configuration options are often different from anything in KBMAG.
For computation with input files representing groups or monoids, automata contains all the functionality contained in the kbprog, autgroup, gpaxioms, and gpminkb components of KBMAG.
Computation with input files representing subgroups is also performed using automata, which also contains the functionality of the makecosfile, kbprogcos, autcos, and gpmakesubwa components of KBMAG.
You can continue to invoke all the KBMAG programs separately rather than using automata if you wish but you may like to note that in MAF, kbprog, gpmakefsa, autgroup, kbprogcos, autcos, are all almost identical to MAF's automata.