Klaus Sutner
The Marxen-Buntrock 5-state busy beaver. Running on an initially empty tape, the machine appears to be caught in some kind of loop; alas, it halts after an absolutely astonishing 47,176,870 steps. The machine was found in 1989, the proof that it really is the 5-state busy beaver was completed in 2024.
Computation & Discrete Math
CDM Course
The Computational Discrete Math course (next incarnation likely Fall 2025) can be found at CDM.DMP Course 2025
The Discrete Math Primer supplementary page is at DMP 25. The actual online course is in OLI format and requires permission.Automata Package
Automata is a Mathematica package that manipulates finite state machines. A few operations on syntactic semigroups and one-dimensional cellular automata are also available. The official release of the package can be found at Automata Paclet. The current version is 1.0.2.
The paclet posted below may be less stable than the one in the repository but typically supports a few extra commands, has a better help browser, more examples and the like. You can get some idea of the available functionality by looking at the demo notebook below. It's a bit rambling, but it provides a reasonable overview of the paclet. All the computations in the notebook should execute without any issues, let me know if there is a problem.
| Automata-1.0.2.paclet | Requires Mathematica 13+ (repository version). |
| AutomataDemo.nb | Usage examples of the package. |
| ConwayFactors.nb | Constructing Conway factor matrices. |
| Frontiers.nb | Tries and frontier automata; visualization. |
| OddParts.nb | Constructing odd parts of regular languages; programming in Automata. |