BB(3,4)

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of Cryptids in the domain being given by the discovery of Bigfoot in BB(3,3). The current BB(3,4) champion is 1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch). It runs for $2\uparrow ^{15}5$ steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

Top Halters

The top 20 longest running halting BB(3,4) TMs are:

Standard format	(approximate) runtime
1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)	$2\uparrow ^{15}5$
1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB (bbch)	$2\uparrow ^{12}4$
1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC (bbch)	$10\uparrow \uparrow {2\,048}$

Phase 1

The initial phase of enumeration and reduction of holdouts took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated ~600B(illion) TMs of which ~42B were holdout TMs. This was reduced to ~435M holdout TMs (a 98.97% reduction). The details will be given in this table:

(done to reduce column size: $*^{1}$= % Reduced, $*^{2}$= Runtime (hours), $*^{3}$= Decided, $*^{4}$= Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Data
	Input	Output			$*^{3}$	$*^{4}$
---	---	---	---	---	---	---	---

Phase 2

Xnoob545 and Lúkos from the bbchallenge discord are working on applying mxdys' deciders/parameters to the remaining holdouts. The details will be given in this table:

(done to reduce column size: $*^{1}$= % Reduced, $*^{2}$= Runtime (hours), $*^{3}$= Decided, $*^{4}$= Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Data
	Input	Output			$*^{3}$	$*^{4}$
---	---	---	---	---	---	---	---