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Some machines are ''right at the edge of computability.'' This means that they are computationally tractable to simulate, but they are literal energy vampires. There are a few such machines that have been found, and all of them should be listed here.  
= Machines at the Edge =
Some machines are ''right at the edge of computability.'' This means that they are computationally tractable to simulate, but they are literal energy vampires. There are a few such machines that have been found, and all of them should be listed here. Some of them, however, are not yet confirmed to be tractable or intractable.  


There are no energy vampire machines for [[BB(3,3)]].
There are no energy vampire machines in [[BB(3,3)]], one unknown in [[BB(2,5)]] and for [[BB(6)]], two machines, seven intractable machines and 9 others, which have not yet been worked out.


== [[BB(6)|6x2]] Machines ==
== [[BB(6)|6x2]] Machines ==


=== {{TM|1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF}} ===
=== {{TM|1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF}} (CRYPTID) ===


* Would take a '''few weeks''' with '''~10 TB of memory.'''
* Would take a '''few weeks''' with '''~10 TB of memory.'''
* '''50% chance of halting''' based on H^114e12(10) mod 4.
* '''50% chance of halting''' based on H^114e12(10) mod 4.
* Mechanism: approximately B(m) ~ B(H^m(10)).
* Mechanism: approximately B(m) ~ B(H^m(10)).
* ~$200 of compute.


=== {{TM|1RB0LA_0RC0RB_1LD1LA_1LC1RE_1RF0RD_1LC---}} ===
=== {{TM|1RB0LA_0RC0RB_1LD1LA_1LC1RE_1RF0RD_1LC---}} ===
Line 16: Line 18:
* Expected to halt on the order of one trillion iterations.
* Expected to halt on the order of one trillion iterations.
* Mechanism: pipe [[Hydra]] residues into another very chaotic machine.
* Mechanism: pipe [[Hydra]] residues into another very chaotic machine.
12 more machines, six of which are probviously halting [[Cryptid|cryptids]]. The rest are all probably tetrational machines.<syntaxhighlight lang="html">
 
1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE CRYPTID
=== Unknown machines - 9 total ===
1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF CRYPTID
The following 6 machines are all possibly tetrational machines, given by Racheline [https://discord.com/channels/960643023006490684/1026577255754903572/1384906806303789178 here]. Wheter they are intractable, is not yet known.<syntaxhighlight lang="html">1RB1LE_0LC1RE_---1LD_0RD1LA_0RF1RF_1RA0LB
1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB CRYPTID
1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA CRYPTID
1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE CRYPTID
1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC CRYPTID (collection of 16 probvious halters)
1RB1LE_0LC1RE_---1LD_0RD1LA_0RF1RF_1RA0LB
1RB1RD_1LC1RA_---1LD_1LE0RA_1LF0LE_0RB0LB
1RB1RD_1LC1RA_---1LD_1LE0RA_1LF0LE_0RB0LB
1RB0RC_0RC0RA_1RD1LA_1LE0LB_0LB1LF_0LD---
1RB0RC_0RC0RA_1RD1LA_1LE0LB_0LB1LF_0LD---
1RB0LF_0RC1RB_1LD0RB_1LE---_1RF1LA_0LC0LE
1RB0LF_0RC1RB_1LD0RB_1LE---_1RF1LA_0LC0LE
1RB0LE_0RC0RA_1LD0LC_1LA0LB_1RA1LF_---0LC
1RB0LE_0RC0RA_1LD0LC_1LA0LB_1RA1LF_---0LC
1RB1RF_1LC0RA_---0LD_0LE0LB_1RF1RB_1RE1LF "Probviously halts after 10^10^O(1) steps, possibly tetrational machine"
1RB1RF_1LC0RA_---0LD_0LE0LB_1RF1RB_1RE1LF - Probviously halts after 10^10^O(1) steps - Racheline</syntaxhighlight>The following 3 machines are all probviously halting [[Cryptid|cryptids]].<syntaxhighlight lang="html">1RB---_0RC0RE_1RD1RF_1LE0LB_1RC0LD_1RC1RA
</syntaxhighlight>
1RB1LD_1RC0LE_1LA1RE_0LF1LA_1RB0RB_---0LB
1RB0RE_1LC0RA_1LA1LD_1LC1LF_0LC0LB_1LE--- - Equivalent to the first in this list (?)</syntaxhighlight>
 
== Intractable 6x2 machines ==
7 more machines, all which are probviously halting [[Cryptid|cryptids]].
 
=== {{TM|1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE}} CRYPTID ===
 
* Uses the [[Hydra function|Hydra map]]
* The lower bound for when it halts is around 10^10^120395, and with each exponentiation it has a 1/4 chance of halting, so I think the expected halting time is around 10^10^10^10^10^120395 - Racheline
 
=== {{TM|1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB}} CRYPTID ===
 
* Next reset in ~10^22.17 iterations of the [[Hydra function|Hydra map]], by [https://discord.com/channels/960643023006490684/1448725136340422717/1450045543710724107 residual-integral]
* It would cost at least $40B and take three million years to simulate
 
=== {{TM|1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA}} CRYPTID ===
 
* Next reset in ~10^1481 iterations of a near-[[Hydra function|Hydra map]], by [https://discord.com/channels/960643023006490684/1448725136340422717/1450045543710724107 residual-integral]
 
=== {{TM|1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE}} CRYPTID ===
 
* Next reset in ~10^446 iterations of [[Hydra function|Hydra map]], by [https://discord.com/channels/960643023006490684/1448725136340422717/1450045543710724107 residual-integral]
 
=== {{TM|1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC}} CRYPTID ===
 
* Next reset in ~10^24684623 iterations of near-[[Hydra function|Hydra map]], by [https://discord.com/channels/960643023006490684/1448725136340422717/1450045543710724107 residual-integral]
* Canonical machine of a class of 16 probable halters.
 
=== {{TM|1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE}} CRYPTID ===
 
* One of the values for the current rules is so large now, that using these rules, simulating is no longer a viable option to show halting. ~10^39991 to next reset.
 
=== {{TM|1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA}} Lucy's Moonlight | CRYPTID ===
 
* Next reset in ~10^2901 iterations of near-[[Hydra function|Hydra map]], by [https://discord.com/channels/960643023006490684/1448725136340422717/1450045543710724107 residual-integral]


== [[BB(2,5)|2x5]] Machines ==
== [[BB(2,5)|2x5]] Machines ==
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* Racheline estimates that it has a 1/8 chance of beating the current champion.
* Racheline estimates that it has a 1/8 chance of beating the current champion.
* Wheter it is tractable to simulate until halting or not is not yet known.

Latest revision as of 18:56, 16 December 2025

Machines at the Edge

Some machines are right at the edge of computability. This means that they are computationally tractable to simulate, but they are literal energy vampires. There are a few such machines that have been found, and all of them should be listed here. Some of them, however, are not yet confirmed to be tractable or intractable.

There are no energy vampire machines in BB(3,3), one unknown in BB(2,5) and for BB(6), two machines, seven intractable machines and 9 others, which have not yet been worked out.

6x2 Machines

1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF (bbch) (CRYPTID)

  • Would take a few weeks with ~10 TB of memory.
  • 50% chance of halting based on H^114e12(10) mod 4.
  • Mechanism: approximately B(m) ~ B(H^m(10)).
  • ~$200 of compute.

1RB0LA_0RC0RB_1LD1LA_1LC1RE_1RF0RD_1LC--- (bbch)

  • Around a day with somewhere in [100, 1000] GB of memory.
  • Expected to halt on the order of one trillion iterations.
  • Mechanism: pipe Hydra residues into another very chaotic machine.

Unknown machines - 9 total

The following 6 machines are all possibly tetrational machines, given by Racheline here. Wheter they are intractable, is not yet known.

1RB1LE_0LC1RE_---1LD_0RD1LA_0RF1RF_1RA0LB
1RB1RD_1LC1RA_---1LD_1LE0RA_1LF0LE_0RB0LB
1RB0RC_0RC0RA_1RD1LA_1LE0LB_0LB1LF_0LD---
1RB0LF_0RC1RB_1LD0RB_1LE---_1RF1LA_0LC0LE
1RB0LE_0RC0RA_1LD0LC_1LA0LB_1RA1LF_---0LC
1RB1RF_1LC0RA_---0LD_0LE0LB_1RF1RB_1RE1LF - Probviously halts after 10^10^O(1) steps - Racheline

The following 3 machines are all probviously halting cryptids.

1RB---_0RC0RE_1RD1RF_1LE0LB_1RC0LD_1RC1RA
1RB1LD_1RC0LE_1LA1RE_0LF1LA_1RB0RB_---0LB
1RB0RE_1LC0RA_1LA1LD_1LC1LF_0LC0LB_1LE--- - Equivalent to the first in this list (?)

Intractable 6x2 machines

7 more machines, all which are probviously halting cryptids.

1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE (bbch) CRYPTID

  • Uses the Hydra map
  • The lower bound for when it halts is around 10^10^120395, and with each exponentiation it has a 1/4 chance of halting, so I think the expected halting time is around 10^10^10^10^10^120395 - Racheline

1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB (bbch) CRYPTID

  • Next reset in ~10^22.17 iterations of the Hydra map, by residual-integral
  • It would cost at least $40B and take three million years to simulate

1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA (bbch) CRYPTID

1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE (bbch) CRYPTID

1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC (bbch) CRYPTID

  • Next reset in ~10^24684623 iterations of near-Hydra map, by residual-integral
  • Canonical machine of a class of 16 probable halters.

1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE (bbch) CRYPTID

  • One of the values for the current rules is so large now, that using these rules, simulating is no longer a viable option to show halting. ~10^39991 to next reset.

1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA (bbch) Lucy's Moonlight | CRYPTID

2x5 Machines

1RB2RA3LB---2LB_2LA0LA4RB0RB1LA (bbch)

  • Racheline estimates that it has a 1/8 chance of beating the current champion.
  • Wheter it is tractable to simulate until halting or not is not yet known.
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