User:Polygon/Page for testing: Difference between revisions

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Placeholder
List of incomplete pages:
{{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD|halt}}
* [[Coq-BB5]]
* [[Finite Automata Reduction]]
* [[CTL]]
* [[Irregular Turing Machine]]
* [[Meet-in-the-Middle Weighted Finite Automata Reduction (MITMWFAR)]]
* [[Skelet 1]]
* [[CPS]] (CPS_LRU, CPS_LRUH)
 
 
* [[Repeated Word List]] (RWL_mod; more detailed description for RWLAcc)
 
== 1RB2LA1RC3RA_1LA2RA2RB0RC_1RZ3LC1RA1RB ==
 
{{machine|1RB2LA1RC3RA_1LA2RA2RB0RC_1RZ3LC1RA1RB}
{{TM|1RB2LA1RC3RA_1LA2RA2RB0RC_1RZ3LC1RA1RB} is a non-halting [[BB(4,3)]] TM discovered by Pavel Kropitz in May 2023.<ref>https://discord.com/channels/960643023006490684/1095740122139480195/1113545691994783804</ref In April 2024, Shawn Ligocki showed the TM to follow an infinite pentational rule, proving it non-halting.<ref>https://discord.com/channels/960643023006490684/1095740122139480195/1230591736829575282</ref
 
=== Analysis by Shawn Ligocki ===
https://discord.com/channels/960643023006490684/1095740122139480195/1230591736829575282
 
<pre>
<pre>
S is any tape configuration
Let D(a, b, c, d, e) = 0^inf 1 2^a 1 3^b 1 01^c 1 2^d <A 2^2e+1 0^inf
1. S D> 2^a S --> S 2^a D> S
 
2. S B> 1^a S --> S 1^a B> S
Level 1: D(a, b, c, 2k+r, e)  -> D(a, b, c, r, e+2k)
3. S 1 B> 0 S --> S <A 1^2 S
Level 2: D(a, b, c, 1, e)  -> D(a, b, 0, 1, f2(c, e))
4. S D> (11)^a S --> S (21)^a D> S
  where f2(c, e) = rep(λx -> 2x+5, c)(e)  ~= 2^c
  S A> (11)^a S --> S (12)^a A> S
Level 3: D(a, b, 0, 1, e) -> D(a, 0, 0, 1, f3(b, e))
5. S (21)^a <C S --> S <C (11)^a S
  where f3(b, e) = rep(λx -> f2(x+2, 1), b)(e) ~= 2^^b
  S (12)^a <A S --> S <A (11)^a S
Level 4: D(2a+r, 0, 0, 1, e) -> D(r, 0, 0, 1, f4(a, e))
6. S (12)^a A> 0^2 S --> S <A (11)^a+1 S
  where f4(a, e) = rep(λx -> f3(2x+7), a)(e) ~= 2^^^a
Level 5: D(0, 0, 0, 1, e)  -> D(0, 0, 0, 1, f4(4e+19, f3(1, 1)))


7. S (12)^a 2 (12)^b A> 0^2 S --> S (12)^a-1 2 (12)^b+2 A> S
8. S (12)^a 2 (12)^b A> 0^inf --> S 2 (12)^b+2a A> 0^inf


9. S (12)^a <D (11)^b 0^inf --> S (12)^a-1 <D (11)^2b+3 0^inf
where the last rule repeats forever.
10. S (12)^a <D (11)^b 0^inf --> S <D (11)^((2^(a))*b+(2^(a))*3-3) 0^inf
11. S (11)^a <D (11)^b 0^inf --> S (11)^a-2 (12)^b+3 <D (11)^3 0^inf
</pre>
</pre>
=== References

Latest revision as of 10:46, 3 April 2026

List of incomplete pages:


1RB2LA1RC3RA_1LA2RA2RB0RC_1RZ3LC1RA1RB

{{machine|1RB2LA1RC3RA_1LA2RA2RB0RC_1RZ3LC1RA1RB} {{TM|1RB2LA1RC3RA_1LA2RA2RB0RC_1RZ3LC1RA1RB} is a non-halting BB(4,3) TM discovered by Pavel Kropitz in May 2023.<ref>https://discord.com/channels/960643023006490684/1095740122139480195/1113545691994783804</ref In April 2024, Shawn Ligocki showed the TM to follow an infinite pentational rule, proving it non-halting.<ref>https://discord.com/channels/960643023006490684/1095740122139480195/1230591736829575282</ref

Analysis by Shawn Ligocki

https://discord.com/channels/960643023006490684/1095740122139480195/1230591736829575282 

Let D(a, b, c, d, e) = 0^inf 1 2^a 1 3^b 1 01^c 1 2^d <A 2^2e+1 0^inf

Level 1: D(a, b, c, 2k+r, e)  ->  D(a, b, c, r, e+2k)
Level 2: D(a, b, c, 1, e)  ->  D(a, b, 0, 1, f2(c, e))
  where f2(c, e) = rep(λx -> 2x+5, c)(e)  ~= 2^c
Level 3: D(a, b, 0, 1, e)  ->  D(a, 0, 0, 1, f3(b, e))
  where f3(b, e) = rep(λx -> f2(x+2, 1), b)(e)  ~= 2^^b
Level 4: D(2a+r, 0, 0, 1, e)  ->  D(r, 0, 0, 1, f4(a, e))
  where f4(a, e) = rep(λx -> f3(2x+7), a)(e)  ~= 2^^^a
Level 5: D(0, 0, 0, 1, e)  ->  D(0, 0, 0, 1, f4(4e+19, f3(1, 1)))


where the last rule repeats forever.

=== References

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