User:Polygon/Page for testing: Difference between revisions

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Added CPS variants
 
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* [[Meet-in-the-Middle Weighted Finite Automata Reduction (MITMWFAR)]]
* [[Meet-in-the-Middle Weighted Finite Automata Reduction (MITMWFAR)]]
* [[Skelet 1]]
* [[Skelet 1]]
* [[CPS]] (CPS_LRU, CPS_LRUH)


= 1RB1LC_1LC1RD_1LA0LB_0RB1RE_1RF0RA_---0RC =
{machine|1RB1LC_1LC1RD_1LA0LB_0RB1RE_1RF0RA_---0RC}}
{TM|1RB1LC_1LC1RD_1LA0LB_0RB1RE_1RF0RA_---0RC}} is a potentially [[probviously]] halting [[BB(6)]] TM.<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1431570792402915408</ref It was analysed by Racheline on Oct 25, 2025.


== Analysis by Racheline ==
* [[Repeated Word List]] (RWL_mod; more detailed description for RWLAcc)
https://discord.com/channels/960643023006490684/1239205785913790465/1431579799180148738
 
== 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>
A(a,b) := 0^inf 1^a 0 C> 1^b 0^inf
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


A(a,b) -> A(2a+4,b-a-1) if a is even and b>=a+3
Level 1: D(a, b, c, 2k+r, e) -> D(a, b, c, r, e+2k)
A(a,b) -> A(2a+3,b-a) if a is odd and b>=a+4
Level 2: D(a, b, c, 1, e) -> D(a, b, 0, 1, f2(c, e))
A(a,a+3) -> A(2a+1,9) if a is odd
  where f2(c, e) = rep(λx -> 2x+5, c)(e) ~= 2^c
A(a,a+2) -> A(1,2a+7)
Level 3: D(a, b, 0, 1, e) -> D(a, 0, 0, 1, f3(b, e))
A(a,a+1) -> A(4,2a+4)
  where f3(b, e) = rep(λx -> f2(x+2, 1), b)(e) ~= 2^^b
A(a,b) -> A(a-b+1,2b+3) if a>=b>=4
Level 4: D(2a+r, 0, 0, 1, e) -> D(r, 0, 0, 1, f4(a, e))
A(a,3) -> halt if a>=2
  where f4(a, e) = rep(λx -> f3(2x+7), a)(e)  ~= 2^^^a
A(a,2) -> A(a-3,7) if a>=4
Level 5: D(0, 0, 0, 1, e) -> D(0, 0, 0, 1, f4(4e+19, f3(1, 1)))
start: A(2,9)


0^inf 1^(2n) C> 1^(2n+5) 0^inf halts for every n
 
where the last rule repeats forever.
</pre>
</pre>


== References  
=== References
 
[Category:BB(6)]]

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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