1RB1LC 1LA1RE 0RD0LA 1RZ1LB 1LD0RF 0RD1RB: Difference between revisions
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m (fix typo) |
m (→Analysis) |
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m1 = b-1 | m1 = b-1 | ||
a,b,x = ((((n+1)*(1<<(m1+k))-1))*(1<<(m2+1))+1), (m2+m1+k+1), x0 | a,b,x = ((((n+1)*(1<<(m1+k))-1))*(1<<(m2+1))+1), (m2+m1+k+1), x0 | ||
else: assert 0 | else: assert 0 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Tape encoding (reversed): | |||
<pre> | <pre> | ||
H1 = 0^inf 1^7 | H1 = 0^inf 1^7 | ||
| Line 67: | Line 66: | ||
</pre> | </pre> | ||
Execution process: | |||
<pre> | <pre> | ||
(57,5,H1) --> | (57,5,H1) --> | ||
| Line 84: | Line 83: | ||
halt | halt | ||
</pre> | </pre> | ||
In each iteration of (a,b,x) --> (a',b',x'), a'≈2^a. It halts after 11010064 iterations of (a,b,x) --> (a',b',x').The omitted numbers in x and b are much smaller than a, and much larger than 66060289. | |||
==References== | ==References== | ||
<references /> | <references /> | ||
[[Category:Stub]] | [[Category:Stub]] | ||
Revision as of 13:16, 17 June 2025
1RB1LC_1LA1RE_0RD0LA_1RZ1LB_1LD0RF_0RD1RB (bbch)
Current BB(6) Champion. Discovered by mxdys on 16 June 2025.
It's in a family of 6 machines with the halting time and sigma score between 10↑↑11010000 and 10↑↑11011000:
1RB1LC_1LA1RE_0RD0LA_---1LB_1LD0RF_0RD1RB 1RB1LC_1LA1RE_0RD0LA_---1LB_1LE0RF_0RD1RB 1RB1LC_1LA1RD_1LA0LA_1LD0RE_0RF1RB_---1LB 1RB1LC_1LA1RD_1LA0LA_1LD0RE_0RF1RB_---1LC 1RB1LC_1LA1RD_1LA0LA_1LF0RE_0RF1RB_---1LB 1RB1LD_1LC1RE_---1LD_1LA0LA_1LE0RF_0RC1RB
Analysis
It's behavior can be described by the python code below:
def LBS(x):
if x=='H1': return 'H1',1,1
if x=='H2': return 'H4',2,2
if x=='H3': print('Halted'); exit()
if x=='H4': return 'H5',1,1
if x=='H5': return 'H1',1,2
w,k0,x = x
if w=='W1':
if k0==0 and x=='H1': return 'H5',1,2
x0,n,k = LBS(x)
k1=k0+k-2
return ('W1',k1,x0),((n+1)*(1<<k1)-2)*4+5,2
if w=='W2':
if k0==0 and x=='H1': return 'H3',1,3
if k0==1 and x=='H1': return 'H2',1,3
x0,n,k = LBS(x)
k1=k0+k-3
return ('W2',k1,x0),((n+1)*(1<<k1)-2)*8+5,3
assert 0
a,b,x = 57,5,'H1'
while 1:
r,m2 = a%3,a//3
x0,n,k = LBS(x)
if r==2:
m1 = b-3
a,b,x = ((((n+1)*(1<<(m1+k))-2)*4+2)*(1<<(m2+1))+1), m2, ('W2',m1+k,x0)
elif r==1:
m1 = b-2
a,b,x = ((((n+1)*(1<<(m1+k))-2)*2+2)*(1<<(m2+1))+1), m2, ('W1',m1+k,x0)
elif r==0:
m1 = b-1
a,b,x = ((((n+1)*(1<<(m1+k))-1))*(1<<(m2+1))+1), (m2+m1+k+1), x0
else: assert 0
Tape encoding (reversed):
H1 = 0^inf 1^7 H2 = 0^inf 1^5 101111 111111 1111 H3 = 0^inf 1^5 111111 1111 H4 = 0^inf 1^7 10 111111 H5 = 0^inf 1^7 111111 (W1,n,l) = l 111111^n 10 111111^2 (W2,n,l) = l 111111^n 1010 111111^3 (a,b,x) = x 111111^b <F0 11^1+a 0^inf
Execution process:
(57,5,H1) --> (66060289,25,H1) --> (_,22020096,(W1,24,H1)) --> (_,_,(W2,22020095,(W1,23,H1))) --> ... (_,_,(...(W2,22020074,(W1,2,H1))...)) --> (_,_,(...(W2,22020073,(W1,1,H1))...)) --> (_,_,(...(W2,22020072,(W1,0,H1))...)) --> (_,_,(...(W2,22020071,H5)...)) --> (_,_,(...(W2,22020070,H1)...)) --> ... (_,_,(...(W2,4,H1)...)) --> (_,_,(...(W2,2,H1)...)) --> (_,_,(...(W2,0,H1)...)) --> (_,_,(...H3...)) --> halt
In each iteration of (a,b,x) --> (a',b',x'), a'≈2^a. It halts after 11010064 iterations of (a,b,x) --> (a',b',x').The omitted numbers in x and b are much smaller than a, and much larger than 66060289.