|
|
A337805
|
|
Lazy Beaver Problem: a(n) is the smallest positive number of steps a(n) such that no n-state Turing machine halts in exactly a(n) steps on an initially blank tape.
|
|
0
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
This sequence and the Busy Beaver (A028444) problem are closely related. Turing machines and the number of steps taken by a Turing machine on an initially blank tape are defined in A028444.
This sequence is computable, while the Busy Beaver problem is noncomputable.
a(n) - 1 <= BB(n), where BB(n) = A028444(n).
a(n) - 1 <= (4n+1)^(2n), the number of n-state Turing machines with 2 symbols, by the pigeonhole principle. (4n+1)^(2n) is nearly A141475 (slightly different formalisms are used).
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 2, there exist 2-state Turing machines which halt in exactly {1, 2, 3, 4, 5, 6} steps (and for no other number of steps) given an initially empty input tape. a(2) = 7 is defined as the lowest positive integer not present in that set of possible step lengths.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|