I'm a bit confused on some of the notation being used for turing machines in one of our exercises in class.
The question gives us a string α ϵ {0,1}* and the function int(α) that changes a binary number to its base 10 form. (example, int(00010) = int(10) = 2)
Now comes the tricky part:
Define the language L ⊆ {0, 1, #}* by:
L = {α#β | α, β ∈ {0, 1}* and |β| ≥ int(α) ≥ 1 and β_{int(α)} = 1}.
This bolded section is confusing me, and it seems like there are different variations of T.M. notation as well...
Could someone give me a rough approximation of what this might mean?
Extra:
Examples for language L:
$\#111 \notin L$
$00010\#11100 \in L$
$00011\#010111 \notin L$
$00011\#11 \notin L$
$1\#\#1 \notin L$
Thanks in advance.