what is meant by EFFECTIVE ENUMERATION i have comes across this word when I was reading about enumerators for Turing machines is it same as LEXICOGRAPHIC ORDER? so effective enumeration is possible for recursive sets but no recursively enumerable sets? i came across this in this question of a competitive exam
L1 is a recursively enumerable language over Σ. An algorithm A effectively enumerates its words as ω1,ω2,ω3,…. Define another language L2 over Σ∪{#}
{wi#wj ∣ wi,wj∈L1, i < j}.
Here # is a new symbol.
Consider the following assertions.
S1:L1 is recursive implies L2 is recursive
S2:L2 is recursive implies L1 is recursive
which of the following is true ?