Translate the following into a formula of first-order logic. "A language L that is regular will have the following property: there will be some number N (that depends on L) such that if s is a string in L (a string is a sequence of characters) whose length is at least N then s can be written as $xyz$ where y is not the empty string and $xy^i z$ is in the language L for every nonnegative integer i."
can anyone help me with this? This is what I came up with so far and it's definitely not right...
My Guess: Universe of Discourse: Language N(x)= x is some number depending on L I(x)= x is non negative integer S(x)= x is string in L
for existential quantifier ill use "bE" and for universal quantifier ill use "bA"
Guess starts here: bEx(N(x) ^ (S(x) > N(x)) --> bEx bEy bEz((S(x)=xyz)^y does not equal S element empty set)) ^ bAx(I(x)
This is probably completely wrong; I don't really get it. Thanks for any input/help.