3-29: "Strings and languages; Finite automata; Basic DFA examples"
What does DFA stand for?
Deterministic Finite Automaton
meaning of "proper prefix"
a prefix that is not equal to the whole string (e.g., "abc" is a prefix of "abc", but not a proper prefix)
meaning of x⋅y
concatenation of strings x and y
meaning of ε
empty string
if x is a string, then what is x^3?
it is xxx (concatenation of three copies of x)
meaning of w^R
reverse of string w
formal definition of "prefix"
x is a prefix of w if Ǝy : xy = w
Let x be a prefix of w. Prove that x^R is a suffix of w^R
∃y : w = xy w^R = (xy)^R = y^R x^R ∃z : w^R = z x^R then z can equal y^R, so x^R is a suffix of w^R
if ∑ = {0, 1}, what is ∑*? (in this case, 0 and 1 are symbols)
∑* = {ε, 0, 1, 00, 11, 01, 10 ... } this set is infinitely large
x is a string. What is equivalent to x^(m + n)?
(x^m)(x^n)