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)