We de$$ned $$ by breaking the

input string into

Equation $$ However$$ we

followed by a single symb ol $$in the

informally think of $$ as describing

string of lab els$$ and if so$$ then it

string in the de$$nition of $$ Show that in fact$$q $$ xy $$q $$ x$$ y

state q and strings x and y $$ Hint $$

$$ Exercise $$ Show that for $$

$$q $$ ax$$q $$ a$$ x $$ Hint $$ Use

Perform

inductive part$$ what happ ens

along a should not matter how

path with a certain we break the input

$$ an induction on jy j$$

any state Exercise $$