P

rove that for every deterministic finite automaton M $=($Q$,\backslash$Sigma $,\backslash$delta $,$ q$0,$ A$),$ L$($M $)$ is an infinite lan$-$

guage if and only if M accepts some string x in $\backslash$Sigma $$ with $|$Q$|<=|$x$|<2|$Q$|($where $|$Q$|$ denotes the cardinality$/$size

of Q$).$

$2$