$=$

$0$

$0$

$,$

$0$

$1$

$,$

$1$

$0$

$,$

$1$

$1$

A string of symbols from $$ defines two rows of $0$s and $1$s$.$ Consider each row to be a

binary number and let

D $=\{$w in $+|$ the top row of w is a smaller number than the bottom row$\}$

For example,

h$0$

$0$

i h$0$

$1$

i h$1$

$0$

i h$1$

$0$

i

in D because, as binary numbers, $0011<0100.$

Construct a finite automaton that accepts D$.$ Note that, due to the linearity of sym$-$

bols in tint, the columns above have to be represented by strings of length $2.$ That is$,$

$=\{00,01,10,11\}.$ And $00011010$ in D because, as binary numbers, $0011<0100$