Consider the language given by the following regular expression: $(ccd{)}^{+}(aab$abb$$bba${)}^{**}(dde{)}^{+}.$

$($a$)$ Design a right$-$linear grammar that generates the language described by the above expression.

$($b$)$ Perform left$-$most derivations of the strings:

i$.$ coddde

ii$.$ codaababbdde

iii. ccdcodbbaaabdde

$($c$)$ Convert your grammar to Chomsky Normal Form.

$($d$)$ Convert your grammar to an equivalent deterministic finite state machine.

Please show work.