$4.$ Use diagrams to support your arguments while discussing the following theoretical computational concepts. Highlight the significance of each concept to modern computation.

$($i$)$ Reducibility$(5$marks$)$

$($ii$)$ P$=$NP$(5$marks$)$

$($iii$)$ Decidability $(5$ marks$)$

$($iv$)$ Dynamic Programming $(5$ marks$)$