2. [8 marks] The DPLL algorithm does something boring (case-split) when it can cannot do anything clever, such as remove tautologies, propagate unit clauses, or remove clauses with pure literals. But can we leave the detection whether we can do something clever to a finite automaton, jin any of the cases? Technically, this boils down to answering the following questions: (a) Is the language of CNFs that contain a tautological clause regular? (b) Is the language of CNFs that contain a pure literal regular? (c) Is the language of CNFs that contain a unit clause regular? Justify your answers with explanations. 2. [8 marks] The DPLL algorithm does something boring (case-split) when it can cannot do anything clever, such as remove tautologies, propagate unit clauses, or remove clauses with pure literals. But can we leave the detection whether we can do something clever to a finite automaton, jin any of the cases? Technically, this boils down to answering the following questions: (a) Is the language of CNFs that contain a tautological clause regular? (b) Is the language of CNFs that contain a pure literal regular? (c) Is the language of CNFs that contain a unit clause regular? Justify your answers with explanations