Algorithms – Can non-fractional DPLL steps be considered regular?

In computer science, the Davis – Putnam – Logemann – Loveland (DPLL) algorithm is a complete search algorithm, based on backtracking, which makes it possible to decide on the satisfiability of propositional logic formulas in conjunctive normal form, c & # 39; that is, to solve the CNF-SAT problem.

I wonder if it is possible to detect a non-case-separated DPLL step on CNFs with the help of a finite automaton.

To begin, I think it is possible to describe a CNF as a regular using the following alphabet:

$$
{A, L, R ,, ∨, ¬ }
$$

Or:

• A is a propositional variable
• The is an opening parenthesis
• R is a closing parentheses

Etc …

Since it is possible to show a CNF as a normal language, I think it should be possible to let a finite automaton detect tautologies, propagate the unit
clauses, or delete clauses with pure literals.

So, I think my question boils down to 3 points:

1. Can a tautological clause in an NCF be considered regular?
2. Can a pure literal in an NCF be considered a regular?
3. Can a unit clause in an NCF be considered a regular customer?

I appreciate all the answers, but can you justify your reasoning so that I can understand. (Apologies if this is off topic)