Is 3-SAT is more difficult than the SAT? (the same problem - the conversion: SAT => 3-SAT)

Question

I have a question. SAT in which all the clauses have three variables (3-SAT) is more difficult than a traditional SAT which may also include clauses one and two variables? (Of course there are also clauses of the three variables but not all have three variables. More than 3 variables in clauses not exist.)

After my converted a traditional SAT to 3-SAT, analysis of the problem 3-SAT is more difficult for SAT solvers? Meybe it not change anything?

It may seem strange but I want to get after the conversion specified function was difficult as possible.

Answer 1

In general we are talking about worst-case complexity for a problem. Every instance of 3-SAT is an instance of SAT, which means that an algorithm to solve SAT must solve 3-SAT. In this sense, SAT is at least as hard as 3-SAT. On the other hand, the fact that there is a polynomial-time reduction from SAT to 3-SAT means that 3-SAT is at least as hard as SAT.

A particular algorithm for SAT might perform better or worse on an instance of SAT than on the reduction of that instance to 3-SAT. My guess is that usually a good SAT solver would be worse on the reduction to 3-SAT. This may be of some practical interest, but it has no bearing on the theoretical aspects of complexity theory.