Given a 3-SAT clause. Is there a way to convert 3-SAT to k-in-3-SAT such that:
The number of new variables introduced are less than the number of clauses (without adding dummy clauses etc.)?
The standard way is by introducing 4 new variables and 3 new clauses as mentioned here: https://en.wikipedia.org/wiki/Boolean_satisfiability_problem
If not is it possible for some N-SAT (N>3)?