I'm solving exercises from Hedman's "First course in logic". Here is Exercise 1.21.
What a step is? Let me take an exampleConsider the following formula in DNF.
Given this formula as input, how many steps will it take the CNF algorithm to halt and output a formula in CNF? Is this algorithm polynomial-time?
Then as I understand
in step 1 I get
in step 2 -
in step 3 -
in step 4 -
in step 5 -
In total 8 steps. Have I read the formula 8 times? So I'd answer that it will take steps and the algorithm is not polynomial-time. Is it correct?
Also I've been thinking as follows. I take first two conjuncts of the given formula and apply CNF algorithm to them. Then I "absorb" the third conjuct and get a new CNF. I repeat this process until the end.