SAT / CNF Optimization

Question

Problem

I am considering a special subset of the SAT optimization problem. For those new to SAT and related topics, here is a related Wikipedia article .

TRUE=(a OR b OR c OR d) AND (a OR f) AND ...

NO and not in conjunctive normal form. It is easily solvable. However, I am trying to minimize the number of true assignments in order to make the whole statement true. I could not find a way to solve this problem.

Possible solutions

I came up with the following ways to solve it:

• Convert to a directed graph and search for a minimal spanning tree spanning only a subset of vertices. There's Edmond's algorithm, but which gives MST for a full graph instead of a subset of vertices.
  • Maybe there is a version of Edmond's algorithm that solves the problem for a subset of vertices?
  • Maybe there is a way to build a graph from the original problem, which is solvable using other algorithms?
• Use a SAT solver, a LIP solver or an exhaustive search. I am not interested in these solutions because I am trying to use this problem as a material for lectures.

Question

Do you have any ideas / comments? Can you come up with other approaches that might work?

Answer 1

This problem is NP-Hard .

You can show the eastern abbreviation for the deletion set :

" " : S1,S2,...,Sn k: set S k, Si S > S, S Si. [ : Si S .)

:
(S1,...,Sn,k) : (S'1 AND S'2 And ... S'n,k) S'i - Si, OR. S'i .

:
→ . hittins, S, , S true, k, S'i v, S Si , , S'i.
→ : build S , true [ , Hitting Set- > This problem].

, NP-Hard, -