Question

I am writing a SAT solver and I started implementing a DPLL algorithm. I understand the algorithm and how it works, I also implemented a variation of it, but what bothers me is the next thing.

function DPLL(Φ)
   if Φ is a consistent set of literals
       then return true;
   if Φ contains an empty clause
       then return false;
   for every unit clause l in Φ
      Φ ← unit-propagate(l, Φ);
   for every literal l that occurs pure in Φ
      Φ ← pure-literal-assign(l, Φ);
   l ← choose-literal(Φ);
   return DPLL(Φ ∧ l) or DPLL(Φ ∧ not(l));

What does it mean, that Φ is a consistent set of literals? I understand that inconsistent implies false, meaning that consistent implies not false. So why can we return true if the current assignment doesn't falsify the problem?

The way I implemented my SAT solver is, that whenever it comes across the assignment that made all clauses true, I returned that assignment and the algorithm was done. But since for given assignment, all clauses must be true in order for it to be a solution to the problem, I don't understand, how can one return true in case that an assignment just satisfies the problem (I assume I am getting something wrong here, but since if Φ is consistent, then it means it is not false, but it can still be undecidable?).

Answer 1

Φ是一组一致的文字，当它只包含文字和文字时，它的否定不会出现在Φ中。 DPLL算法通过纯单元规则逐步将子句列表转换为满足所有原始子句的文字列表。算法在发生时完成（Φ是一组一致的文字），或者当文本分配用完时尝试并且最顶层的DPLL调用返回false。

DPLL What is a consistent set of literals?

1 个答案: