6

What's the best upper bounds based on number of clauses? In this question shown fastest algorithms for SAT, but there bounds depends from number of variables ( $O(const^n)$ where n is number of variables).

I know that variables bounds can be converted to clauses bounds. If k-SAT formula contains $m$ clauses then $n \leq \frac{k * m}{2}$, consequently if algorithm bounded by $O(const^n)$, it also bounded by $O(const^ \frac{k * m}{2}) = O((const^ \frac{k}{2})^m)$. In that way PPSZ for 3-SAT can be bounded by $O(1.496^m)$. But I'm interested in algorithms which bounds "natively" depends from number of clauses.

  • https://duckduckgo.com/?q=%22An+algorithm+for+the+SAT+problem+for+formulae+of+linear+length%22 $;$ –  Sep 22 '15 at 10:57

1 Answers1

6

It's of the order 2^{0.30897m}, see http://logic.pdmi.ras.ru/~hirsch/abstracts/sodafull.html

(I am not aware of improvements for the number of clauses.)

hirsch
  • 250
  • 1
  • 5