World's most popular travel blog for travel bloggers.

[Solved]: Convert $\sum x_i = y$ to 3-sat

, , No Comments
Problem Detail: 

I have a simple looking question. What is the most efficient conversion of $\sum_{i=1}^n x_i = y$ to 3-sat? Here $x_i$ is either $1$ or $0$ and $y$ is some positive integer.

Can you do better than making a SATISFIABILITY instance with $\binom{n}{y}$ clauses, each of which is the conjunction of $y$ positive literals and $n-y$ negative literals and then just feeding the whole thing into the Tseitin transform?

Asked By : Lembik

Answered By : D.W.

Many better techniques for enforcing cardinality constraints are described in this answer. For the special case $y=1$, see also Encoding 1-out-of-n constraint for SAT solvers. Read those links; they suggest more efficient conversions, though I'm not aware of any reason to expect that they are necessarily optimal, so they don't answer your question about the most efficient conversion.

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/14640

3.2K people like this

 Download Related Notes/Documents

0 comments:

Post a Comment

Let us know your responses and feedback