Geometric properties of satisfying assignments of random $ε$-1-in-k SAT

Details Geometric properties of satisfying assignments of random $ε$-1-in-k SAT Geometric properties of satisfying assignments of random $ε$-1-in-k SAT

2008-11-19

arxiv.org/abs/0811.3116v1

International Journal of Computer Mathematics, 86(12), pp. 2029-2039, 2009

Computer Science

Computational Complexity

Scientific paper

We study the geometric structure of the set of solutions of random $\epsilon$-1-in-k SAT problem. For $l\geq 1$, two satisfying assignments $A$ and $B$ are $l$-connected if there exists a sequence of satisfying assignments connecting them by changing at most $l$ bits at a time. We first prove that w.h.p. two assignments of a random $\epsilon$-1-in-$k$ SAT instance are $O(\log n)$-connected, conditional on being satisfying assignments. Also, there exists $\epsilon_{0}\in (0,\frac{1}{k-2})$ such that w.h.p. no two satisfying assignments at distance at least $\epsilon_{0}\cdot n$ form a "hole" in the set of assignments. We believe that this is true for all $\epsilon >0$, and thus satisfying assignments of a random 1-in-$k$ SAT instance form a single cluster.

Affiliated with

Also associated with

No associations

Rating

Geometric properties of satisfying assignments of random $ε$-1-in-k SAT does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric properties of satisfying assignments of random $ε$-1-in-k SAT, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric properties of satisfying assignments of random $ε$-1-in-k SAT will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-429247