DeepAI AI Chat
Log In Sign Up

Nearly all k-SAT functions are unate

by   József Balogh, et al.
Iowa State University of Science and Technology
University of Illinois at Urbana-Champaign
Harvard University

We prove that 1-o(1) fraction of all k-SAT functions on n Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer k and as n →∞. This resolves a conjecture by Bollobás, Brightwell, and Leader from 2003. This paper is the second half of a two-part work solving the problem. The first part, by Dong, Mani, and Zhao, reduces the conjecture to a Turán problem on partially directed hypergraphs. In this paper we solve this Turán problem.


page 1

page 2

page 3

page 4


Solving the Satisfiability Problem Through Boolean Networks

In this paper we present a new approach to solve the satisfiability prob...

A note on the properties of associated Boolean functions of quadratic APN functions

Let F be a quadratic APN function of n variables. The associated Boolean...

Nearly Optimal Separation Between Partially And Fully Retroactive Data Structures

Since the introduction of retroactive data structures at SODA 2004, a ma...

On SAT representations of XOR constraints

We study the representation of systems S of linear equations over the tw...

A Kernel Method for Positive 1-in-3-SAT

This paper illustrates the power of Gaussian Elimination by adapting it ...

Min (A)cyclic Feedback Vertex Sets and Min Ones Monotone 3-SAT

In directed graphs, we investigate the problems of finding: 1) a minimum...

Partially APN Boolean functions and classes of functions that are not APN infinitely often

In this paper we define a notion of partial APNness and find various cha...