Sharp thresholds of graph properties, and the $k$-sat problem

Sharp Thresholds of Graph properties and the k sat Problem

Given a monotone graph property P consider p P the proba bility that a random graph with edge probability p will have P The function d p P dp is the key to understanding the threshold behavior of the property P We show that if d p P dp is small corresponding to a non sharp threshold then there is a list of graphs of bounded size such that P can be approximated by the property of having one of t...

Thresholds in Random Graphs and k-sat

In their seminal work [6],[7], Erdos and Renyi invented the notion of random graphs and made the fundamental observation that when the parameter controlling the edge probability varies, the random system undergoes a dramatic and swift qualitative change. “Much like water that freezes abruptly as its temperature drops below zero the structure of the random graph quickly changes from a primordial...

Thresholds for Random Geometric k-SAT

We study two geometric models of random k-satisfiability which combine random k-SAT with the Random Geometric Graph: boolean literals are placed uniformly at random or according to a Poisson process in a cube, and for each set of k literals contained in a ball of a given radius, a clause is formed. For k = 2 we find the exact location of the satisfiability threshold (as either the radius or int...

On Sharp Thresholds of Monotone Properties

the problem of divine hiddenness

این رساله به مساله احتجاب الهی و مشکلات برهان مبتنی بر این مساله میپردازد. مساله احتجاب الهی مساله ای به قدمت ادیان است که به طور خاصی در مورد ادیان ابراهیمی اهمیت پیدا میکند. در ادیان ابراهیمی با توجه به تعالی خداوند و در عین حال خالقیت و حضور او و سخن گفتن و ارتباط شهودی او با بعضی از انسانهای ساکن زمین مساله ای پدید میاید با پرسشهایی از قبیل اینکه چرا ارتباط مستقیم ویا حداقل ارتباط وافی به ب...