Notes on Probabilistic Method

Remarks on Testing Probabilistic Processes

We develop a general testing scenario for probabilistic processes, giving rise to two theories: probabilistic may testing and probabilistic must testing. These are applied to a simple probabilistic version of the process calculus CSP. We examine the algebraic theory of probabilistic testing, and show that many of the axioms of standard testing are no longer valid in our probabilistic setting; e...

Random Graphs and the Probabilistic Method

These notes accompany a lecture given in the summer of 2006 at the Center for Combinatorics at Nankai University. They are provided as a reference (and especially bibliography) for students new to the probabilistic method. The goal in these notes is twofold. First we wish to demonstrate the basics of the probabilistic method, covering both the expectation and second moment applications. Second,...

The Probabilistic Method

In this lecture, we will study some basic principles of the probabilistic method, a combinatorial tool with many applications in computer science. This method is a powerful tool for demonstrating the existence of combinatorial objects. We introduce the basic idea through several examples drawn from early lecture notes, and follow that by a detailed study of the maximum satisfiability (MAX-SAT) ...

Notes on the Probabilistic Method

Preface This manuscript contains my personal and informal notes on the probabilistic method as it is applied in graph theory. It hasn't been properly proofread , and it is by no means intended for wider distribution. For an introduction to the probabilistic method, I refer the reader to the textbooks mentioned in the bibliography. I'm very grateful for the assistance and advice I have received ...

Improvements to exact Boltzmann sampling using probabilistic divide-and-conquer and the recursive method