Notes on the 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 We examine the algebraic theory of probabilistic testing, and show that many of the axioms of standard testing are no longer valid in our probabilistic setting; e...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 Probabilistic Method

Probabilistic analysis of stability of chain pillars in Tabas coal mine in Iran using Monte Carlo simulation

Performing a probabilistic study rather than a determinist one is a relatively easy way to quantify the uncertainty in an engineering design. Due to the complexity and poor accuracy of the statistical moment methods, the Monte Carlo simulation (MCS) method is wildly used in an engineering design. In this work, an MCS-based reliability analysis was carried out for the stability of the chain pill...