Probablistic methods as a proof technique
نویسندگان
چکیده
The probabilistic method is a nonconstructive method, primarily used in combinatorics, was pioneered by Paul Erdös, for proving the existence of a prescribed kinds of mathematical objects. Suppose we want to show that an object of a specific class with a certain property exists. Often it might be difficult to show the existence by explicitly constructing such an object. In the light of this difficulty, the main idea of probabilistic method is that if one randomly chooses objects from a specified class, such that the probability of the result having the said property is more than zero, then an object with the said property exists! Note that although the proof uses probability, the final conclusion is determined for certain. In this article, we demonstrate the use of probabilistic methods using two problems as described in sections 2 and 3.
منابع مشابه
Programming Research Group Proof Rules for Probablistic Loops
Probabilistic predicate transformers provide a semantics for imperative programs containing both demonic and probabilistic nondeterminism. Like the (standard) predicate transformers popularised by Dijkstra, they model programs as functions from nal results to the initial conditions su cient to achieve them. This paper presents practical proof rules, using the probabilistic transformers, for rea...
متن کاملA New Proof of FDR Control Based on Forward Filtration
For multiple testing problems, Benjamini and Hochberg (1995) proposed the false discovery rate (FDR) as an alternative to the family-wise error rate (FWER). Since then, researchers have provided many proofs to control the FDR under different assumptions. Storey et al. (2004) showed that the rejection threshold of a BH step-up procedure is a stopping time with respect to the reverse filtration g...
متن کاملProbablistic Control of Human Robot Interaction: Experiments with A Robotic Assistant for Nursing Homes
Probablistic Control of Human Robot Interaction: Experiments with A Robotic Assistant for Nursing Homes Joelle Pineau1, Michael Montemerlo1, Martha Pollack2, Nicholas Roy1 and Sebastian Thrun1 1Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 15232, USA 2Dept. of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, 48019, USA http://www.cs.cmu.edu/ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012