Theoretical computer science | Mathematical theorems

Full-employment theorem

In computer science and mathematics, a full employment theorem is a term used, often humorously, to refer to a theorem which states that no algorithm can optimally perform a particular task done by some class of professionals. The name arises because such a theorem ensures that there is endless scope to keep discovering new techniques to improve the way at least some specific task is done. For example, the full employment theorem for compiler writers states that there is no such thing as a provably perfect size-optimizing compiler, as such a proof for the compiler would have to detect non-terminating computations and reduce them to a one-instruction infinite loop. Thus, the existence of a provably perfect size-optimizing compiler would imply a solution to the halting problem, which cannot exist. This also implies that there may always be a better compiler since the proof that one has the best compiler cannot exist. Therefore, compiler writers will always be able to speculate that they have something to improve. A similar example in practical computer science is the idea of no free lunch in search and optimization, which states that no efficient general-purpose solver can exist, and hence there will always be some particular problem whose best known solution might be improved. Similarly, Gödel's incompleteness theorems have been called full employment theorems for mathematicians. Tasks such as virus writing and detection, and spam filtering and filter-breaking are also subject to Rice's theorem. (Wikipedia).

Video thumbnail

Convolution Theorem: Fourier Transforms

Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.

From playlist Partial differential equations

Video thumbnail

The Mean Value Theorem From Calculus Explanation and Example of Finding c

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Mean Value Theorem From Calculus Explanation and Example of Finding c

From playlist Calculus 1 Exam 2 Playlist

Video thumbnail

Harmonic functions: Mean value theorem

Free ebook https://bookboon.com/en/partial-differential-equations-ebook What is the mean value theorem for harmonic functions are how is it useful? This video discusses and proves the main result. The ideas important in the formulation of maximum principles for partial differential equat

From playlist Partial differential equations

Video thumbnail

Multivariable Calculus | Definition of partial derivatives.

We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

Video thumbnail

ETH Lecture 12. Nonlinear Dynamics of Economic Cycles II (08/12/2011)

Course: Systems Dynamics and Complexity (Fall 2011) from ETH Zurich. Source: http://www.video.ethz.ch/lectures/d-mtec/2011/autumn/351-0541-00L.html

From playlist ETH Zürich: Systems Dynamics and Complexity (Fall 2011) | CosmoLearning Mathematics

Video thumbnail

The Coase Theorem

Enjoying the lectures? Come join Prof. Ayres' on Coursera! Enrolling in his course will allow you to join in discussions with fellow learners, take assessments on the material, and earn a certificate! Link - https://www.coursera.org/learn/law-student Whether you are an advanced law studen

From playlist A Law Student's Toolkit

Video thumbnail

Calculus 5.3 The Fundamental Theorem of Calculus

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

Video thumbnail

(ML 19.2) Existence of Gaussian processes

Statement of the theorem on existence of Gaussian processes, and an explanation of what it is saying.

From playlist Machine Learning

Video thumbnail

R - Two-Way Between Subjects ANCOVA Example

Lecturer: Dr. Erin M. Buchanan Missouri State University Spring 2018 This video replaces a previous live in-class video. This video covers ANCOVA - especially focusing on doing correct post hoc tests using R. You will walk through data screening, post hoc tests, effect size, graphs, and

From playlist Learn and Use G*Power

Video thumbnail

A Completeness Theorem for Pseudo-Linear Functions with App... - Charanjit Jutla

Charanjit Jutla IBM T. J. Watson Research Center February 28, 2010 We prove completeness results for certain class of functions which have implications for automatic proving of universally-composable security theorems for ideal and real functionalities composed of if-then-else programs wi

From playlist Mathematics

Video thumbnail

You and AI - the future of work by Professor Joseph E Stiglitz

AI already supports many of the products and services we interact with on a daily basis, and technological advances are creating systems that can perform increasingly sophisticated tasks. Alongside these advances, come questions about the impact of AI on work and working life, and its impl

From playlist You and AI

Video thumbnail

Why We Should Invest In Rat Massage

Go to https://NordVPN.com/minuteearth to get 75% off a 3 year plan and use code MINUTEEARTH for an extra month for free. Protect yourself online today. Basic research can seem wasteful, but it's actually a great economic investment. Thanks also to our Patreon patrons https://www.patreon.co

From playlist Biology

Video thumbnail

Calculus - The Fundamental Theorem, Part 5

The Fundamental Theorem of Calculus. How an understanding of an incremental change in area helps lead to the fundamental theorem

From playlist Calculus - The Fundamental Theorem of Calculus

Video thumbnail

Understanding economic growth | AP Macroeconomics | Khan Academy

In this video, learn about the definition of economic growth and how growth occurs. AP(R) Macroeconomics on Khan Academy: Macroeconomics is all about how an entire nationÕs performance is determined and improved over time. Learn how factors like unemployment, inflation, interest rates, eco

From playlist Long-run consequences of stabilization policies | AP Macroeconomics | Khan Academy

Video thumbnail

Macroeconomics Graphs Review

Thank you for watching my econ videos. In an AP or introductory college macroeconomic course you must draw, shift, and explain different graphs, including: aggregate demand and supply, the money market, and foreign exchange. In this video I explain the key graphs you need and how they inte

From playlist Macro Unit 6: Open Economy- International Trade and Finance

Video thumbnail

Fourier transforms: Shifting theorem

Free ebook https://bookboon.com/en/partial-differential-equations-ebook First shifting theorem of Fourier transforms. The result is presented, proved and applied. Such ideas find important applications in solving partial differential equations.

From playlist Partial differential equations

Video thumbnail

Long run self adjustment | AP Macroeconomics | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/ap-macroeconomics/national-income-and-price-determinations/long-run-self-adjustment-ap/v/long-run-self-adjustment-ap-macroeconomics-khan-academy

From playlist AP Macroeconomics

Video thumbnail

Reconsidering `functions' in modern mathematics | Arithmetic and Geometry Math Foundations 43

The general notion of `function' does not work in mathematics, just as the general notions of `number' or `sequence' don't work. This video explains the distinction between `closed' and `open' systems, and suggests that mathematical definitions should respect the open aspect of mathemat

From playlist Math Foundations

Video thumbnail

Claire Voisin - Schiffer variations of hypersurfaces and the generic Torelli theorem - WAGON

The generic Torelli theorem for hypersurfaces of degree d and dimension n-1 was proved by Donagi in the 90's. It works under the assumption that d is at least 7 and d does not divide n+1, which in particular excludes the Calabi-Yau case in all dimensions. We prove that the generic Torelli

From playlist WAGON

Related pages

Rice's theorem | Mathematics | Infinite loop | Gödel's incompleteness theorems | Halting problem | No free lunch in search and optimization