In computational complexity theory, the complexity class FP is the set of function problems that can be solved by a deterministic Turing machine in polynomial time. It is the function problem version of the decision problem class P. Roughly speaking, it is the class of functions that can be efficiently computed on classical computers without randomization. The difference between FP and P is that problems in P have one-bit, yes/no answers, while problems in FP can have any output that can be computed in polynomial time. For example, adding two numbers is an FP problem, while determining if their sum is odd is in P. Polynomial-time function problems are fundamental in defining polynomial-time reductions, which are used in turn to define the class of NP-complete problems. (Wikipedia).
Shmuel Onn: Sparse integer programming is FPT
We show that sparse integer programming, in variable dimension, with linear or separable convex objective, is fixed-parameter tractable. This is a culmination of a long line of research with many colleagues. We also discuss some of the many consequences of this result, which provides a new
From playlist Workshop: Tropical geometry and the geometry of linear programming
Depth complexity and communication games - Or Meir
Or Meir Institute for Advanced Study; Member, School of Mathematics September 30, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Algorithms Explained: Computational Complexity
An overview of computational complexity including the basics of big O notation and common time complexities with examples of each. Understanding computational complexity is vital to understanding algorithms and why certain constructions or implementations are better than others. Even if y
From playlist Algorithms Explained
Theory of Computation. 4. Minimizing FSMs
From playlist Theory of Computation - aduni
The Essence of Functional Programming
This talk dives into the origins of functional programming, going all the way back to where the term was first introduced, to see how it evolved over time into our modern understanding of what FP essentially involves. PUBLICATION PERMISSIONS: Original video was published with the Creative
From playlist Functional Programming
Range of Multivariable Function f(x, y) = x^2 + y^2
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Range of Multivariable Function f(x, y) = x^2 + y^2
From playlist Calculus
Big O Notation: A Few Examples
This video is about Big O Notation: A Few Examples Time complexity is commonly estimated by counting the number of elementary operations (elementary operation = an operation that takes a fixed amount of time to preform) performed in the algorithm. Time complexity is classified by the nat
From playlist Computer Science and Software Engineering Theory with Briana
Determine Time Complexity Function and Time Complexity Using Big-O Notation: f(n)=(cn(n-1))/2
This video explains how to determine the time complexity of given code. http://mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
Optional: Complexity - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Lecture 15: TC of F_p (corrected)
In this video, we compute TC of the field F_p with p-elements. As an application of this computation we deduce that THH of F_p-algebras is in a highly compatible fashion an Module over HZ. This relates to fundamental work of Kaledin and has some subtle aspects to it, which we carefully dis
From playlist Topological Cyclic Homology
Akhil Mathew - Some recent advances in syntomic cohomology (3/3)
Bhatt-Morrow-Scholze have defined integral refinements $Z_p(i)$ of the syntomic cohomology of Fontaine-Messing and Kato. These objects arise as filtered Frobenius eigenspaces of absolute prismatic cohomology and should yield a theory of "p-adic étale motivic cohomology" -- for example, the
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Lecture 4: The Connes operator on HH
Correction: The formula we give for the Connes operator B is slightly wrong, there needs to be a '+' instead of a '-' in between the two summands. In this video, we discuss the Connes operator on Hochschild homology. Feel free to post comments and questions at our public forum at https:
From playlist Topological Cyclic Homology
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 2
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
Lecture 3: Classical Hochschild Homology
In this video, we introduce classical Hochschild homology and discuss the HKR theorem. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-muenster.de/IVV5WS/Web
From playlist Topological Cyclic Homology
Many of us in the functional programming community believe that FP is a significant improvement over object oriented programming, arguably the dominant programming paradigm today. That of course begs the question: how did an inferior paradigm grab so much mindshare and market share and ris
From playlist Functional Programming
Testing Correlations and Inverse Theorems - Hamed Hatami
Hamed Hatami Institute for Advanced Study/Princeton University February 23, 2010 The uniformity norms are defined in different contexts in order to distinguish the ``typical'' random functions, from the functions that contain certain structures. A typical random function has small uniform
From playlist Mathematics
Čech cohomology part II, Čech-to-derived spectral sequence, Mayer-Vietoris, étale cohomology of quasi-coherent sheaves, the Artin-Schreier exact sequence and the étale cohomology of F_p in characteristic p.
From playlist Étale cohomology and the Weil conjectures
In this video, we prove certain formal properties of THH, for example that it has a universal property in the setting of commutative rings. We also show base-change properties and use these to compute THH of perfect rings. Feel free to post comments and questions at our public forum at h
From playlist Topological Cyclic Homology
Digression: The cotangent complex and obstruction theory
We study the cotangent complex more in depth and explain its relation to obstruction theory. As an example we construct the Witt vectors of a perfect ring. This video is a slight digression from the rest of the lecture course and could be skipped. Feel free to post comments and questions
From playlist Topological Cyclic Homology
The chaotic complexity of natural numbers | Data structures in Mathematics Math Foundations 175
This is a sobering and perhaps disorienting introduction to the fact that arithmetic with bigger numbers starts to look quite different from the familiar arithmetic that we do with the small numbers we are used to. The notion of complexity is key in our treatment of this. We talk about bot
From playlist Math Foundations