Theoretical computer science | Computational problems

Computational problem

In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring "Given a positive integer n, find a nontrivial prime factor of n." is a computational problem. A computational problem can be viewed as a set of instances or cases together with a, possibly empty, set of solutions for every instance/case. For example, in the factoring problem, the instances are the integers n, and solutions are prime numbers p that are the nontrivial prime factors of n. Computational problems are one of the main objects of study in theoretical computer science. The field of computational complexity theory attempts to determine the amount of resources (computational complexity) solving a given problem will require and explain why some problems are intractable or undecidable. Computational problems belong to complexity classes that define broadly the resources (e.g. time, space/memory, energy, circuit depth) it takes to compute (solve) them with various abstract machines. For example, the complexity class P for classical machines, and BQP for quantum machines. It is typical of many problems to represent both instances and solutions by binary strings, namely elements of {0, 1}*. For example, numbers can be represented as binary strings using binary encoding. (Wikipedia).

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This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

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From playlist Algorithms Explained

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Calculus: Optimization Problems

In this video, I discuss optimization problems. I give an outline for how to approach these kinds of problems and worth through a couple of examples.

From playlist Calculus

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From playlist Solve a System Algebraically | Algebra 2

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The problem with `functions' | Arithmetic and Geometry Math Foundations 42a

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From playlist Math Foundations

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Turing Machines and The Halting Problem (Part 2)

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From playlist Math

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How to use a system of equations to solve a word problem

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From playlist Solve a System Algebraically | Algebra 2

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From playlist Solve a System Algebraically | Algebra 2

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The Diffie-Hellman Problem and Security of ElGamal Systems

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From playlist Computer - Cryptography and Network Security

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From playlist Computing/Tech/Engineering

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The P versus NP problem - Efficient computation and the limits of human knowledge - AVI Wigderson

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From playlist Public Lectures

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The Map of Quantum Computing | Quantum Computers Explained

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From playlist Quantum Physics Videos - Domain of Science

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Anders Hansen: What is the Solvability Complexity Index SCI....

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From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"

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Vivien Kendon: How to compute using quantum walks

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From playlist Numerical Analysis and Scientific Computing

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From playlist Map Videos - Domain of Science

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HEDS | Using quantum computers to simulate a toy problem of laser-plasma interaction

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From playlist High Energy Density Science Seminar Series

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Krysta Svore - One Entangled Evening

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From playlist One Entangled Evening - 1/26/2016

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From playlist Solve a System Algebraically | Algebra 2

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Combinatorial optimization | Promise problem | Counting problem (complexity) | String (computer science) | Property testing | Undecidable problem | Travelling salesman problem | Theoretical computer science | Decision problem | Hardness of approximation | Computational complexity | Function problem | Model of computation | Relation (mathematics) | Operations research | Regular expression | Transcomputational problem | Set (mathematics) | Independent set (graph theory) | Interactive proof system | BQP | Search problem | Abstract machine | Computational complexity theory | P (complexity) | Optimization problem | Algorithm | Analysis of algorithms | Complexity class