In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into the input, along with a logarithmic number of fixed-size integers. It is possible that such a machine may not have space to write down its own output, so the only requirement is that any given bit of the output be computable in log-space. Formally, this reduction is executed via a log-space transducer. Such a machine has polynomially-many configurations, so log-space reductions are also polynomial-time reductions. However, log-space reductions are probably weaker than polynomial-time reductions; while any non-empty, non-full language in P is polynomial-time reducible to any other non-empty, non-full language in P, a log-space reduction from an NL-complete language to a language in L, both of which would be languages in P, would imply the unlikely L = NL. It is an open question if the NP-complete problems are different with respect to log-space and polynomial-time reductions. Log-space reductions are normally used on languages in P, in which case it usually does not matter whether many-one reductions or Turing reductions are used, since it has been verified that L, SL, NL, and P are all closed under Turing reductions, meaning that Turing reductions can be used to show a problem is in any of these classes. However, other subclasses of P such as NC may not be closed under Turing reductions, and so many-one reductions must be used. Just as polynomial-time reductions are useless within P and its subclasses, log-space reductions are useless to distinguish problems in L and its subclasses; in particular, every non-empty, non-full problem in L is trivially L-complete under log-space reductions. While even weaker reductions exist, they are not often used in practice, because complexity classes smaller than L (that is, strictly contained or thought to be strictly contained in L) receive relatively little attention. The tools available to designers of log-space reductions have been greatly expanded by the result that L = SL; see SL for a list of some SL-complete problems that can now be used as subroutines in log-space reductions. (Wikipedia).
Solving a logarithmic equation in two different ways
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Learn the basics of solving a logarithmic equation
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Solving an logarithmic equation
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Math tutorial for solving a multi step logarithmic equation
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Solving a natural logarithmic equation
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Math tutorial for solving logarithmic equation using inverse operations
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Reviewed log space: NL is a subset of SPACE(log^2n) and NL is a subse
From playlist MIT 18.404J Theory of Computation, Fall 2020
Assaf Naor: Coarse dimension reduction
Recording during the thematic meeting "Non Linear Functional Analysis" the March 7, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Ma
From playlist Analysis and its Applications
Complexity Theory, Quantified Boolean Formula
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From playlist [Shai Simonson]Theory of Computation
Fabrizio Andreatta - A p-adic criterion for good reduction of curves
Séminaire Paris Pékin Tokyo / Mardi 14 octobre 2014 abstract : Given a curve over a dvr of mixed characteristic 0-p with smooth generic fiber and with semistable reduction, I will present a criterion for good reduction in terms of the (unipotent) p-adic étale fundamental group of its gene
From playlist Conférences Paris Pékin Tokyo
Solving a logarithim, log81 (x) = 3/4
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
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Metric dimension reduction: A snapshot of the Ribe program – Assaf Naor – ICM2018
Plenary Lecture 16 Metric dimension reduction: A snapshot of the Ribe program Assaf Naor Abstract: The purpose of this article is to survey some of the context, achievements, challenges and mysteries of the field of ‘metric dimension reduction’, including new perspectives on major older
From playlist Plenary Lectures
Learn how to solve a natural logarithmic equation by using inverse operations
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Dimensionality Reduction | Stanford CS224U Natural Language Understanding | Spring 2021
For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai To learn more about this course visit: https://online.stanford.edu/courses/cs224u-natural-language-understanding To follow along with the course schedule and sy
From playlist Stanford CS224U: Natural Language Understanding | Spring 2021
Resolution of singularities of complex algebraic varieties – D. Abramovich – ICM2018
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From playlist Algebraic & Complex Geometry
Most odd degree hyperelliptic curves have only one rational point - Bjorn Poonen
Bjorn Poonen Massachusetts Institute of Technology March 26, 2015 We prove that the probability that a curve of the form y2=f(x)y2=f(x) over ℚQ with degf=2g+1degf=2g+1 has no rational point other than the point at infinity tends to 1 as gg tends to infinity. This is joint work with Micha
From playlist Mathematics
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations