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Mansa Musa was the ruler of the Mali Empire in West Africa. Details recorded here should be sourced; unknown information is left blank.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In computational complexity theory, non-deterministic space or NSPACE is the computational resource describing the memory space for a non-deterministic Turing machine. It is the non-deterministic counterpart of DSPACE.
The measure NSPACE is used to define the complexity class whose solutions can be determined by a non-deterministic Turing machine. The complexity class NSPACE(f(n)) is the set of decision problems that can be solved by a non-deterministic Turing machine, M, using space O(f(n)), where n is the length of the input.[1]
Several important complexity classes can be defined in terms of NSPACE. These include:
The Immerman–Szelepcsényi theorem states that NSPACE(s(n)) is closed under complement for every function s(n) ≥ log n.
A further generalization is ASPACE, defined with alternating Turing machines.
NSPACE is the non-deterministic counterpart of DSPACE, the class of memory space on a deterministic Turing machine. First by definition, then by Savitch's theorem, we have that:
NSPACE can also be used to bound the deterministic time complexity of a problem, by the following theorem:
If a language L is decided in space S(n) (where S(n) ≥ log n) by a non-deterministic Turing machine, then there exists a constant C such that L is decided in time O(CS(n)) by a deterministic one.[2]
The measure of space complexity in terms of DSPACE is useful because it represents the total amount of memory that an actual computer would need to solve a given computational problem with a given algorithm. The reason is that DSPACE describes the space complexity used by deterministic Turing machines, which can represent actual computers. On the other hand, NSPACE describes the space complexity of non-deterministic Turing machines, which are not useful when trying to represent actual computers. For this reason, NSPACE is limited in its usefulness to real-world applications.
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In theoretical computer science, a probabilistic Turing machine is a non-deterministic Turing machine that chooses between the available transitions at each point according to some probability distribution. As a consequence, a probabilistic Turing machine can (unlike a deterministic Turing machine) have stochastic results; that is, on a given input and instruction state machine, it may have different run times, or it may not halt at all; furthermore, it may accept an input in one execution and reject the same input in another execution. In the case of equal probabilities for the transitions, probabilistic Turing machines can be defined as deterministic Turing machines having an additional "write" instruction where the value of the write is uniformly distributed in the Turing machine's alphabet (generally, an equal likelihood of writing a "1" or a "0" on to the tape). Another common reformulation is simply a deterministic Turing machine with an added tape full of random bits called the "random tape". A quantum computer (or quantum Turing machine) is another model of computation that is inherently probabilistic.
In computational complexity theory, an alternating Turing machine (ATM) is a non-deterministic Turing machine (NTM) with a rule for accepting computations that generalizes the rules used in the definition of the complexity classes NP and co-NP. The concept of an ATM was set forth by Chandra and Stockmeyer and independently by Kozen in 1976, with a joint journal publication in 1981.
Alan Turing (1912–1954), a pioneer computer scientist, mathematician, and philosopher, is the eponym of all of the things listed below. Alan Turing Building, Manchester, England The Turing School, Eastbourne, England Alan Turing Centenary Conference, Manchester, England Alan Turing Institute, London, England Alan Turing law Alan Turing Memorial, Manchester, England Alan Turing sculpture, Eugene, Oregon, United States Statue of Alan Turing, Bletchley Park, England Alan Turing: The Enigma Alan Turing Year The Annotated Turing Church–Turing thesis Church–Turing–Deutsch principle Good–Turing frequency estimation Object-Oriented Turing (programming language) Super-Turing computation Turing-acceptable language Turing Award Turing (cipher) Turing College, Kent, England Turing completeness Turing computability Turing degree Turing Foundation, Amsterdam, Netherlands Turing Gateway to Mathematics, Cambridge, England The Turing Guide Turing House School Turing Institute, Glasgow, Scotland Turing jump Turing Lecture Turing machine Alternating Turing machine Multi-track Turing machine Multitape Turing machine Neural Turing machine Non-deterministic Turing machine Post–Turing machine Probabilistic Turing machine Quantum Turing machine Read-only right moving Turing machines Read-only Turing machine Symmetric Turing machine Unambiguous Turing machine Universal Turing machine Wolfram's 2-state 3-symbol Turing machine Turing Machine (band) Turing (microarchitecture) Turing OS Turing pattern Turing Pharmaceuticals Turing (programming language) Turing reduction Turing Robot, China Turing scheme Turing table Turing tarpit Turing test CAPTCHA (Completely Automated Public Turing test to tell Computers and Humans Apart) Computer game bot Turing Test Graphics Turing Test Reverse Turing test Subject matter expert Turing test The Turing Test (novel) The Turing Test (video game) Visual Turing Test The Turing Trust Turing Tumble Turing's method Turing's proof Turing's Wager Turing+ (programming language) Turing.jl (probabilistic programming) Turingery Turingismus Turmite Turochamp Other items Alan Turing (MI) Building, University of Wolverhampton, England Turing Street, East London, England Turing Gate, Bletchley Turing Close, Leeds NE Turing Street, near Microsoft headquarters in Redmond, Washington
In computational complexity theory, non-deterministic space or NSPACE is the computational resource describing the memory space for a non-deterministic Turing machine. It is the non-deterministic counterpart of DSPACE.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Shirley Chisholm, elected in 1968.
![{\displaystyle {\mathsf {DSPACE}}[s(n)]\subseteq {\mathsf {NSPACE}}[s(n)]\subseteq {\mathsf {DSPACE}}[(s(n))^{2}].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ecd4ae2f63770c1eb464eab1a65c457990883b00)