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Hypothetical computing devices
A Turing machine is a hypothetical computing device, first conceived by Alan Turing in 1936. Turing machines manipulate symbols on a potentially infinite
Turing_machine_equivalents
Computation model defining an abstract machine
Church's work intertwined with Turing's to form the basis for the Church–Turing thesis. This thesis states that Turing machines, lambda calculus, and other
Turing_machine
Type of Turing machine
science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, as described by Alan Turing in his seminal paper
Universal_Turing_machine
Model of quantum computation
particular quantum Turing machine. However, the computationally equivalent quantum circuit is a more common model. Quantum Turing machines can be related
Quantum_Turing_machine
Theoretical model of computation
computation with a deterministic computer. Alan Turing first developed the concept of Turing machine in 1936, imagining it as a simple computer that reads
Nondeterministic Turing machine
Nondeterministic_Turing_machine
Mathematical model of computation
probabilities for the transitions, probabilistic Turing machines can be defined as deterministic Turing machines having an additional "write" instruction where
Probabilistic_Turing_machine
Abstract calculator
Post machine or Post–Turing machine is a "program formulation" of a type of Turing machine, comprising a variant of Emil Post's Turing-equivalent model
Post–Turing_machine
Hypothetical computing device
can be printed. Turing machine Universal Turing machine Alternating Turing machine Probabilistic Turing machine Turing machine equivalents Sipser, Michael
Multitape_Turing_machine
Type of recurrent neural network
A neural Turing machine (NTM) is a recurrent neural network model of a Turing machine. The approach was published by Alex Graves et al. in 2014. NTMs combine
Neural_Turing_machine
Ability of a computing system to simulate Turing machines
cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician
Turing_completeness
Turing machine that halts for any input
relationship between partial Turing machines and total Turing machines: Can every partial function computable by a partial Turing machine be extended (that is
Decider_(Turing_machine)
Turing machine or two-way deterministic finite-state automaton (2DFA) is class of models of computability that behave like a standard Turing machine and
Read-only_Turing_machine
prove that a two-track Turing machine is equivalent to a standard Turing machine. This can be generalized to a n-track Turing machine. Let L be a recursively
Multi-track_Turing_machine
Abstract computation model
Turing machine (or to be more precise, the definition of acceptance for such a machine) alternates between these modes. An alternating Turing machine
Alternating_Turing_machine
to supplement the article Turing machine. The following table is Turing's very first example (Turing 1937): "1. A machine can be constructed to compute
Turing_machine_examples
Test of a machine's ability to imitate human intelligence
The Turing test was designed by Alan Turing to assess a machine's ability to exhibit intelligent behaviour equivalent to that of a human by imitating
Turing_test
Topics referred to by the same term
A Turing machine is an abstract mathematical computational device named after Alan Turing; see the box for variants of this meaning. Turing machine may
Turing machine (disambiguation)
Turing_machine_(disambiguation)
Computation model, equivalent to Turing machines
queue machine is equivalent to a Turing machine by showing that a queue machine can simulate a Turing machine and vice versa. A Turing machine can be
Queue_automaton
Topics referred to by the same term
a universal Turing machine Turing degree equivalence (of sets), having the same level of unsolvability Turing machine equivalents Turing test (disambiguation)
Turing_equivalence
Hypothetical computational model
Zeno machines (abbreviated ZM, and also called accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that
Zeno_machine
Model of computation in computer science
machines and nondeterministic Turing machines. An unambiguous Turing machine is defined as a nondeterministic Turing machine with the property that for every
Unambiguous_Turing_machine
Type of formal grammar
(construction of an equivalent Turing machine from a given unrestricted grammar, p.221, cf. Section #Equivalence to Turing machines) tacitly requires finiteness
Unrestricted_grammar
Mathematical model of abstract computation
2-state 5-symbol Turing machine, and conjectured that a particular 2-state 3-symbol Turing machine (hereinafter (2,3) Turing machine) might be universal
Wolfram's 2-state 3-symbol Turing machine
Wolfram's_2-state_3-symbol_Turing_machine
A symmetric Turing machine is a Turing machine that has a configuration graph that is undirected (that is, configuration i yields configuration j if and
Symmetric_Turing_machine
Finite-state machine
Read-only right-moving Turing machines are a particular type of Turing machine that only moves right; these are almost exactly equivalent to DFAs. The definition
Deterministic finite automaton
Deterministic_finite_automaton
Problem in computer science
computer programs on a fixed Turing-complete model of computation. This model of computation includes all programs in Turing-equivalent programming languages
Halting_problem
Abstract model of computation
machine (the so-called Harvard architecture). The RA-machine's equivalent of the universal Turing machine – with its program in the registers as well as its
Random-access_machine
English computer scientist (1912–1954)
as a never-before-published memoir by Turing's older brother John F. Turing. Turing, Sara (2012). Alan M. Turing. Cambridge University Press. ISBN 978-1-107-02058-0
Alan_Turing
Thesis on the nature of computability
numbers is called Turing computable if some Turing machine computes the corresponding function on encoded natural numbers. Turing proposed that effectively
Church–Turing_thesis
Concept in computability theory
{\displaystyle B\leq _{T}A.} The equivalence classes of Turing equivalent sets are called Turing degrees. The Turing degree of a set X {\displaystyle X} is written
Turing_reduction
Mathematical model of computation
order. The finite-state machine has less computational power than some other models of computation such as the Turing machine. The computational power
Finite-state_machine
basic machine B is an extremely simple computational model equivalent to the Turing machine. It is "the first formulation of a Turing-machine theory
Wang_B-machine
Thought experiment on artificial intelligence
understanding the argument, including symbol processing, Turing machines, Turing completeness, and the Turing test. Searle's arguments are not usually considered
Chinese_room
Type of abstract computing machine
a register machine is a generic class of abstract machines, analogous to a Turing machine and thus Turing complete. Unlike a Turing machine that uses a
Register_machine
Complexity class used to classify decision problems
nondeterministic Turing machine in O ( n k ) {\displaystyle O(n^{k})} time. Equivalently, NP can be defined using deterministic Turing machines as verifiers
NP_(complexity)
1950 scientific paper by Alan Turing
Turing test to the general public. Turing's paper considers the question "Can machines think?" Turing says that since the words "think" and "machine"
Computing Machinery and Intelligence
Computing_Machinery_and_Intelligence
Models of computation
super-Turing computation is a set of hypothetical models of computation that can provide outputs that are not Turing-computable. For example, a machine that
Hypercomputation
Intentionally obscure programming language
A Turing tarpit (or Turing tar-pit) is any programming language or computer interface that allows for flexibility in function but is difficult to learn
Turing_tarpit
Automata that lists elements of some given set
type of Turing machine variant and is equivalent with Turing machine. An enumerator E {\displaystyle E} can be defined as a 2-tape Turing machine (Multitape
Enumerator_(computer_science)
Proof by Alan Turing
Turing's proof is a proof by Alan Turing submitted on 12 November 1936 and first published in 1937 with the title "On Computable Numbers, with an Application
Turing's_proof
Codebreaking device created at Bletchley Park (United Kingdom)
Machine Laboratory. A simulator for both Turing and US Navy Bombes Breaking German Navy Ciphers - The U534 Enigma M4 messages: Cracked with a Turing Bombe
Bombe
Programmable machine that processes data
by Alan Turing in his seminal 1936 paper, On Computable Numbers. Turing proposed a simple device that he called "Universal Computing machine" and that
Computer
Measure of unsolvability
In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures
Turing_degree
Operation in computability theory
In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem X a successively
Turing_jump
2014 film by Morten Tyldum
the 1983 biography Alan Turing: The Enigma by Andrew Hodges. The film's title quotes the name of the game cryptanalyst Alan Turing proposed for answering
The_Imitation_Game
Abstract machine used to study decision problems
{\mathsf {NP}}^{R}} can be defined analogously. An oracle machine can be conceived as a Turing machine connected to an oracle. The oracle, in this context,
Oracle_machine
Study of computable functions and Turing degrees
(Turing) computable, or recursive function if there is a Turing machine that, on input n, halts and returns output f(n). The use of Turing machines here
Computability_theory
Concept in theoretical computer science
programs used in the game are n-state Turing machines, one of the first mathematical models of computation. Turing machines consist of an infinite tape, and
Busy_beaver
Type of computer
machines extend push-down automata with additional load/store operations or multiple stacks and hence are Turing-complete. Most or all stack machine instructions
Stack_machine
Mathematical function that can be computed by a program
many equivalent models of computation, including Turing machines General recursive functions Lambda calculus Post machines (Post–Turing machines and tag
Computable_function
Book by Stephen Wolfram
technical result in describing the Turing completeness of the Rule 110 cellular automaton. Very small Turing machines can simulate Rule 110, which Wolfram
A_New_Kind_of_Science
Abstract machine used in a formal logic and theoretical computer science
universality is proved only by simulation (e.g., many Turing tarpits, the smallest-known universal Turing machines, etc.). The proof is preceded by some interesting
Counter_machine
Academic subfield of computer science
Description was given by Turing Award winner Stephen Cook. Aside from a Turing machine, other equivalent (see Church–Turing thesis) models of computation
Theory_of_computation
Method of comparing problems by transforming one into another in computability theory
{\displaystyle B} if A {\displaystyle A} is Turing reducible to B {\displaystyle B} via a single (oracle) Turing machine that produces a total function relative
Reduction (computability theory)
Reduction_(computability_theory)
Formal language in mathematics and computer science
the Kleene closure of an alphabet. Equivalently, a formal language is recursive if there exists a Turing machine that decides the formal language. In
Recursive_language
Ability to solve a problem by an effective procedure
techniques. Turing machine Also similar to the finite state machine, except that the input is provided on an execution "tape", which the Turing machine can read
Computability
Turing machine on a two-dimensional grid
and declared "equivalent to Turing machines". Independently, in 1988, Allen H. Brady considered the idea of two-dimensional Turing machines with an orientation
Turmite
Type of AI with wide-ranging abilities
meant to confirm human-level AGI have been considered. The Turing test was proposed by Alan Turing in his 1950 paper "Computing Machinery and Intelligence"
Artificial general intelligence
Artificial_general_intelligence
Impact of English computer scientist
Institute Turing Lecture Turing machine Turing patterns Turing reduction Turing test Turing Award Various institutions have paid tribute to Turing by naming
Legacy_of_Alan_Turing
Attempts to formalize the concept of algorithms
and (2) the Turing machine or its Turing equivalents—the primitive register-machine or "counter-machine" model, the random-access machine model (RAM)
Algorithm_characterizations
Chatbot that arguably passed the Turing test
100th birthday of the test's author, Alan Turing, Goostman won a competition promoted as the largest-ever Turing test contest, in which it successfully convinced
Eugene_Goostman
Set of problems in computational complexity theory
Turing machine so that it is possible for the machine to store the entire input (it can be shown that in terms of computability the two-tape Turing machine
Complexity_class
Type of automaton
about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below). Deterministic
Pushdown_automaton
Concept in computer science
available. The reversible Turing machine (RTM) is a foundational model in reversible computing. An RTM is defined as a Turing machine whose transition function
Reversible_computing
and A. M. Turing ... . The first two definitions are proved equivalent in I. The third is proved equivalent to the first two by A. M. Turing, Computability
History of the Church–Turing thesis
History_of_the_Church–Turing_thesis
Any type of calculation
expressed in terms of the initialisation parameters of a Turing machine. Other (mathematically equivalent) definitions include Alonzo Church's lambda-definability
Computation
Theorem in computability theory
Given a set A {\displaystyle A} , the Turing jump A ′ {\displaystyle A'} is the set of indices of oracle Turing machines that halt on input 0 {\displaystyle
Post's_theorem
Class of problems in computer science
only deterministic Turing machines. A language L is in PP if and only if there exists a polynomial p and deterministic Turing machine M, such that M runs
PP_(complexity)
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
problem in NP can be reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem. The theorem is named after Stephen
Cook–Levin_theorem
Decryption of World War II cipher
keyboard, Alan Turing reviewed decrypted messages and determined that the word eins ("one") appeared in 90% of messages.[citation needed] Turing automated
Cryptanalysis_of_the_Enigma
First working programmable, fully automatic digital computer
branch instruction. Nevertheless, the Z3 was Turing-complete – how to implement a universal Turing machine on the Z3 was shown in 1998 by Raúl Rojas. He
Z3_(computer)
Mathematical logic concept
computable. According to the Church–Turing thesis, any effectively calculable function is calculable by a Turing machine, and thus a set S is computably enumerable
Computably_enumerable_set
Real number that can be computed within arbitrary precision
computability available at the time. Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal representation
Computable_number
Class of computational complexity
equivalent to P S P A C E {\displaystyle {\mathsf {PSPACE}}} , because a deterministic Turing machine can simulate a nondeterministic Turing machine while
PSPACE
Abstract machine that uses only one instruction
Arithmetic-based Turing-complete machines use an arithmetic operation and a conditional jump. Like the two previous universal computers, this class is also Turing-complete
One-instruction_set_computer
Complexity class consisting of all recursive languages
problems solvable by a Turing machine, which is the set of all recursive languages (also called decidable languages). R is equivalent to the set of all total
R_(complexity)
workshop, the first AI program, Logic Theorist, was presented by future Turing Awardee Allen Newell and future Nobel Laureate Herbert A. Simon, with help
History of artificial intelligence
History_of_artificial_intelligence
reducing the complexity of Turing computable tasks and are still restricted to tasks within the scope of Turing machines. [citation needed] [clarification
Philosophy of artificial intelligence
Philosophy_of_artificial_intelligence
Hierarchy of classes of formal grammars
or Turing-recognizable languages. Note that this is different from the recursive languages, which can be decided by an always-halting Turing machine. When
Chomsky_hierarchy
19th century proposed mechanical computer
and so the language as conceived would have been Turing-complete as later defined by Alan Turing. Three different types of punch cards were used: one
Analytical_engine
Impossible task in computing
λ-calculus, and by Alan Turing the next year with his concept of Turing machines. Turing immediately recognized that these are equivalent models of computation
Entscheidungsproblem
Esoteric, minimalist programming language
1964 to describe a family of Turing machines. Note: A Brainfuck variant with a finite tape and finite cell values is not Turing-complete. It has only finitely
Brainfuck
Simulators of quantum mechanical systems
Turing machines are useful for simulating quantum systems. This is known as quantum supremacy, the idea that there are problems only quantum Turing machines
Quantum_simulator
Measure of algorithmic complexity
encoding for Turing machines, where an encoding is a function which associates to each Turing Machine M a bitstring <M>. If M is a Turing Machine which, on
Kolmogorov_complexity
Sequence of operations for a task
size of inputs increase. Any algorithm can be computed by any Turing complete model. Turing completeness only requires four instruction types—conditional
Algorithm
Formal language
enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the
Recursively enumerable language
Recursively_enumerable_language
Computational complexity
nondeterministic Turing machine using a logarithmic amount of memory space. NL is a generalization of L, the class for logspace problems on a deterministic Turing machine
NL_(complexity)
Mathematical model of analog computers
deterministic variant of) the GPAC is equivalent, in computability terms, to Turing machines, thereby proving the physical Church–Turing thesis for the class of systems
General purpose analog computer
General_purpose_analog_computer
Given more time, a Turing machine can solve more problems
about time-bounded computation on Turing machines. Informally, these theorems say that given more time, a Turing machine can solve more problems. For example
Time_hierarchy_theorem
Two-dimensional cellular automaton
Conway. Theoretically, the Game of Life has the power of a universal Turing machine: anything that can be computed algorithmically can be computed within
Conway's_Game_of_Life
One of several equivalent definitions of a computable function
the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are
General_recursive_function
Hypothetical consciousness in artificial systems
for testing machine intelligence is the Turing test, which assesses the ability to have a human-like conversation. But passing the Turing test does not
Artificial_consciousness
available. In 1936, Alan Turing also published his seminal work on the Turing machines, an abstract digital computing machine which is now simply referred
History_of_computer_science
Unsolved problem in computer science
deterministic polynomial-time Turing machine. Meaning, P = { L : L = L ( M ) for some deterministic polynomial-time Turing machine M } {\displaystyle {\mathsf
P_versus_NP_problem
Halting probability of a random computer program
there is a Turing machine that computes it, in the sense that for any finite binary strings x and y, F(x) = y if and only if the Turing machine halts with
Chaitin's_constant
String rewriting system
p. 149 Post, following Turing, technically makes use of the undecidability of the printing problem (whether a Turing machine ever prints a particular
Semi-Thue_system
Mathematical-logic system based on functions
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. Its namesake, the
Lambda_calculus
AI research laboratory
DeepMind introduced neural Turing machines (neural networks that can access external memory like a conventional Turing machine). The company has created
Google_DeepMind
Concept in computer science
time) is the complexity class of problems for which a probabilistic Turing machine exists with these properties: It always returns the correct YES or NO
ZPP_(complexity)
Concept in complexity theory
numbers with the property that f(n) can be constructed from n by a Turing machine in the time of order f(n). The purpose of such a definition is to exclude
Constructible_function
TURING MACHINE-EQUIVALENTS
TURING MACHINE-EQUIVALENTS
Male
Hebrew
Variant spelling of Hebrew Yakiyn, YACHIN means "he establishes" or "whom God strengthens."Â
Girl/Female
Bengali, Indian
Machine
Girl/Female
American, Australian, Bengali, British, Christian, English, Indian
Springtime; Spring Season; Rapid Movement
Female
German
German form of Scottish Malvina, MALWINE means "smooth-brow."
Female
French
French feminine form of Latin Martinus, MARTINE means "of/like Mars."Â
Male
English
Pet form of English Sacheverell, SACHIE means "roe-buck leap."
Female
English
Variant spelling of English Maureen, MAURINE means "obstinacy, rebelliousness" or "their rebellion."
Female
Scottish
Feminine form of Scottish Lachlan, LACHINA means "lake-land."
Girl/Female
Australian, Japanese
Child of Machi
Male
French
French form of Latin Macarius, MACAIRE means "blessed."
Female
Native American
Native American Hopi name KACHINA means "sacred dancer; spirit."
Male
Hindi/Indian
(सचिन) Hindi myth name borne by Indra, SACHIN means "pure."
Female
French
Feminine form of French Marin, MARINE means "of the sea."
Surname or Lastname
English
English : variant spelling of Machen.Spanish (MachÃn) : probably a nickname from machÃn ‘boor’, ‘lout’, often applied to a blacksmith’s apprentice.French : nickname from Old French machin ‘scheming’.
Male
Scottish
Pet form of Scottish Gaelic Lachlann, LACHIE means "lake-land."
Boy/Male
American, Australian
Weighing Machine
Female
Yiddish
(×™Ö·×—Ö°× Ö¶×¢) Yiddish form of Hebrew Yochana, YACHNE means "God is gracious."Â
Girl/Female
Indian
Lively, Entertainer, From a stream or a Spring, The Spring season, The Spring season
Female
English
Feminine form of English Max, MAXINE means either "the greatest rival" or "the stream of Mack."Â
Female
Hawaiian
Hawaiian name MAHINA means "moon; moonlight."
TURING MACHINE-EQUIVALENTS
TURING MACHINE-EQUIVALENTS
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from a place in Lancashire named Brindle, from Old English burna ‘stream’ + hyll ‘hill’.Altered spelling of South German Brindl, Bründl, a topographic name for someone who lived by a spring or stream, from a diminutive of Middle High German brun(ne) ‘spring’, ‘stream’, or of Brendle or Brendel.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Excellent; Talented; Expert; Skilled; Fulfilled; Extra Ordinary Person
Female
English
Variant spelling of Scottish unisex Ainsley, AINSLIE means "hermitage meadow."Â
Boy/Male
Tamil
Snehin | ஸà¯à®¨à¯‡à®¹à®¿à®‚Â
A friend
Boy/Male
Tamil
That which does not disappear
Surname or Lastname
English and Scottish
English and Scottish : metronymic from Lett.
Boy/Male
Hindu
Decorated, An object that gives light, And never stops doing so
Boy/Male
Hindu
Girl/Female
Arabic, Muslim
Beautiful
Girl/Female
British, Dutch, English, Hebrew
Variant of Maria; Bitterness
TURING MACHINE-EQUIVALENTS
TURING MACHINE-EQUIVALENTS
TURING MACHINE-EQUIVALENTS
TURING MACHINE-EQUIVALENTS
TURING MACHINE-EQUIVALENTS
n.
One who or operates a machine; a machinist.
n.
The pieces, or chips, detached in the process of turning from the material turned.
pl.
of Tachina
n.
A tiring-room.
n.
A series of tubes; tubes, collectively; a length or piece of a tube; material for tubes; as, leather tubing.
n.
The working parts of a machine, engine, or instrument; as, the machinery of a watch.
imp. & p. p.
of Machine
prep.
In the time of; as long as the action or existence of; as, during life; during the space of a year.
n.
Alt. of Goring cloth
a.
Of or pertaining to machines.
n.
The act or process of one who, or that which, bores; as, the boring of cannon; the boring of piles and ship timbers by certain marine mollusks.
n.
A combination of persons acting together for a common purpose, with the agencies which they use; as, the social machine.
v. t.
To subject to the action of machinery; to effect by aid of machinery; to print with a printing machine.
v. t.
To wind marline around; as, to marline a rope.
a.
Of or pertaining to cows; pertaining to, derived from, or caused by, vaccinia; as, vaccine virus; the vaccine disease.
n.
A machine for curing hay in rainy weather.
n.
A hole made by boring.
n.
Machines, in general, or collectively.