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Turing machine that halts for any input
computability theory, a decider is a Turing machine that halts for every input. A decider is also called a total Turing machine as it represents a total
Decider_(Turing_machine)
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
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
Topics referred to by the same term
Maher: The Decider, a stand-up comedy special Decider (Turing machine), a Turing machine that eventually halts for every input "The Decider", a recurring
Decider
English computer scientist (1912–1954)
the halting problem for Turing machines is undecidable: it is not possible to decide algorithmically whether a Turing machine will ever halt. This paper
Alan_Turing
Finite-state machine
eliminating isomorphic automata. Read-only right-moving Turing machines are a particular type of Turing machine that only moves right; these are almost exactly
Deterministic finite automaton
Deterministic_finite_automaton
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
Formal language in mathematics and computer science
Turing machine that decides the formal language. In theoretical computer science, such always-halting Turing machines are called total Turing machines or
Recursive_language
Problem in computer science
Chapter 7 "Turing Machines." A book centered around the machine-interpretation of "languages", NP-Completeness, etc. Hodges, Andrew (1983). Alan Turing: the
Halting_problem
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
Concept in computability theory
theory, a Turing reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine that decides problem
Turing_reduction
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
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
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
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
Formal language
recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable
Recursively enumerable language
Recursively_enumerable_language
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
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
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
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
1965:291) Turing 1937 in (Davis 1967:118) Turing 1937 in (Davis 1967:116) Turing 1937 in (Davis 1967:117) Turing 1937 in (Davis 1967:138) Turing 1937 in
History of the Church–Turing thesis
History_of_the_Church–Turing_thesis
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
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
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
Impossible task in computing
calculability" based on his λ-calculus, and by Alan Turing the next year with his concept of Turing machines. Turing immediately recognized that these are equivalent
Entscheidungsproblem
Intelligence of machines
8–17), Moravec (1988, p. 3) Turing's original publication of the Turing test in "Computing machinery and intelligence": Turing (1950) Historical influence
Artificial_intelligence
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
Transformation of one computational problem to another
suppose R is a decider for E. We will use this to produce a decider S for H (which we know does not exist). Given input M and w (a Turing machine and some input
Reduction_(complexity)
Whether a decision problem has an effective method to derive the answer
decision problem is decidable if there exists an effective method for deriving the correct answer. Logical systems are decidable if membership in their
Decidability_(logic)
Mathematical function that can be computed by a program
including Turing machines General recursive functions Lambda calculus Post machines (Post–Turing machines and tag machines). Register machines Although
Computable_function
Inherent difficulty of computational problems
deterministic Turing machine, but many complexity classes are based on non-deterministic Turing machines, Boolean circuits, quantum Turing machines, monotone
Computational complexity theory
Computational_complexity_theory
Ability to solve a problem by an effective procedure
computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the field
Computability
Study of abstract machines and automata
different names by different research communities. The earlier concept of Turing machine was also included in the discipline along with new forms of infinite-state
Automata_theory
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
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
Subset of artificial intelligence
Annotation Game: On Turing (1950) on Computing, Machinery, and Intelligence", in Epstein, Robert; Peters, Grace (eds.), The Turing Test Sourcebook: Philosophical
Machine_learning
Complexity class used to classify decision problems
deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. NP is the
NP_(complexity)
Complexity class consisting of all recursive languages
of decision problems solvable by a Turing machine, which is the set of all recursive languages (also called decidable languages). R is equivalent to the
R_(complexity)
American computer scientist (born 1964)
the web. In 2005, he founded and became the director of the university's Turing Center. The center investigated problems in data mining, natural language
Oren_Etzioni
Attempts to formalize the concept of algorithms
and Turing [1936]. For example, according to Savage [1987], an algorithm is a computational process defined by a Turing machine. Church and Turing did
Algorithm_characterizations
Algorithmic complexity class
the set of all decision problems that are solvable by a deterministic Turing machine in exponential time, i.e., in O(2p(n)) time, where p(n) is a polynomial
EXPTIME
Yes-or-no question that cannot ever be solved by a computer
input, decide whether the program finishes running or will run forever. Alan Turing proved in 1936 that a general algorithm running on a Turing machine that
Undecidable_problem
Deterministic model of computation
1, the set of m-tag systems is Turing-complete; i.e., for each m > 1, it is the case that for any given Turing machine T, there is an m-tag system that
Tag_system
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)
Complexity class (logarithmic space)
tapes of a logspace Turing machine, the machine also takes a read-only one-way tape filled with random bits. The Turing machine has to halt for every
L_(complexity)
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
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
Unsolved problem in computer science
{\displaystyle \Sigma \cup \{\#\}} is decidable by a deterministic Turing machine in polynomial time. A Turing machine that decides LR is called a verifier for
P_versus_NP_problem
Real number that can be computed within arbitrary precision
between 0 and 1: A computable number [is] one for which there is a Turing machine which, given n on its initial tape, terminates with the nth digit of
Computable_number
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
Class of computational complexity
PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space. If we denote by S P A C E ( f (
PSPACE
Given more time, a Turing machine can solve more problems
the Turing machine M. Let m be the size of the tuple ([M], x). We know that we can decide membership of Hf by way of a deterministic Turing machine R,
Time_hierarchy_theorem
1952 puzzle video game
by Alan Turing starting in 1945. The project was delayed for many months, however, due to technical, political, and economic reasons, and Turing abandoned
Checkers_(video_game)
Sequence of characters, data type
characters in a word (8 for 8-bit ASCII on a 64-bit machine, 1 for 32-bit UTF-32/UCS-4 on a 32-bit machine, etc.). If the length is not bounded, encoding a
String_(computer_science)
Computational problems no algorithm can solve
configuration). Determining whether a Turing machine is a busy beaver champion (i.e., is the longest-running among halting Turing machines with the same number of states
List_of_undecidable_problems
Category of mathematical proof
doi:10.1112/plms/s2-43.6.544). This is the epochal paper where Turing defines Turing machines and shows that it (as well as the Entscheidungsproblem) is unsolvable
Proof_of_impossibility
Determination of whether a given program halts for each input
model of Turing machines as the model of programs implementing computable functions would have the goal of deciding whether a given Turing machine is a total
Termination_analysis
Relation between deterministic and nondeterministic space complexity
if a nondeterministic Turing machine can solve a problem using f ( n ) {\displaystyle f(n)} space, a deterministic Turing machine can solve the same problem
Savitch's_theorem
Class in computational complexity theory
Similarly, NC is equivalent to the problems solvable on an alternating Turing machine restricted to at most two options at each step with O(log n) space and
NC_(complexity)
Theorem in computability theory
theorem implies that in dynamically typed programming languages that are Turing-complete, it is impossible to verify the absence of type errors. On the
Rice's_theorem
Memory space for a deterministic Turing machine
resource describing the resource of memory space for a deterministic Turing machine. It represents the total amount of memory space that a "normal" physical
DSPACE
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
Hypothesis in computational complexity theory
machine must be sufficiently powerful to emulate the sequential machine in time polynomially related to the sequential space; compare Turing machine,
Parallel_computation_thesis
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
Hypothesized risk to human existence
August 2025. Turing, Alan (1951). Intelligent machinery, a heretical theory (Speech). Lecture given to '51 Society'. Manchester: The Turing Digital Archive
Existential risk from artificial intelligence
Existential_risk_from_artificial_intelligence
Study of mathematical analysis seen through computability theory
Turing machines. The tape configuration and interpretation of mathematical structures are described as follows. A Type 2 Turing machine is a Turing machine
Computable_analysis
Estimate of time taken for running an algorithm
deterministic Turing machine in polynomial time NP: The complexity class of decision problems that can be solved on a non-deterministic Turing machine in polynomial
Time_complexity
British engineer and robotics researcher
Reading, which also featured parallel-paired Turing tests. In 2012, he co-organised with Huma Shah a series of Turing tests held at Bletchley Park. According
Kevin_Warwick
Complexity class
solution in polynomial time by a deterministic Turing machine (or solvable by a non-deterministic Turing machine in polynomial time). NP-hard Class of problems
NP-hardness
Computer science concept
within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines. It is a resource-bounded counterpart to the arithmetical
Polynomial_hierarchy
1951 chess program
influenced by Alan Turing. Prinz then runs his chess program, which he has been developing since 1949, on the Mark I. Quickly, Turing and Prinz conclude
Chess_(Dietrich_Prinz)
Lemma that defines a property of regular languages
{\displaystyle q_{s}} for such a state. The transitions that take the machine from the first encounter of state q s {\displaystyle q_{s}} to the second
Pumping lemma for regular languages
Pumping_lemma_for_regular_languages
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
Computational input that relies on the length but not content of the input
computational complexity theory, an advice string is an extra input to a Turing machine that is allowed to depend on the length n of the input, but not on the
Advice_(complexity)
Computer science field
temporal logic specification was done by Amir Pnueli, who received the 1996 Turing award for "seminal work introducing temporal logic into computing science"
Model_checking
American cognitive scientist (1927–2016)
learning machine, SNARC.[citation needed] In 1962, he worked on small universal Turing machines and published his well-known 7-state, 4-symbol machine.[better source needed]
Marvin_Minsky
Type of pumping lemma
context-free Visibly pushdown Regular Star-free Finite Turing machine Decider Linear-bounded PTIME Turing Machine Nested stack Thread automaton restricted Tree
Pumping lemma for context-free languages
Pumping_lemma_for_context-free_languages
Randomized polynomial time class of computational complexity theory
the complexity class of decision problems for which a probabilistic Turing machine exists with these properties: It always runs in polynomial time in the
RP_(complexity)
List of concepts in artificial intelligence
1936 paper, A. M. Turing defined the class of abstract machines that now bear his name. A Turing machine is a finite-state machine associated with a special
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Type of a context-free grammar
It is decidable whether a given grammar G is LL(k), but it is not decidable whether an arbitrary grammar is LL(k) for some k. It is also decidable if a
LL_grammar
Formal grammar
∩ L2, L1 ∪ L2, and L1 \ L2 are also regular tree languages, and it is decidable whether L1 ⊆ L2, and whether L1 = L2. Regular tree grammars are a generalization
Regular_tree_grammar
Class of problems solvable in polynomial time
contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's
P_(complexity)
Complexity class
2EXPTIME) is the set of all decision problems solvable by a deterministic Turing machine in O(22p(n)) time, where p(n) is a polynomial function of n. In terms
2-EXPTIME
Model of computation
single circuit (in contrast to the Turing machine model, in which a language is fully described by a single Turing machine). A language is instead represented
Boolean_circuit
all input, is undecidable. Suppose we have a decider for it, D {\displaystyle D} . For any Turing machine M {\displaystyle M} and input w {\displaystyle
Computation_history
Israeli mathematician and computer scientist (1931–2026)
computer scientist who was co-recipient, with Dana Scott, of the 1976 ACM Turing Award for their work on computational complexity. Rabin was born in 1931
Michael_O._Rabin
Halting probability of a random computer program
number. It is Turing equivalent to the halting problem and thus at level Δ 0 2 of the arithmetical hierarchy. Not every set that is Turing equivalent to
Chaitin's_constant
Type of Turing reduction
enumerable sets that are neither decidable nor m-complete, and hence that there exist nonuniversal Turing machines whose individual halting problems
Many-one_reduction
Type of relativistic spacetime
certain non-Turing computable tasks (hypercomputation). The idea is for an observer at some event in p's past to set a computer (Turing machine) to work
Malament–Hogarth_spacetime
Generative AI chatbot by OpenAI
Nature article that "ChatGPT broke the Turing test". Stanford researchers reported that GPT-4 "passes a rigorous Turing test, diverging from average human
ChatGPT
Branch of computational complexity theory
nondeterministic Turing machine. The machine may be specified by one of any of the standard formulations. One usually considers the one-tape Turing machine, but the
Parameterized_complexity
Complexity class
polynomial p ( n ) {\displaystyle p(n)} and a polynomial-time bounded Turing machine M such that for every instance x, x is a no-instance if and only if:
Co-NP
Concept in computational complexity theory
set of decision problems that can be solved by a non-deterministic Turing machine using time 2 n O ( 1 ) {\displaystyle 2^{n^{O(1)}}} . In terms of NTIME
NEXPTIME
problem. For Turing machines, the halting problem can be stated as follows: Given a Turing machine, and an input, decide whether the machine halts when
Mortality (computability theory)
Mortality_(computability_theory)
Data structure representing a finite set of strings
DAFSA using an array of integers (Archived 22 July 2022 at the Wayback Machine) "Caroline Word Graph or CWG" – JohnPaul Adamovsky teaches how to construct
Deterministic acyclic finite state automaton
Deterministic_acyclic_finite_state_automaton
Binary sequence
random to any algorithm running on a (prefix-free or not) universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet
Algorithmically random sequence
Algorithmically_random_sequence
Sequence of rational numbers
(xm) can be given using an enumeration of Turing machines. Let {n}(n) denote the action of the n-th Turing machine on the number n. Then let the n-th decimal
Specker_sequence
context-free Visibly pushdown Regular Star-free Finite Turing machine Decider Linear-bounded PTIME Turing Machine Nested stack Thread automaton restricted Tree
Local language (formal language)
Local_language_(formal_language)
Methods in artificial intelligence research
unclear terminology: Turing award winner Judea Pearl offers a critique of machine learning which, unfortunately, conflates the terms machine learning and deep
Symbolic artificial intelligence
Symbolic_artificial_intelligence
DECIDER TURING-MACHINE
DECIDER TURING-MACHINE
Male
Welsh
Welsh name derived from the element aur, EURIG means "gold."
Female
English
English name derived from the season name, "spring," (Mar. 21 thru Jun. 21), derived from the verb spring, "to burst forth," from Proto-Indo-European *sprengh-, SPRING means "rapid movement."Â
Boy/Male
Muslim
Judge, Justice, Decider
Boy/Male
Indian
Loving, Caring, Daring
Boy/Male
Hindu, Indian
To Decide
Boy/Male
Muslim
Loving, Caring, Daring
Boy/Male
Hindu
Fostered by God
Female
English
Elaborated form of English Tara, TARINA means "hill."
Boy/Male
Indian
Judge, Justice, Decider
Girl/Female
Indian
Lively, Entertainer, From a stream or a Spring, The Spring season, The Spring season
Boy/Male
Arabic, Australian, German, Muslim
Judge; Decider; Justice
Boy/Male
Hindu, Indian
A Thought
Girl/Female
American, Australian, Bengali, British, Christian, English, Indian
Springtime; Spring Season; Rapid Movement
Surname or Lastname
French
French : from Old French denier, originally the name of a copper coin, later a term for money in general, hence probably a metonymic occupational name for a moneyer or minter.English : variant spelling of Denyer, cognate with 1.
Boy/Male
Muslim/Islamic
Loving Caring, Daring
Surname or Lastname
German and Jewish (Ashkenazic)
German and Jewish (Ashkenazic) : from Middle High German hærinc ‘herring’, German Hering, a nickname for someone supposedly resembling a herring or a metonymic occupational name for a fish seller. In some cases the Jewish surname is ornamental.English : variant spelling of Herring.
Boy/Male
Gujarati, Hindu, Indian, Marathi, Telugu
Decided
Surname or Lastname
English
English : habitational name from places in Oxfordshire and West Sussex named Goring, from Old English GÄringas ‘people of GÄra’, a short form of the various compound names with the first element gÄr ‘spear’.German (Göring) : see Goering.
Surname or Lastname
English
English : perhaps be a nickname from Middle English daring ‘trembling’, ‘crouching or transfixed with fear’.
Surname or Lastname
English
English : of uncertain origin. Early examples, as for example William Spring (Yorkshire 1280), all point to a personal name or nickname, perhaps going back to an Old English byname derived from the verb springan ‘to jump or leap’ (see Springer 1). Alternatively, it could be a topographic name from Middle English spring ‘young wood’, ‘spring’. Compare Springer. Reaney derives the surname from the word denoting the season, although the word is not attested in this sense until the 16th century, the usual Middle English word being lenten. Compare Lenz. The surname has also been established in Ireland (County Kerry) for several centuries.German : from Middle High German sprinc, Middle Low German sprink ‘spring’, ‘well’, hence a topographic name for someone who lived by a spring or well, or habitational name from Springe near Hannover.Jewish (Ashkenazic) : variant of Springer.John Spring emigrated from England and settled in Watertown, MA, in 1634.
DECIDER TURING-MACHINE
DECIDER TURING-MACHINE
Male
Arthurian
, the Red Knight of the Red Lands.
Boy/Male
Indian
Supplanter, Supplant, Replace, Derived from the latin jacomus
Surname or Lastname
English, Dutch, and North German
English, Dutch, and North German : patronymic from the personal name Albert.
Girl/Female
Hindu
Ragam
Boy/Male
Hindu
Surname or Lastname
English
English : nickname for someone thought to resemble a curlew in some way, Anglo-Norman French curleu, Old French corlieu. The spelling Corlew is recorded in Sussex in 1327, but now appears to have died out in the British Isles, replaced by the modern form Curlew.
Male
Slavic
Variant spelling of Slavic Dimitriy, DIMITRI means "loves the earth" or "follower of Demeter."
Boy/Male
Hindu, Indian, Traditional
Gautamn
Boy/Male
Assamese, Indian, Jain
Touch; Gold
Boy/Male
English American
Beloved.
DECIDER TURING-MACHINE
DECIDER TURING-MACHINE
DECIDER TURING-MACHINE
DECIDER TURING-MACHINE
DECIDER TURING-MACHINE
n.
One who deludes; a deceiver; an impostor.
prep.
In the time of; as long as the action or existence of; as, during life; during the space of a year.
n.
A tiring-room.
n.
One who derides, or laughs at, another in contempt; a mocker; a scoffer.
imp. & p. p.
of Deride
v. t.
To give forth in action or exercise; to discharge; as, to deliver a blow; to deliver a broadside, or a ball.
v. i.
To determine; to form a definite opinion; to come to a conclusion; to give decision; as, the court decided in favor of the defendant.
n.
The pieces, or chips, detached in the process of turning from the material turned.
imp. & p. p.
of Decide
a.
Free from doubt or wavering; determined; of fixed purpose; fully settled; positive; resolute; as, a decided opinion or purpose.
n.
A group or division of ten; esp., a period of ten years; a decennium; as, a decade of years or days; a decade of soldiers; the second decade of Livy.
n.
One who decides.
n.
Alt. of Goring cloth
n.
A series of tubes; tubes, collectively; a length or piece of a tube; material for tubes; as, leather tubing.
a.
Bold; fearless; adventurous; as, daring spirits.
n.
A hole made by boring.
n.
Boldness; fearlessness; adventurousness; also, a daring act.
a.
Free from ambiguity; unequivocal; unmistakable; unquestionable; clear; evident; as, a decided advantage.
n.
A vessel which has a deck or decks; -- used esp. in composition; as, a single-decker; a three-decker.
n.
The chips or fragments made by boring.