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Ability of a computing system to simulate Turing machines
scientist Alan Turing). This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way
Turing_completeness
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
Concept in computability theory
Turing complete for X {\displaystyle {\mathcal {X}}} . Turing completeness, as just defined above, corresponds only partially to Turing completeness in
Turing_reduction
Computation model defining an abstract machine
are based on different designs that, unlike Turing machines, use random-access memory. Turing completeness is the ability for a model of computation or
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
Concept from evolutionary biology
The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis", which describes
Turing_pattern
Thesis on the nature of computability
computable by a Turing machine. The thesis is named after American mathematician Alonzo Church and the British mathematician Alan Turing. Before the precise
Church–Turing_thesis
Complexity class
consequence of the definition of NP-completeness is that if we had a polynomial time algorithm (on a UTM, or any other Turing-equivalent abstract machine) for
NP-completeness
Programming language that uses first order logic
Horn clauses, which is Turing-complete. Turing completeness of Prolog can be shown by using it to simulate a Turing machine: turing(Tape0, Tape) :- perform(q0
Prolog
List
language) Super-Turing computation Turing-acceptable language Turing Award Turing (cipher) Turing College, Kent, England Turing completeness Turing computability
List of things named after Alan Turing
List_of_things_named_after_Alan_Turing
Deterministic model of computation
Universal Turing machine, as was done by Wang (1963) and by Cocke & Minsky (1964). Conversely, a Turing machine can be shown to be a Universal Turing Machine
Tag_system
Problem in computer science
problem considered in Turing's 1936 paper ("does a Turing machine starting from a blank tape ever print a given symbol?"). However, Turing equivalence is rather
Halting_problem
Process calculus
the absence of replication/recursion, the π-calculus ceases to be Turing-complete. This can be seen by the fact that bisimulation equivalence becomes
Π-calculus
Game and demonstration of logic gates
Turing Tumble is a game and demonstration of logic gates via mechanical computing. Named after Alan Turing, the game could, in the abstract, duplicate
Turing_Tumble
English computer scientist (1912–1954)
algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father
Alan_Turing
Computation model, equivalent to Turing machines
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 simulated
Queue_automaton
German computer scientist and engineer (1910–1995)
jumps, the Z3 was a Turing complete computer. However, Turing-completeness was never considered by Zuse (who was unaware of Turing's work and had practical
Konrad_Zuse
2-dimensional esoteric programming language
80x25 grid, and while not Turing-complete, subsequent extensions like Funge-98 expanded the concept to achieve Turing completeness. The name "Befunge" originated
Befunge
Contractual transaction on a decentralized platform
Machine. Due to the halting problem and other security problems, Turing-completeness is considered to be a risk and is deliberately avoided by languages
Smart_contract
Sequence of operations for a task
inputs increase. Any algorithm can be computed by any Turing complete model. Turing completeness only requires four instruction types—conditional GOTO
Algorithm
Arbitrary code execution exploit
information leakage to get their exact positions in memory. Although Turing-complete ROP compilers exist, it is usually non-trivial to create a ROP chain
Sigreturn-oriented programming
Sigreturn-oriented_programming
Elementary cellular automaton
elementary cellular automata, Rule 110 is the only one for which Turing completeness has been directly proven, although proofs for several similar rules
Rule_110
Cellular automaton
three or more dimensions can be used to simulate a Turing machine and are therefore Turing complete. There exist several generalizations of the sandpile
Abelian_sandpile_model
Topics referred to by the same term
containing Turing List of things named after Alan Turing Turing machine (disambiguation) Turing test (disambiguation) Turing completeness, ability of
Turing_(disambiguation)
1998 esoteric programming language
of writing programs in Malbolge as well as some thoughts on its Turing completeness. Olmstead believed Malbolge to be a linear bounded automaton. There
Malbolge
19th century proposed mechanical computer
general-purpose computer that could be described in modern terms as Turing-complete. In other words, the structure of the analytical engine was essentially
Analytical_engine
Mathematical model describing how an output of a function is computed given an input
machines Post machines (Post–Turing machines and tag machines). Pushdown automata Register machines Random-access machines Turing machines Decision tree model
Model_of_computation
Programmable machine that processes data
The Church–Turing thesis is a mathematical statement of this versatility: any computer with a minimum capability (being Turing-complete) is, in principle
Computer
First working programmable, fully automatic digital computer
conditional 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
Z3_(computer)
Type of conservative logic circuit
Miranda and Isaac Ramos published a paper showing that 2D billiards are Turing complete. In this work they show that even classical planar billiard systems
Billiard-ball_computer
Topics referred to by the same term
up completeness, complete, completed, or incompleteness in Wiktionary, the free dictionary. Complete may refer to: Completeness (logic) Completeness of
Completeness
Esoteric, minimalist programming language
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
Computer built from mechanical components such as levers and gears
calculations, and perform other complicated tasks. Turing Tumble, 2017 – An educational Turing-complete computer partially inspired by the Digi-Comp II.
Mechanical_computer
American annual computer science prize
Staff (2014). "ACM's Turing Award prize raised to $1 million". Communications of the ACM. 57 (12): 20. doi:10.1145/2685372. "A. M. Turing Award". Association
Turing_Award
1952 scholarly article by Alan Turing
patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation
The Chemical Basis of Morphogenesis
The_Chemical_Basis_of_Morphogenesis
Music tracker and modular synthesizer developed by Alexander "NightRadio" Zolotov
SunVox, also known as SunVox Modular Music Creation Studio, is a 2008 music creation tool built around the SunVox Engine, a software-based modular synthesizer
SunVox
English programmer, venture capitalist, and writer (born 1964)
language." It was used by Graham to illustrate a comparison, beyond Turing completeness, of programming language power, and more specifically to illustrate
Paul_Graham_(programmer)
Two-dimensional cellular automaton
Turing machine, so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints; it is Turing complete
Conway's_Game_of_Life
Mathematical model of abstract computation
universal 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
List of unsolved computational problems
on two given strings of length n {\displaystyle n} ? What is the Turing completeness status of all unique elementary cellular automata? Determine whether
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Study of computable functions and Turing degrees
Church, Rózsa Péter, Alan Turing, Stephen Kleene, and Emil Post. The fundamental results the researchers obtained established Turing computability as the correct
Computability_theory
1950 scientific paper by Alan Turing
what is now known as the Turing test to the general public. Turing's paper considers the question "Can machines think?" Turing says that since the words
Computing Machinery and Intelligence
Computing_Machinery_and_Intelligence
Topics referred to by the same term
Turing equivalence may refer to: As related to Turing completeness, Turing equivalence means having computational power equivalent to a universal Turing
Turing_equivalence
Abstract machine that uses only one instruction
one-instruction set computer (and has only 178 transistors). In a Turing-complete model, each memory location can store an arbitrary integer, and – depending
One-instruction_set_computer
Theoretical model of computation
nondeterministic computation with a deterministic computer. Alan Turing first developed the concept of Turing machine in 1936, imagining it as a simple computer that
Nondeterministic Turing machine
Nondeterministic_Turing_machine
Impact of English computer scientist
Alan Turing Institute Church–Turing thesis Good–Turing frequency estimation Turing completeness Turing degree Turing fixed-point combinator Turing Institute
Legacy_of_Alan_Turing
High-level computer programming conceptualization
language Flow-based programming Modeling language Programming domain Turing completeness Von Neumann programming languages "Multi-Paradigm Programming Language"
Programming_paradigm
Programming language for experimentation or art
examples of minimal Turing tarpits and needlessly obfuscated language features. Brainfuck is related to the P′′ family of Turing machines. While esoteric
Esoteric_programming_language
genetics". Turing's 1948 paper has been re-printed as Turing AM. Intelligent Machinery. In: Ince DC, editor. Collected works of AM Turing — Mechanical
Unorganized_machine
included. A programming language does not need to be imperative or Turing-complete, but must be executable and so does not include markup languages such
List_of_programming_languages
Test to determine whether a user is human
in contrast to the standard Turing test that is administered by a human, CAPTCHAs are sometimes described as reverse Turing tests. Two widely used CAPTCHA
CAPTCHA
Task to construct a program meeting a formal specification
Robert S.; Moore, J. Strother (May 1983). A Mechanical Proof of the Turing Completeness of Pure Lisp (PDF) (Technical report). Institute for Computing Science
Program_synthesis
English mathematician (1815–1852)
2012. Fuegi & Francis 2003. Turing, Alan (2004). Stuart Shieber (ed.). "Computing Machinery and Intelligence". The Turing Test: Verbal Behavior as the
Ada_Lovelace
Feature in the C++ programming language
Templates and C# Generics (C# Programming Guide)". 12 March 2024. Demonstration of the Turing-completeness of C++ templates (Lambda calculus implementation)
Template_(C++)
Computing language
execution models, and hybrid depth- and breadth-first evaluation with Turing completeness. As an explanatory analogy, Apache TinkerPop and Gremlin are to graph
Gremlin_(query_language)
Use of functions that call themselves
functions and procedures that can be evaluated by a computer (see Turing completeness) can be expressed in terms of recursive functions; iterative control
Recursion_(computer_science)
Security architecture implemented in hardware
"non-Turing-machine" logic (raw combinatorial logic or simple state machines). One approach, referred to as "hardsec", uses FPGAs to implement non-Turing-machine
Hardware_security
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 other
Rice's_theorem
in Technology International Hall of Fame inductees Timeline of computing Turing Award Women in computing Mario Tokoro, ed. (2010). "9". e: From Understanding
List of pioneers in computer science
List_of_pioneers_in_computer_science
Programming language
contracts are inherently difficult to reason about directly, and the Turing-completeness of Solidity means that verification of arbitrary properties cannot
Solidity
First electronic general-purpose digital computer
computer, completed in 1945. Other computers had some of these features, but ENIAC was the first to have them all. ENIAC was Turing-complete and able to
ENIAC
Fundamental theorem in mathematical logic
Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is soundness, the fact that only logically
Gödel's_completeness_theorem
Puzzle video game
exponentially-unlikely set of mines. Kaye also proved that infinite Minesweeper is Turing-complete. Board puzzles with algebra of binary variables Edwards, Benj (8 October
Minesweeper_(video_game)
Simple Turing complete logic
mathematical theory of algorithms because it is an extremely simple Turing complete language. It can be likened to a reduced version of the untyped lambda
SKI_combinator_calculus
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
NP_(complexity)
Topics referred to by the same term
(chemistry) Equivalence point Equivalent weight Turing equivalence (theory of computation), or Turing completeness Semantic equivalence in computer metadata
Equivalence
Book by Stephen Wolfram
new technical result in describing the Turing completeness of the Rule 110 cellular automaton. Very small Turing machines can simulate Rule 110, which
A_New_Kind_of_Science
German polymath (1646–1716)
formal systems, such as Turing completeness, where computation was used to define equivalent universal languages (see Turing degree). Leibniz has been
Gottfried_Wilhelm_Leibniz
String rewriting system
process exactly follows the run of the Turing machine encoded. This proves that string rewrite systems are Turing complete. The reason for having two halted
Semi-Thue_system
Programming paradigm based on applying and composing functions
Turing proved that the lambda calculus and Turing machines are equivalent models of computation, showing that the lambda calculus is Turing complete.
Functional_programming
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
American mathematician
cellular automaton is Turing-complete. Cook was born in Morgantown, West Virginia and grew up in Evanston, Illinois. He completed his undergraduate studies
Matthew_Cook
British early electronic serial stored-program computer
British electronic serial stored-program computer design by Alan Turing. Turing completed the ambitious design in late 1945. The ACE was not built, but a
Automatic_Computing_Engine
Mathematical-logic system based on functions
cost measure, as any Turing machine may be encoded in the lambda calculus in size linearly proportional to the size of the Turing machine. The true cost
Lambda_calculus
Spreadsheet editor by Microsoft
With the introduction of LAMBDA on December 3, 2020, Excel became Turing complete. The Windows version of Excel supports programming through Microsoft's
Microsoft_Excel
Computer programming language
semantics of BCL, apart from eta-reduction (which is not required for Turing completeness), may be very compactly specified by the following rewriting rules
Binary_combinatory_logic
Relationship between programs and proofs
functional programming, is to eliminate unrestricted recursion (and forgo Turing completeness, although still retaining high computational complexity), using more
Curry–Howard_correspondence
Theorem about a certain class of control-flow graphs
the selection statement into subprocedures. Structured programming Turing completeness Kozen & Tseng 2008. University at Buffalo 2004. Barendregt 2019,
Structured_program_theorem
Programming language used in many domains
Turing-complete, meaning that they can theoretically solve any computational problem. Domain-specific languages are often similarly Turing-complete but
General-purpose programming language
General-purpose_programming_language
described by computer scientist Alan Turing, who set out the idea in his seminal 1936 paper, On Computable Numbers. Turing reformulated Kurt Gödel's 1931 results
History_of_computing_hardware
Computer language specialized to a specific set of requirements or function
general-purpose programming language later on. In contrast, PostScript is a Turing-complete language, and in principle can be used for any task, but in practice
Domain-specific_language
File format and programming language
in the electronic publishing and desktop publishing realm, but as a Turing complete programming language, it can be used for many other purposes as well
PostScript
Collectible card game
Turing complete.[further explanation needed] By proving this, the researchers assert that Magic: The Gathering is so complex as to be Turing complete
Magic:_The_Gathering
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
P_versus_NP_problem
Text processing programming language
especially designed to support one-liner programs, the language is Turing-complete, and even the early Bell Labs users of AWK often wrote well-structured
AWK
Analysis of computer programs without executing them
reduction to the halting problem, it is possible to prove that (for any Turing complete language), finding all possible run-time errors in an arbitrary program
Static_program_analysis
Computer architecture for educational purposes
control, and input/output capabilities. SAP-2 and SAP-3 are fully Turing-complete. The instruction set architecture (ISA) that the computer final version
Simple-As-Possible_computer
1938 doctoral thesis by Alan Turing
id.tue.nl/lecturenotes/DDM110%20CAS/Turing/Turing-1939%20Sysyems%20of%20logic%20based%20on%20ordinals.pdf "Turing's Princeton Dissertation". Princeton
Systems of Logic Based on Ordinals
Systems_of_Logic_Based_on_Ordinals
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
a list of 21 NP-complete problems. Karp also introduced the notion of completeness used in the current definition of NP-completeness (i.e., by polynomial-time
Cook–Levin_theorem
Esoteric programming language
compilers exist. One interpretation of the language has been proven Turing-complete. LOLCODE's keywords are drawn from the heavily compressed (shortened)
LOLCODE
Programming paradigm based on modeling the logic of a computation
a subset of Prolog. But because it lacks compound terms, it is not Turing-complete.[citation needed] Most Datalog systems execute programs bottom-up,
Declarative_programming
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
Discrete model of computation
research assistant Matthew Cook showed that one of these rules is Turing-complete. The primary classifications of cellular automata, as outlined by Wolfram
Cellular_automaton
2D cellular automaton devised by Brian Silverman in 1987
Wireworld is particularly suited to simulating transistors, and is Turing-complete. A Wireworld cell can be in one of four different states, usually numbered
Wireworld
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
List_of_undecidable_problems
Esoteric programming languages
programming languages, or Turing tarpits, esoteric programming languages designed to be as small as possible but still Turing-complete. Both systems use only
Iota_and_Jot
Abstract machine used to study decision problems
of oracle Turing machines, as discussed below. The one presented here is from van Melkebeek (2003, p. 43). An oracle machine, like a Turing machine, includes:
Oracle_machine
Type of abstract computing machine
generic class of abstract machines, analogous to a Turing machine and thus Turing complete. Unlike a Turing machine that uses a tape and head, a register machine
Register_machine
Declarative logic programming language
P-complete (See Theorem 4.4 in ). P-completeness for data complexity means that there exists a fixed Datalog query for which evaluation is P-complete.
Datalog
Proof by Alan Turing
Turing's proof is a proof by Alan Turing, first published in November 1936 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem"
Turing's_proof
TURING COMPLETENESS
TURING COMPLETENESS
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.
Surname or Lastname
English
English : patronymic from Dear 1.German : probably a variant of Döring (see Doering).
Boy/Male
Muslim
Loving, Caring, Daring
Surname or Lastname
English
English : from a pet form of the personal name Hugh.
Boy/Male
Indian
Loving, Caring, Daring
Boy/Male
Muslim/Islamic
Loving Caring, Daring
Surname or Lastname
English (Kent)
English (Kent) : unexplained.Possibly an altered spelling of the German surname Dulling, which is likewise unexplained.
Surname or Lastname
English
English : patronymic from Dear 1.German (Döring) : see Doering.
Boy/Male
Hindu, Indian
A Thought
Surname or Lastname
English
English : perhaps be a nickname from Middle English daring ‘trembling’, ‘crouching or transfixed with fear’.
Surname or Lastname
English
English : ethnic name from Old French Lohereng ‘man from Lorraine’ (see Lorraine).
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
Female
English
Elaborated form of English Tara, TARINA means "hill."
Girl/Female
American, Australian, Bengali, British, Christian, English, Indian
Springtime; Spring Season; Rapid Movement
Girl/Female
Indian
Lively, Entertainer, From a stream or a Spring, The Spring season, The Spring season
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
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.
Surname or Lastname
English
English : variant of Darling.
Surname or Lastname
English and French
English and French : from an Anglo-Norman French form of the Old Norse personal name þórfinnr, composed of the elements þórr, the name of the god of thunder in Scandinavian mythology (see Thor) + the ethnic name Finnr ‘Finn’. This may have absorbed another name, Turpius, Turpinus (from Latin turpis ‘ugly’, ‘base’), one of the self-abasing names adopted as a mark of humility by the early Christians. It was borne by the archbishop of Rheims in the Charlemagne legend.A Turpin of unknown geographic origin is documented in Montreal in 1681.
TURING COMPLETENESS
TURING COMPLETENESS
Boy/Male
Hindu
Lord Shiva
Girl/Female
Muslim/Islamic
Beautiful charitable, loving
Female
English
Variant spelling of English Alana, possibly ALANNA means "little rock."Â
Biblical
my lady; my prince of rest
Boy/Male
Indian
Type of Bird or Fragrance; One with Blue Body
Boy/Male
Arabic, Biblical
A Vapour; A Cloud of God
Boy/Male
Indian, Sanskrit
Fire of the Sky; The Sun
Girl/Female
French
Birthday. Feminine of Noel. Commonly refers to Christ's birth and Christmas festival.
Boy/Male
French, German, Greek, Polish
Bearer of Christ
Boy/Male
Indian, Telugu
Lord Balaji
TURING COMPLETENESS
TURING COMPLETENESS
TURING COMPLETENESS
TURING COMPLETENESS
TURING COMPLETENESS
n.
Alt. of Goring cloth
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.
The act or state of that which curls; as, the curling of smoke when it rises; the curling of a ringlet; also, the act or process of one who curls something, as hair, or the brim of hats.
n.
The pieces, or chips, detached in the process of turning from the material turned.
n.
A variety of the domestic pigeon remarkable for its habit of tumbling, or turning somersaults, during its flight.
n.
The chips or fragments made by boring.
n.
A tiring-room.
n.
An obscure road; a way turning from the main road.
n.
A hole made by boring.
prep.
In the time of; as long as the action or existence of; as, during life; during the space of a year.
n.
A series of tubes; tubes, collectively; a length or piece of a tube; material for tubes; as, leather tubing.
n.
A line for hauling the reef cringle to the yard; -- also called reef earing.
n.
A line used to fasten the upper corners of a sail to the yard or gaff; -- also called head earing.
a.
Consuming; intense; inflaming; exciting; vehement; powerful; as, burning zeal.
n.
Boldness; fearlessness; adventurousness; also, a daring act.
n.
An instrument turning on a center, for boring holes. See Bit, n., 3.
n.
An exposure to air, or to a fire, for warming, drying, etc.; as, the airing of linen, or of a room.
a.
Bold; fearless; adventurous; as, daring spirits.