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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
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
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
English computer scientist (1912–1954)
Enigma machine. He also contributed the Turing test to philosophy of artificial intelligence and the Turing pattern concept to mathematical and theoretical
Alan_Turing
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
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
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
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
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
Type of conservative logic circuit
ball bouncing from the walls of a curved billiards table is already Turing complete. Unconventional computing Fluidics Fredkin, Edward; Toffoli, Tommaso
Billiard-ball_computer
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
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
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
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
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
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
Elementary cellular automaton
systems, then 2-tag system, and then Turing machines. The final stage has exponential time overhead because the Turing machine's tape is encoded with a unary
Rule_110
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
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
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
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
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
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
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
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
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
Esoteric, minimalist programming language
to describe a family of Turing machines. A Brainfuck variant with a finite tape and finite cell values is not Turing-complete. It has only finitely many
Brainfuck
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
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
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
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
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
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
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
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)
German mathematician (1912–2003)
so the calculating machines have the same cardinality as Turing machines re:Turing completeness. Hermes' textbooks, as well as his scientific work, persuaded
Hans_Hermes
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
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
Programmable machine that processes data
seminal 1936 paper, On Computable Numbers, Alan Turing proposed the principle of the modern computer. Turing proposed a simple device that he called "Universal
Computer
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
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)
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
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
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
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
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
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
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
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
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
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
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
Concept in artificial intelligence
software as well as its hardware. This system forms a sort of generalist Turing-complete programmer which can in theory develop and run any kind of software
Recursive_self-improvement
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
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)
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
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)
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)
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
Puzzle video game genre
exponentially-unlikely set of mines. Kaye also proved that infinite Minesweeper is Turing-complete. Board puzzles with algebra of binary variables 1990s in video games
Minesweeper_(video_game)
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
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
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
Generic type features in C++
Templates and C# Generics (C# Programming Guide)". 12 March 2024. Demonstration of the Turing-completeness of C++ templates (Lambda calculus implementation)
Template_(C++)
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
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
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)
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
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
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
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
Early British cryptanalysis computer
that Colossus was designed by Turing, not Flowers, to aid the cryptanalysis of the Enigma but an earlier machine that Turing designed was the electromechanical
Colossus_computer
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
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
Measure of popularity of programming languages
valuable when making various strategic decisions. TIOBE focuses on Turing complete programming languages, and provides no information on the popularity
TIOBE_index
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
Concept in computer security
For example, a weird machine may exist because an input format is Turing-complete, because of memory corruption vulnerabilities in the program, or because
Weird_machine
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
Mathematical-logic system
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
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
Codebreaking device created at Bletchley Park (United Kingdom)
re-opening on 23 June 2018. Virtual Bombe - Online 3D simulation of a Turing-Welchman Bombe Turing Bombe and US Navy Bombe simulator Cryptanalysis of the Enigma
Bombe
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
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
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 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
Functional programming language
operator (written `, the backquote character). These alone make it Turing-complete, but there are also some input/output (I/O) functions to enable interacting
Unlambda
Impossible task in computing
algorithm was proven to be impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of First-order logic, a statement is universally
Entscheidungsproblem
Programming language
contracts are inherently difficult to reason about directly, and the Turing-completeness of Solidity means that verification of arbitrary properties cannot
Solidity
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
2016 video game
2020. The Turing Test is a puzzle video game with gameplay experienced from a first-person perspective. The player assumes the role of Ava Turing, an International
The_Turing_Test_(video_game)
Method for solving one problem using another
Pavan, A.; Venugopalan, Rajeswari (2014). Separating Cook Completeness from Karp-Levin Completeness under a Worst-Case Hardness Hypothesis. 34th International
Polynomial-time_reduction
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
Programming principle
Turing-complete, those that are in fact Turing-complete though one is led not to use them that way (XSLT, SQL), those that are functional and Turing-complete
Rule_of_least_power
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
Open-source blockchain computing platform
development of a new platform with a more robust scripting language—a Turing-complete programming language—that would eventually become Ethereum. Ethereum
Ethereum
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
Typesetting system
the results across different computer hardware, and includes a real, Turing-complete programming language, following intense lobbying by Guy Steele. In
TeX
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
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
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TURING COMPLETENESS
TURING COMPLETENESS
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TURING COMPLETENESS
TURING COMPLETENESS
TURING COMPLETENESS
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