Turing machine

Definition

A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm.

Related concepts

ANSI C Abstract logic Abstract machine Ackermann set theory Alan Turing Aleph number Algebraic logic Algorithm Alonzo Church Alphabet (formal languages)Alternating Turing machine Analytical engine Andrew Hodges Aperiodic finite state automaton Argument Arithmetic model of computation Arithmetical hierarchy Arity Assembly language Association for Symbolic Logic Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Automatic Computing Engine Automaton Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Batch processing Bekenstein bound Bijection Binary operation Binary search BlooP and FlooP Boaz Barak Boolean algebra Boolean algebras canonically defined Boolean function Busy beaver Calculus ratiocinator Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Central processing unit Chaitin's constant Charles Babbage Charles Petzold Chinese room Chomsky hierarchy Christos Papadimitriou Church encoding Church–Turing thesis Class (set theory)Classical logic Claude Shannon Codomain Combinational logic Compactness theorem Complement (set theory)Complete theory Completeness (logic)Computability Computability theory Computable function Computable set Computably enumerable set Computation Computational complexity theory Computer Computer algorithm Computer science Computer storage Computing Machinery and Intelligence Concrete category Conservative extension Consistency Consistency proof Constructible universe Construction of the real numbers Constructive set theory Context-free grammar Context-free language Context-sensitive grammar Context-sensitive language Continuum hypothesis Conway's Game of Life Countable set Counter machine David Hilbert Decidability (logic)Decider (Turing machine)Decision problem Deductive system Deterministic acyclic finite state automaton Deterministic context-free grammar Deterministic context-free language Deterministic finite automaton Deterministic pushdown automaton Diagram (mathematical logic)Digital infinity Diophantine equation Diophantine set Discrete mathematics Domain of a function Donald Knuth EDVAC Effective calculability Effective method Elaine Weyuker Electronic computer Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Embedded pushdown automaton Emil Post Empty set Encyclopedia of Mathematics Entscheidungsproblem Enumeration Enumerator (computer science)Equiconsistency Equivalence relation Euclid's Elements Euclidean algorithm Euclidean geometry European Mathematical Society Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Finitary relation Finite-state machine Finite-valued logic Finite language Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set General set theory Genetix George Boolos George Stibitz Goto Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel number Gödel numbering Halting problem Hao Wang (academic)Hartley Rogers, Jr.Harvard architecture Heinrich Behmann Hereditary set Higher-order logic Hilbert's axioms Hilbert's problems Hilbert's tenth problem Hilbert system History of logic History of mathematical logic Howard Aiken Image (mathematics)Imperative programming Inaccessible cardinal Independence (mathematical logic)Indexed grammar Indexed language Inference Infinite-valued logic Infinite loop Infinite set Information theory Inhabited set Injective function Input/output automaton Interactivity Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Isomorphism J. B. Rosser Jack Copeland Jeffrey Ullman John Hopcroft John P. Burgess Journal of Symbolic Logic Journal of the ACM King's College, Cambridge Kolmogorov complexity Konrad Zuse Kripke's theory of truth Kripke–Platek set theory Kurt Gödel LIFO (computing)Lambda calculus Langton's ant Large cardinal Legacy of Alan Turing Lego Lemma (mathematics)Leonardo Torres Quevedo Lindström's theorem Linear bounded automaton Linear context-free rewriting language Linear context-free rewriting system List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC List of things named after Alan Turing Logarithm Logic Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Louis Couffignal Löwenheim–Skolem theorem M. H. A. Newman MIT Press Many-valued logic Map (mathematics)Martin Davis (mathematician)Marvin Minsky Material conditional Mathematical logic Mathematical model of computation Mathematical object Mathematics Maurice d'Ocagne Memory allocation Metalanguage Michael Sipser Minimal axioms for Boolean algebra Model complete theory Model of computation Model theory Modified Harvard architecture Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory Multi-tape Turing machine Multi-track Turing machine Multitape Turing machine NFA to DFA conversion NP (complexity)Naive set theory Natural deduction Negation Nested stack automaton Nested word Neural Turing machine New Foundations Non-Euclidean geometry Non-deterministic Turing machine Non-logical symbol Non-recursive grammar Non-standard model Non-standard model of arithmetic Nondeterministic Turing machine Nondeterministic finite automaton Omega (computer science)On Computable Numbers, with an Application to the Entscheidungsproblem Open formula Operation (mathematics)Oracle machine Ordinal analysis Ordinal number Out of memory Oxford University Press PTIME P (complexity)P versus NP problem Paradoxes of set theory Partial function Partition of a set Pascal (programming language)Peano axioms Percy Ludgate Peter van Emde Boas Philosophy of mathematics Post–Turing machine Power set Predicate (mathematical logic)Predicate logic Predicate variable Prime model Primitive recursive arithmetic Primitive recursive function Princeton University Press Principia Mathematica Probabilistic Turing machine Programming language Proof of impossibility Proof theory Proper subset Proposition Propositional calculus Propositional formula Propositional variable Pushdown automata Pushdown automaton Quantifier (logic)Quantifier rank Quantum Turing machine R. E. Stearns Random-access machine Random-access memory Random-access stored-program machine Range concatenation grammars Range concatenation language Read-only right moving Turing machines Recursion Recursion theory Recursive language Recursive set Recursively enumerable language Recursively enumerable set Register machine Regular grammar Regular language Relation (mathematics)Relays Repeated squaring Reverse mathematics Richard Jeffrey Robin Gandy Robinson arithmetic Roger Penrose Rolf Herken Rule of inference Russell's paradox SIGACT News Sanjeev Arora Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequent calculus Set (mathematics)Set theory Signature (logic)Simon and Schuster Singleton (mathematics)Skolem arithmetic Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Stanford Encyclopedia of Philosophy Star-free language Stephen Cole Kleene Stephen Hawking Stephen Kleene Stored-program computer Strength (mathematical logic)String (formal languages)Strongly polynomial Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Symmetric Turing machine Syntax (logic)Systems of Logic Based on Ordinals T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic The Chemical Basis of Morphogenesis The Emperor's New Mind Theorem Theories of truth Theory (mathematical logic)Theory of computation Thread automaton Three-valued logic Timeline of mathematical logic Transfer principle Transition system Transitive set Tree-adjoining grammar Tree stack automaton True arithmetic Truth predicate Truth table Truth value Tuple Turing's Thesis Turing's proof Turing completeness Turing computable Turing degree Turing machine Turing machine (disambiguation)Turing machine equivalents Turing machine examples Turing pattern Turing reduction Turing tarpit Turing test Turmite Turochamp Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Unambiguous Turing machine Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal Turing machine Universal quantification Universal set Universe (mathematics)Unorganized machine Unrestricted grammar Urelement Validity (logic)Vannevar Bush Variable (mathematics)Venn diagram Von Neumann architecture Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Wiktionary World War II Zeno machine Zermelo–Fraenkel set theory Zohar Manna

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