Universal Turing machine

A Turing machine that simulates any Turing machine when supplied with an encoded description of that machine and its input.

Turing machine: An abstract model of computation that manipulates symbols on a tape according to a finite set of rules. A universal Turing machine is itself a Turing machine, equipped to interpret encoded machines.
Alan Turing: A British mathematician who developed foundational models of computation and contributed to wartime codebreaking. Turing introduced the universal machine in his analysis of computable numbers.
Turing machine configuration: A snapshot of a Turing machine’s state, tape contents, and tape-head position. Simulation proceeds by encoding and updating the simulated machine’s configuration.
Stored-program computer: A computer architecture that stores program instructions in memory alongside data. The universal machine’s treatment of descriptions as data anticipates the stored-program principle.
Finite-state machine: A computational model with finitely many states and no unbounded memory tape. Unlike a universal Turing machine, it cannot simulate arbitrary Turing machines.
Turing machine encoding: A finite representation of a Turing machine’s states, symbols, and transition rules. The universal machine reads this description as data to reconstruct the simulated machine’s steps.
On Computable Numbers, with an Application to the Entscheidungsproblem: Alan Turing’s 1936 paper defining machine computation and demonstrating a universal machine. This paper presents the construction that gave the concept its classic formulation.
Gödel numbering: A method of encoding formal symbols and expressions as natural numbers. Number encodings illustrate how finite machine descriptions can be treated as manipulable data.
Programmable computer: A computer whose behavior can be changed by loading different programs rather than rebuilding its hardware. Universality gives a formal account of why one machine can perform many distinct tasks.
Turing machine variants: Alternative Turing-machine models that vary tape layout, head count, or transition rules while preserving computational power. Many variants remain universal despite changing the simulator’s mechanical details.

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