universal Turing machine

A universal Turing machineMathworldPlanetmathPlanetmath U is a Turing machineMathworldPlanetmath with a single binary one-way read-only input tape, on which it expects to find the encoding of an arbitrary Turing machine M. The set of all Turing machine encodings must be prefix-free, so that no special end-marker or ‘blank’ is needed to recognize a code’s end. Having transferred the description of M onto its worktape, U then proceeds to simulate the behaviour of M on the remaining contents of the input tape. If M halts, then U cleans up its worktape, leaving it with just the output of M, and halts too.

If we denote by M() the partial functionMathworldPlanetmath computed by machine M, and by <M> the encoding of machine M as a binary string, then we have U(<M>x)=M(x).

There are two kinds of universal Turing machine, depending on whether the input tape alphabet of the simulated machine is {0,1,#} or just {0,1}. The first kind is a plain Universal Turing machine; while the second is a prefix Universal Turing machine, which has the nice property that the set of inputs on which it halts is prefix free.

The letter U is commonly used to denote a fixed universalPlanetmathPlanetmathPlanetmath machine, whose type is either mentioned explicitly or assumed clear from context.

Title universal Turing machine
Canonical name UniversalTuringMachine
Date of creation 2013-03-22 13:43:46
Last modified on 2013-03-22 13:43:46
Owner tromp (1913)
Last modified by tromp (1913)
Numerical id 7
Author tromp (1913)
Entry type Definition
Classification msc 68Q05
Related topic ArtificialInteglligence
Related topic StrongAIThesis