Machine with unlimited registers

In Data-processing, a machine with unlimited registers or URM (of the English: Unlimited Register Machine ) is a Modèle abstract of the operation of the mechanical apparatuses of calculation, just like the machines of Turing and the Lambda-calculation. A URM is Turing-complete.

Notations

The register S of the machine are represented by:

$\backslash \; mathcal\; \{R\}\; =\; \backslash \; \{R\_i\; \backslash \}\; \_\; \{I\; \backslash \; geq\; 1\}$

and can contain elements of $\backslash \; mathbb\; \{NR\}$.

A program for this machine is represented by any continuation of the form:

$P\; =\; \backslash \; \{I\_i\; \backslash \}\; \_\; \{i=1\}\; ^\; \{i=n\}$

who contains a finished succession of instructions.

An instruction can be:

• a restoring of the I - ème register: Z (I) ;
• incrementing of the I - ème register: S (I) ;
• the transfer of the contents of the I - ème register in the J - ème register: T (I, J) ;
• a conditional jump with the K - ème instruction when the I - ème and J - ème registers is equal: J (I, J, K) .

Operation

A URM carries out the instructions of a program sequentially, except when it meets an instruction of jump.

The configuration or the state of a program is the whole of the values $\backslash \; \{a\_\; \{I\}\; \backslash \}\; \_\; \{I\; \backslash \; geq1\}$ contained in the registers. The initial configuration of a program is that where the first registers contain the data:

$\backslash \; \{D\; \backslash \}\; ^\; \{i=d\}\; \_\; \{i=1\}$

and where all the other registers are to zero:

$R\_i$ contains $d\_i$ if $i\; \backslash \; the\; d$;

$R\_i$ contains $0$ if $i\; >\; d$.

See too

• Calculabilité
• Machine of Turing
• Lambda calculation

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