Definition: LOOP Command, LOOP Program
Let \(M\) be a unitcost random access machine with the registers \(r_1,\ldots, r_n\).
\((1)\) The syntax of a LOOP command and a LOOP program
The syntax of a LOOP command and a LOOP program is defined by induction.
Base case
* \(\mathtt{r_i:=r_i + 1}\) is both, a LOOP command and LOOP program for all \(r_i\).
* \(\mathtt{r_i:=r_i  1}\) is both, a LOOP command and LOOP program for all \(r_i\).
Induction step: Let \(P_1,P_2\) be two LOOP programs. Then
* \(\mathtt{P_1;P_2}\) is a LOOP program.
* \(\mathtt{LOOP~r_i~DO~P_1~END}\) is both, a LOOP command and a LOOP program for all \(r_i\).
A LOOP program terminates, if there are no more LOOP commands / LOOP programs left to be executed.
\((2)\) The semantics of a LOOP command and a LOOP program
The semantics of the LOOP commands and a LOOP programs described above is as follows:
 \(\mathtt{r_i:=r_i + 1}\) means that \(M\) increments the natural number, which is contained in the register \(r_i\).
 If \(r_i > 0\), \(\mathtt{r_i:=r_i  1}\) means that \(M\) decrements the natural number contained in the register \(r_i\).
 If \(r_i=0\), \(\mathtt{r_i:=r_i  1}\) means that \(M\) does not change the register \(r_i\) at all.
 \(\mathtt{P_1;P_2}\) means that \(M\) executes the program \(\mathtt {P_1}\). After the termination of this program, \(M\) continues with the execution of the program \(\mathtt {P_2}\).
 \(\mathtt{LOOP~r_i~DO~P~END}\) means that \(M\) executes the program \(\mathtt P\) exactly \(n\) times, where \(n\) is the natural number stored in the register \(r_i\).
Table of Contents
Examples: 1
Mentioned in:
Algorithms: 1 2 3 4 5 6 7
Definitions: 8 9
Examples: 10
Proofs: 11 12
Theorems: 13
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References
Bibliography
 Erk, Katrin; Priese, Lutz: "Theoretische Informatik", Springer Verlag, 2000, 2nd Edition