Abstract
A computational model of associative type is proposed. For it a program is written which does not contain loops and has the following properties. The program's original data are a normal algorithmA (its notation) and a worda, while the results are a Boolean value and a wordR. IfA is applicable to worda, then we can indicate a finite memory such that the program, having worked on this memory, yields the valuetrue as andA(a) asR. However, ifA is not applicable toa, then the program does not work on any (finite) memory and always yields the valuefalse as, If the program works on an infinite memory, then after its work takes the valuetrue if and only ifA is applicable toa; moreover, in the case of applicabilityR takes the valueA(a). The present paper contains a more detailed exposition of the result published in Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk USSR,70 (1977).
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