# On Generalized Primitive Recursive String Functions

## Keywords:

String function, Primitive recursive string function, Superposition, Alphabetic primitive recursion## Abstract

The notion of generalized primitive recursive string function is introduced and relations between such functions and primitive recursive string functions in the usual sense ([1], [2]) are investigated. It is proved that any generalized primitive recursive string function is everywhere defined if and only if it is a primitive recursive string function in the usual sense.

## References

A. I. Malcev, Algorithms and Recursive Functions, 2nd edition, Moscow, “Nauka”, (in Russian), 1986.

M. H.Khachatryan, “On the representation of arithmetical and string functions in formal languages”, Transactions of the IIAP of NAS of RA, Mathematical problems of computer science, vol. 27, pp. 37-53, 2006.

I.D. Zaslavsky, “On some generalizations of the primitive recursive arithmetic”, Theoretical Computer Science, vol. 322, pp. 221-230, 2004.

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*Mathematical Problems of Computer Science*,

*43*, 42–46. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/206

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