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A complete characterization of primitive recursive intensional behaviours

P. Valarcher (2008)

RAIRO - Theoretical Informatics and Applications

We give a complete characterization of the class of functions that are the intensional behaviours of primitive recursive (PR) algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers.

Aleatoreidad e inmunidad.

J. F. Prida (1995)

Revista Matemática de la Universidad Complutense de Madrid

By introducing the concept of randomness through notions of recursion theory, the set of the random numbers is effectively immune. The proof of this well-known result makes an essential use of the recursion theorem. In this paper, randomness is introduced starting from the more common notion of definability in Robinson's arithmetic and the same result is obtained using an extension of the fixed-point theorem, which we prove at the end of the paper. Finally we define a recursive function dominating...

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