منابع مشابه
Unary Primitive Recursive Functions
In this article, we will study certain reductions in the schemes that conform unary primitive recursive functions (i.e. primitive recursive functions of one argument) and we will extend some results previously researched by R. M. Robinson in [15]. Furthermore, we will introduce formal notation for unary primitive recursive functions. §
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1 I n t r o d u c t i o n Let N be the set of naturals i.e. N = {0,1, 2, . . .}. Consider a fixed alphabet A = {a l ,a2 , . . . ,at}, r > 2 and denote by A* the free monoid generated by A under concatenation (with e the null string). The elements of A* are called strings; if reffering to strings, " < " denotes the lexicographical order induced by al < a2 < . . . < at. Denote by Fnc (respectivel...
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1. Definition of recursive functions. In this paper, we shall consider certain reductions in the recursion scheme for defining primitive recursive functions. Hereafter, we shall refer to such functions simply as recursive functions. In §1, we define what is meant by a recursive function, and also define some recursive functions which will be used. The statement of the principal results of the p...
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— In this paper we extend the notion of primitive recursive function to the case in which the domain is N* and the range is a subset oj N*. We give a rigorvus characterization oj tins class oj functions and show différences icith the classical primitive recursive functions. Résumé. — Dans cette note nous étendons la notion de f onction primitive recursive à tous les cas dans lesquels le domaine...
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— In this paper we give a characterization of primitive recursive functions ƒ : N~* N{r^0, s>0) and define a Hierarchy of classes b^O) of these functions by a syntactic measure ofeomplexity. The behavior ofthe classes J^a+b^ respect to different operators is also analyzed. The classes J^ + b coincide with the ones ofCleavé's hierarchy for a^2,b^0 and give a refinement of the Meyer-Ri...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2008
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1230396909