Examples of using Recursive function in English and their translations into Portuguese
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it has a very high complexity that dominates every multiply recursive function.
An introduction to recursive function theory", Cambridge University Press, 1980.
Such a proof establishes that the consistency of a theory"T" implies the consistency of a theory"S" by producing a primitive recursive function that can transform any proof of an inconsistency from"S" into a proof of an inconsistency from"T.
is a unary total recursive function that is not primitive recursive. .
recursive predicate R's parameters,:(x1),…,(xn)(Ey) R( y, xi,… xn) implies that μyR(y, xi,… xn)">is a total recursive function.
when given the graph of a partial recursive function, always returns the graph of a partial recursive function.
Such a proof establishes that the consistency of a theory T implies the consistency of a theory S by producing a primitive recursive function that can transform any proof of an inconsistency from S into a proof of an inconsistency from T. One sufficient condition for a consistency proof to be finitistic is the ability to formalize it in PRA.
there is a primitive recursive function s of two arguments with the following property: for every Gödel
This is what recursive functions do.
The terminology for recursive functions and sets is not completely standardized.
ISBN 0-7204-2103-9* Rogers, H."Theory of Recursive Functions and Effective Computability", MIT Press.
Recursive functions of symbolic expressions and their computation by machine, Part I.
Without minimisation is the class of primitive recursive functions.
References==* Rogers, H."The Theory of Recursive Functions and Effective Computability", MIT Press.
From these basic functions, we can build other elementary recursive functions.
And, in the context of partial recursive functions Kleene later admits a third outcome:"μ undecided.
The broader class of partial recursive functions is defined by introducing an unbounded search operator.
And, in the context of"partial" recursive functions Kleene later admits a third outcome:"μ undecided", pp.
The set of all recursive functions is known as R in computational complexity theory.
Relationship to recursive functions==The broader class of partial recursive functions is defined by introducing an unbounded search operator.