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About 8,512 papers for “Recursive functions”

Recursive Functions

Goff, Christopher D. · Scholarly Commons (University of the Pacific) · 2011

https://scholarlycommons.pacific.edu/cop-facbooks/1132/thumbnail.jpg

Cited by 0

Recursive functions

Dean, Walter · Warwick Research Archive Portal (University of Warwick) · 2020

Cited by 3

Recursive Functions

Maribel Fernández · Undergraduate topics in computer science · 2009

Cited by 0

Recursive functions

Péter, Rózsa 1905-1977 · REAL-EOD (Library of the Hungarian Academy of Sciences and the Information Center Oriental Collection) · 1967

Cited by 1

Recursive Functions

John P. Burgess · Cambridge University Press eBooks · 2007

The intuitive notion of an effectively computable function is the notion of a function for which there are definite, explicit rules, following which one could in principle compute its value for any given arguments. This chapter studies an extensive class of effectively computable functions, the recursively computable, or simply recursive, functions. According to Church's thesis, these are in fact all the effectively computable functions. Evidence for Church's thesis will be developed in this chapter by accumulating examples of effectively computable functions that turn out to be recursive. The subclass of primitive recursive functions is introduced in section 6.1, and the full class of recursive functions in section 6.2. The next chapter contains further examples. The discussion of recursive computability in this chapter and the next is entirely independent of the discussion of Turing and abacus computability in the preceding three chapters, but in the chapter after next the three notions of computability will be proved equivalent to each other.

Cited by 0

Recursive functions

Martin Hils, François Loeser · Student mathematical library · 2019

Cited by 0

Recursive Functions

Kevin Broughan · 2023

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Recursive functions

Roozbeh Hazrat · Springer undergraduate mathematics series · 2010

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From recursive toIR-recursive functions

Manuel Lameiras Campagnolo, Jose Felix Costa · 1997

The quest for limits of computer simulations of the physical (real) world embraces a theory of analog computing. Moore proposed a recursion theory on the reals and de ned the class of IR-recursive functions that includes functions which are not computable in the traditional sense. In this paper we prove Turing universality of IR-recursive functions using recursive function theory. Therefore, we establish a direct link between both theories. 1

Cited by 0

Probabilistic recursive functions

Irwin Mann · Transactions of the American Mathematical Society · 1973

The underlying question considered in this paper is whether or not the purposeful introduction of random elements, effectively governed by a probability distribution, into a calculation may lead to constructions of number-theoretic functions that are not available by deterministic means. A methodology for treating this question is developed, using an effective mapping of the space of infinite sequences over a finite alphabet into itself. The distribution characterizing the random elements, under the mapping, induces a new distribution. The property of a distribution being recursive is defined. The fundamental theorem states that recursive distributions induce only recursive distributions. A function calculated by any probabilistic means is called <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi"> <mml:semantics> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:annotation encoding="application/x-tex">\psi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-calculable. For a class of such calculations, these functions are recursive. Relative to Church’s thesis, this leads to an extension of that thesis: Every <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi"> <mml:semantics> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:annotation encoding="application/x-tex">\psi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-effectively calculable function is recursive. In further development, a partial order on distributions is defined through the concept of “inducing.” It is seen that a recursive atom-free distribution induces any recursive distribution. Also, there exist distributions that induce, but are not induced by, any recursive distribution. Some open questions are mentioned.

Cited by 6

Recursive Lyapunov Functions

A. Olas · Journal of Dynamic Systems Measurement and Control · 1989

The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

Cited by 3