General recursive functions of natural numbers

@article{Kleene1936GeneralRF,
  title={General recursive functions of natural numbers},
  author={Stephen Cole Kleene},
  journal={Mathematische Annalen},
  year={1936},
  volume={112},
  pages={727-742}
}
  • S. Kleene
  • Published 1936
  • Mathematics
  • Mathematische Annalen
The History and Concept of Computability
  • R. Soare
  • Computer Science, Mathematics
  • Handbook of Computability Theory
  • 1999
TLDR
The chapter considers the Church–Turing thesis that the intuitively computable functions coincide with the formally computable ones and considers using the thesis as a definition. Expand
A SCHEMATIC DEFINITION OF QUANTUM POLYNOMIAL TIME COMPUTABILITY
  • T. Yamakami
  • Computer Science, Mathematics
  • The Journal of Symbolic Logic
  • 2020
TLDR
A new, schematic definition of quantum functions mapping finite-dimensional Hilbert spaces to themselves, which avoids the cumbersome introduction of the well-formedness condition imposed on a quantum Turing machine model as well as of the uniformity condition necessary for a quantum circuit model. Expand
Max Dehn, Axel Thue, and the Undecidable
The word problem for finitely presented groups and semigroups is a famous problem in combinatorial group theory. This question originally came up independently in topology and mathematical logic. AsExpand
Where are the data?
  • J. Reich
  • Computer Science, Medicine
  • Nature Structural &Molecular Biology
  • 2016
TLDR
It is argued that the proposed data concept matches the concept of characteristics (Merkmale) of the automation industry and is mathematically conceptualized as typed information based on the two concepts of information and computable functionality. Expand
Probabilistic Recursion Theory and Implicit Computational Complexity
TLDR
Probabilistic computable functions can be characterized by a natural generalization of Church and Kleene’s partial recursive functions, and the obtained algebra can be restricted so as to capture the notion of a polytime sampleable distribution, a key concept in average-case complexity and cryptography. Expand
Probabilistic Recursion Theory and Implicit Computational Complexity
TLDR
It is shown that probabilistic computable functions can be characterized by a natural generalization of Church and Kleene's partial recursive functions, and the obtained algebra can be restricted so as to capture the notion of polytime sampleable distributions, a key concept in average-case complexity and cryptography. Expand
Naming and Diagonalization, from Cantor to Gödel to Kleene
  • H. Gaifman
  • Mathematics, Computer Science
  • Log. J. IGPL
  • 2006
TLDR
A historical reconstruction of the way Godel probably derived his proof from Cantor's diagonalization, through the semantic version of Richard, and how Kleene's recursion theorem is obtained along the same lines is shown. Expand
Diagonalisation and Church's Thesis: Kleene's Homework
In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1 In some cases it is enough to assume the enumerability of Y while inExpand
Models of computation - exploring the power of computing
TLDR
In Models of Computation, John Savage re-examines theoretical computer science, offering a fresh approach that gives priority to resource tradeoffs and complexity classifications over the structure of machines and their relationships to languages. Expand
Time Lower Bounds For CREW-PRAM Computation Of Monotone Functions
It is shown that the time to compute a monotone boolean function depending upon n variables on a CREW-PRAM satisfies the lower bound T=Θ(logl+(log n)/l), where l is the size of the largest primeExpand
...
1
2
3
4
5
...

References

SHOWING 1-3 OF 3 REFERENCES
Zum Hilbertschen Aufbau der reellen Zahlen
Um den Beweis fiir die yon Cantor aufgestellte Vermutung zu e~bringen, dal~ sich die Menge der ree|len Zahlen, d. h. der zaMentheoretischen I~unktionen, mi~ Hilfe der Zahlen de~ zweiten ZahlklasseExpand