A recursion theoretic foundation of computation over real numbers
- MathematicsJ. Log. Comput.
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by Gödel (1931, 1934) and Kleene…
The History and Concept of Computability
- PhilosophyHandbook of Computability Theory
A SCHEMATIC DEFINITION OF QUANTUM POLYNOMIAL TIME COMPUTABILITY
- Computer ScienceThe Journal of Symbolic Logic
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.
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. As…
Where are the data?
- Computer ScienceNature Structural &Molecular Biology
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.
Ju n 20 14 Probabilistic Recursion Theory and Implicit Complexity ∗
- Computer Science, Mathematics
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.
Monoidal computer II: Normal complexity by string diagrams
- Computer ScienceArXiv
This formalization brings to the foreground the concept of normal complexity measures, which allow decompositions akin to Kleene’s normal form, where evaluating the complexity of a program does not require substantially more resources than evaluating the program itself.
Naming and Diagonalization, from Cantor to Gödel to Kleene
- MathematicsLog. J. IGPL
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.
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 in…
- Computer ScienceProcesses, Terms and Cycles
Some undecidability results for “primitive” term rewriting systems, which encode primitive-recursive definitions, are presented in the manner suggested by Klop and some results for orthogonal and non-orthogonal rewriting are reprove by applying standard results in recursion theory.
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