Topic
Computability
About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.
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01 May 1997
TL;DR: A new model of query and computation on the Web is presented, focusing on two important aspects that distinguish theAccess to Web data from the access to a standard database system: the navigational nature of the access and the lack of concurrency control.
Abstract: We present a new formal model of query and computation on the Web. We focus on two important aspects that distinguish the access to Web data from the access to a standard database system: the navigational nature of the access and the lack of concurrency control. We show that these two issues have significant effects on the computability of queries. To illustrate the ideas and how they can be used in practice for designing appropriate Web query languages, we consider a particular query language, the Web calculus, an abstraction and extension of the practical Web query language WebSQL.
108 citations
Book•
30 Apr 1996
TL;DR: Sigmadefinability and the Godel Incompleteness Theorem, and Computability on Admissible Sets.
Abstract: Sigmadefinability and the Godel Incompleteness Theorem. Computability on Admissible Sets. Selected Topics. Appendix. Index.
107 citations
TL;DR: It is shown that augmenting those postulates about algorithmic computation with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's Thesis, as Gödel and others suggested may be possible.
Abstract: Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's Thesis, as Godel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and—in particular—the effectively-computable functions on string representations of numbers.
104 citations
Journal Article•
TL;DR: A detailed treatment of the ``bit-model'' of computability and complexity of real functions and subsets of R^n, and it is argued that this is a good way to formalize many problems of scientific computation.
Abstract: We give a detailed treatment of the ``bit-model'' of computability and complexity of real functions and subsets of R^n, and argue that this is a good way to formalize many problems of scientific computation. In the introduction we also discuss the alternative Blum-Shub-Smale model. In the final section we discuss the issue of whether physical systems could defeat the Church-Turing Thesis.
104 citations