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 Jul 2013
TL;DR: A review of a few recent results which look at nonlinear dynamical systems from a computational perspective, especially information concerning their long-term evolution.
Abstract: Nonlinear dynamical systems abound as models of natural phenomena. They are often characterized by highly unpredictable behaviour which is hard to analyze as it occurs, for example, in chaotic systems. A basic problem is to understand what kind of information we can realistically expect to extract from those systems, especially information concerning their long-term evolution. Here we review a few recent results which look at this problem from a computational perspective.
10 citations
01 Nov 2007
TL;DR: In this paper, it was shown that the result of Goncharov/Harizanov/Laskowski/Lempp/McCoy (2003) is best possible for trivial strongly minimal theories in terms of computable model theory.
Abstract: We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes 0". This result shows that the result of Goncharov/Harizanov/Laskowski/Lempp/McCoy (2003) is best possible for trivial strongly minimal theories in terms of computable model theory. We conclude with some remarks about axiomatizability.
10 citations
01 Jan 2007
TL;DR: In this paper, the authors introduce and study a notion of effectivity for test functions and for distributions using the theory of effective (Scott-Ershov) domains and effe...
Abstract: In this thesis we introduce and study a notion of effectivity (or computability) for test functions and for distributions. This is done using the theory of effective (Scott-Ershov) domains and effe ...
9 citations
TL;DR: Two novel computing models based on an infinite tessellation of space-time are introduced, one of which is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets.
Abstract: Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.
9 citations
04 Nov 2013
TL;DR: A domain for string decision variables of bounded length is presented, combining features from fixed-length and unbounded-length string solvers to reason on an interval defined by languages of prefixes and suffixes.
Abstract: We present a domain for string decision variables of bounded length, combining features from fixed-length and unbounded-length string solvers to reason on an interval defined by languages of prefixes and suffixes. We provide a theoretical groundwork for constraint solving on this domain and describe propagation techniques for several common constraints.
9 citations