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Computability

About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.


Papers
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Journal ArticleDOI
TL;DR: The background to the project is explained and a first-order proof in Isabelle/HOL of the theorem “no inertial observer can travel faster than light” is demonstrated.
Abstract: Logicians at the Renyi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first-order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally unsolvable questions such as the Halting Problem and the consistency of set theory. As part of a joint project, researchers at Sheffield have recently started generating rigorous machine-verified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate a first-order proof in Isabelle/HOL of the theorem "no inertial observer can travel faster than light". This approach to physical theories and physical computability has several pay-offs, because the precision with which physical theories need to be formalised within automated proof systems forces us to recognise subtly hidden assumptions.

18 citations

Journal ArticleDOI
01 Nov 1989

18 citations

Book ChapterDOI
14 Jun 2011
TL;DR: Some decidable and undecidable problems closely related to PB-realizability problem are presented thus demonstrating its 'borderline' status with respect to computability.
Abstract: The chamber hitting problem (CHP) for linear maps consists in checking whether an orbit of a linear map specified by a rational matrix hits a given rational polyhedral set. The CHP generalizes some wellknown open computability problems about linear recurrent sequences (e.g., the Skolem problem, the nonnegativity problem). It is recently shown that the CHP is Turing equivalent to checking whether an intersection of a regular language and the special language of permutations of binary words (the permutation filter) is nonempty (PB-realizability problem). In this paper we present some decidable and undecidable problems closely related to PB-realizability problem thus demonstrating its 'borderline' status with respect to computability.

18 citations

Book ChapterDOI
08 Jun 2005
TL;DR: This paper extends the logical approach to computable analysis via Σ–definability to higher type continuous data such as functionals and operators to introduce computation of functionals from arbitrary domain to the real numbers.
Abstract: This paper extends the logical approach to computable analysis via Σ–definability to higher type continuous data such as functionals and operators. We employ definability theory to introduce computability of functionals from arbitrary domain to the real numbers. We show how this concept works in particular cases.

18 citations

Journal ArticleDOI
01 May 2002
TL;DR: Simulations work in practice because they exploit higher-level organizing principles in nature as discussed by the authors, and good code writing requires faithfulness to these principles and the discipline not to exceed their limits of validity.
Abstract: Simulations work in practice because they exploit higher-level organizing principles in nature. Good code writing requires faithfulness to these principles and the discipline not to exceed their limits of validity. An important exception is the use of simulation to search for new kinds of emergence.

18 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202344
2022119
202189
202098
2019111
201897