3,461 research outputs found
Metric complements of overt closed sets
We show that the set of points of an overt closed subspace of a metric
completion of a Bishop-locally compact metric space is located. Consequently,
if the subspace is, moreover, compact, then its collection of points is Bishop
compact.Comment: 9 pages, 1 figur
The descriptive theory of represented spaces
This is a survey on the ongoing development of a descriptive theory of
represented spaces, which is intended as an extension of both classical and
effective descriptive set theory to deal with both sets and functions between
represented spaces. Most material is from work-in-progress, and thus there may
be a stronger focus on projects involving the author than an objective survey
would merit.Comment: survey of work-in-progres
Ellipsis, economy, and the (non)uniformity of traces
A number of works have attempted to account for the interaction between movement and ellipsis in terms of an economy condition Max- Elide. We show that the elimination of MaxElide leads to an empirically superior account of these interactions. We show that a number of the core effects attributed to MaxElide can be accounted for with a parallelism condition on ellipsis. The remaining cases are then treated with a generalized economy condition that favors shorter derivations over longer ones. The resulting analysis has no need for the ellipsisspecific economy constraint MaxElide
Continuous Team Semantics
Peer reviewe
Computing Haar Measures
According to Haar's Theorem, every compact group admits a unique
(regular, right and) left-invariant Borel probability measure . Let the
Haar integral (of ) denote the functional integrating any continuous function with
respect to . This generalizes, and recovers for the additive group
, the usual Riemann integral: computable (cmp. Weihrauch 2000,
Theorem 6.4.1), and of computational cost characterizing complexity class
#P (cmp. Ko 1991, Theorem 5.32). We establish that in fact every computably
compact computable metric group renders the Haar integral computable: once
asserting computability using an elegant synthetic argument, exploiting
uniqueness in a computably compact space of probability measures; and once
presenting and analyzing an explicit, imperative algorithm based on 'maximum
packings' with rigorous error bounds and guaranteed convergence. Regarding
computational complexity, for the groups and
we reduce the Haar integral to and from Euclidean/Riemann
integration. In particular both also characterize #P. Implementation and
empirical evaluation using the iRRAM C++ library for exact real computation
confirms the (thus necessary) exponential runtime
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