1,311 research outputs found
Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism
We give extensional and intensional characterizations of nondeterministic
functional programs: as structure preserving functions between biorders, and as
nondeterministic sequential algorithms on ordered concrete data structures
which compute them. A fundamental result establishes that the extensional and
intensional representations of non-deterministic programs are equivalent, by
showing how to construct a unique sequential algorithm which computes a given
monotone and stable function, and describing the conditions on sequential
algorithms which correspond to continuity with respect to each order.
We illustrate by defining may and must-testing denotational semantics for a
sequential functional language with bounded and unbounded choice operators. We
prove that these are computationally adequate, despite the non-continuity of
the must-testing semantics of unbounded nondeterminism. In the bounded case, we
prove that our continuous models are fully abstract with respect to may and
must-testing by identifying a simple universal type, which may also form the
basis for models of the untyped lambda-calculus. In the unbounded case we
observe that our model contains computable functions which are not denoted by
terms, by identifying a further "weak continuity" property of the definable
elements, and use this to establish that it is not fully abstract
Predicative toposes
We explain the motivation for looking for a predicative analogue of the
notion of a topos and propose two definitions. For both notions of a
predicative topos we will present the basic results, providing the groundwork
for future work in this area
Calculus of functors and model categories II
This is a continuation, completion, and generalization of our previous joint
work with B. Chorny. We supply model structures and Quillen equivalences
underlying Goodwillie's constructions on the homotopy level for functors
between simplicial model categories satisfying mild hypotheses.Comment: 47 pages. Version 3 contains a new introduction and further small
changes, based on suggestions of the referee. To appear in "Algebraic and
Geometric Topology
Some remarks on the local class field theory of Serre and Hazewinkel
We give a new approach for the local class field theory of Serre and
Hazewinkel. We also discuss two-dimensional local class field theory in this
framework.Comment: 23 pages; final versio
Lower and Upper Conditioning in Quantum Bayesian Theory
Updating a probability distribution in the light of new evidence is a very
basic operation in Bayesian probability theory. It is also known as state
revision or simply as conditioning. This paper recalls how locally updating a
joint state can equivalently be described via inference using the channel
extracted from the state (via disintegration). This paper also investigates the
quantum analogues of conditioning, and in particular the analogues of this
equivalence between updating a joint state and inference. The main finding is
that in order to obtain a similar equivalence, we have to distinguish two forms
of quantum conditioning, which we call lower and upper conditioning. They are
known from the literature, but the common framework in which we describe them
and the equivalence result are new.Comment: In Proceedings QPL 2018, arXiv:1901.0947
Derived moduli of complexes and derived Grassmannians
In the first part of this paper we construct a model structure for the
category of filtered cochain complexes of modules over some commutative ring
and explain how the classical Rees construction relates this to the usual
projective model structure over cochain complexes. The second part of the paper
is devoted to the study of derived moduli of sheaves: we give a new proof of
the representability of the derived stack of perfect complexes over a proper
scheme and then use the new model structure for filtered complexes to tackle
moduli of filtered derived modules. As an application, we construct derived
versions of Grassmannians and flag varieties.Comment: 54 pages, Section 2.4 significantly extended, minor corrections to
the rest of the pape
Relative Riemann-Zariski spaces
In this paper we study relative Riemann-Zariski spaces attached to a morphism
of schemes and generalizing the classical Riemann-Zariski space of a field. We
prove that similarly to the classical RZ spaces, the relative ones can be
described either as projective limits of schemes in the category of locally
ringed spaces or as certain spaces of valuations. We apply these spaces to
prove the following two new results: a strong version of stable modification
theorem for relative curves; a decomposition theorem which asserts that any
separated morphism between quasi-compact and quasi-separated schemes factors as
a composition of an affine morphism and a proper morphism. (In particular, we
obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat
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