5,823 research outputs found
Locality of Queries and Transformations
Locality is a standard notion of finite model theory. There are two well known flavors of it, based on Hanfâs and Gaifmanâs theorems. Essentially they say that structures that locally look alike cannot be distinguished by first-order sentences. Very recently these standard notions have been generalized in two ways. The first extension makes the notion of âlooking alike â depend on logical indistinguishability, rather than isomorphism, of local neighborhoods. The second extension considers transformations defined by FO formulae, and requires that small neighborhoods be preserved by those transformations. In this survey we explain these new notions â as well as the standard ones â and show how they behave with respect to Hanfâs and Gaifmanâs conditions
Deductive Optimization of Relational Data Storage
Optimizing the physical data storage and retrieval of data are two key
database management problems. In this paper, we propose a language that can
express a wide range of physical database layouts, going well beyond the row-
and column-based methods that are widely used in database management systems.
We use deductive synthesis to turn a high-level relational representation of a
database query into a highly optimized low-level implementation which operates
on a specialized layout of the dataset. We build a compiler for this language
and conduct experiments using a popular database benchmark, which shows that
the performance of these specialized queries is competitive with a
state-of-the-art in memory compiled database system
Computation in generalised probabilistic theories
From the existence of an efficient quantum algorithm for factoring, it is
likely that quantum computation is intrinsically more powerful than classical
computation. At present, the best upper bound known for the power of quantum
computation is that BQP is in AWPP. This work investigates limits on
computational power that are imposed by physical principles. To this end, we
define a circuit-based model of computation in a class of operationally-defined
theories more general than quantum theory, and ask: what is the minimal set of
physical assumptions under which the above inclusion still holds? We show that
given only an assumption of tomographic locality (roughly, that multipartite
states can be characterised by local measurements), efficient computations are
contained in AWPP. This inclusion still holds even without assuming a basic
notion of causality (where the notion is, roughly, that probabilities for
outcomes cannot depend on future measurement choices). Following Aaronson, we
extend the computational model by allowing post-selection on measurement
outcomes. Aaronson showed that the corresponding quantum complexity class is
equal to PP. Given only the assumption of tomographic locality, the inclusion
in PP still holds for post-selected computation in general theories. Thus in a
world with post-selection, quantum theory is optimal for computation in the
space of all general theories. We then consider if relativised complexity
results can be obtained for general theories. It is not clear how to define a
sensible notion of an oracle in the general framework that reduces to the
standard notion in the quantum case. Nevertheless, it is possible to define
computation relative to a `classical oracle'. Then, we show there exists a
classical oracle relative to which efficient computation in any theory
satisfying the causality assumption and tomographic locality does not include
NP.Comment: 14+9 pages. Comments welcom
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