5,312 research outputs found
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
On the confluence of lambda-calculus with conditional rewriting
The confluence of untyped \lambda-calculus with unconditional rewriting is
now well un- derstood. In this paper, we investigate the confluence of
\lambda-calculus with conditional rewriting and provide general results in two
directions. First, when conditional rules are algebraic. This extends results
of M\"uller and Dougherty for unconditional rewriting. Two cases are
considered, whether \beta-reduction is allowed or not in the evaluation of
conditions. Moreover, Dougherty's result is improved from the assumption of
strongly normalizing \beta-reduction to weakly normalizing \beta-reduction. We
also provide examples showing that outside these conditions, modularity of
confluence is difficult to achieve. Second, we go beyond the algebraic
framework and get new confluence results using a restricted notion of
orthogonality that takes advantage of the conditional part of rewrite rules
Rewriting Modulo \beta in the \lambda\Pi-Calculus Modulo
The lambda-Pi-calculus Modulo is a variant of the lambda-calculus with
dependent types where beta-conversion is extended with user-defined rewrite
rules. It is an expressive logical framework and has been used to encode logics
and type systems in a shallow way. Basic properties such as subject reduction
or uniqueness of types do not hold in general in the lambda-Pi-calculus Modulo.
However, they hold if the rewrite system generated by the rewrite rules
together with beta-reduction is confluent. But this is too restrictive. To
handle the case where non confluence comes from the interference between the
beta-reduction and rewrite rules with lambda-abstraction on their left-hand
side, we introduce a notion of rewriting modulo beta for the lambda-Pi-calculus
Modulo. We prove that confluence of rewriting modulo beta is enough to ensure
subject reduction and uniqueness of types. We achieve our goal by encoding the
lambda-Pi-calculus Modulo into Higher-Order Rewrite System (HRS). As a
consequence, we also make the confluence results for HRSs available for the
lambda-Pi-calculus Modulo.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759
Deciding Confluence and Normal Form Properties of Ground Term Rewrite Systems Efficiently
It is known that the first-order theory of rewriting is decidable for ground
term rewrite systems, but the general technique uses tree automata and often
takes exponential time. For many properties, including confluence (CR),
uniqueness of normal forms with respect to reductions (UNR) and with respect to
conversions (UNC), polynomial time decision procedures are known for ground
term rewrite systems. However, this is not the case for the normal form
property (NFP). In this work, we present a cubic time algorithm for NFP, an
almost cubic time algorithm for UNR, and an almost linear time algorithm for
UNC, improving previous bounds. We also present a cubic time algorithm for CR
Hopping magneto-transport via nonzero orbital momentum states and organic magnetoresistance
In hopping magnetoresistance of doped insulators, an applied magnetic field
shrinks the electron (hole) s-wave function of a donor or an acceptor and this
reduces the overlap between hopping sites resulting in the positive
magnetoresistance quadratic in a weak magnetic field, B. We extend the theory
of hopping magnetoresistance to states with nonzero orbital momenta. Different
from s-states, a weak magnetic field expands the electron (hole) wave functions
with positive magnetic quantum numbers, m > 0, and shrinks the states with
negative m in a wide region outside the point defect. This together with a
magnetic-field dependence of injection/ionization rates results in a negative
weak-field magnetoresistance, which is linear in B when the orbital degeneracy
is lifted. The theory provides a possible explanation of a large low-field
magnetoresistance in disordered pi-conjugated organic materials (OMAR).Comment: 4 pages, 3 figure
Influence of junction angle on three-dimensional flow structure and bed morphology at confluent meander bends during different hydrological conditions
© 2014 John Wiley & Sons, Ltd. Recent field and modeling investigations have examined the fluvial dynamics of confluent meander bends where a straight tributary channel enters a meandering river at the apex of a bend with a 90° junction angle. Past work on confluences with asymmetrical and symmetrical planforms has shown that the angle of tributary entry has a strong influence on mutual deflection of confluent flows and the spatial extent of confluence hydrodynamic and morphodynamic features. This paper examines three-dimensional flow structure and bed morphology for incoming flows with high and low momentum-flux ratios at two large, natural confluent meander bends that have different tributary entry angles. At the high-angle (90°) confluent meander bend, mutual deflection of converging flows abruptly turns fluid from the lateral tributary into the downstream channel and flow in the main river is deflected away from the outer bank of the bend by a bar that extends downstream of the junction corner along the inner bank of the tributary. Two counter-rotating helical cells inherited from upstream flow curvature flank the mixing interface, which overlies a central pool. A large influx of sediment to the confluence from a meander cutoff immediately upstream has produced substantial morphologic change during large, tributary-dominant discharge events, resulting in displacement of the pool inward and substantial erosion of the point bar in the main channel. In contrast, flow deflection is less pronounced at the low-angle (36°) confluent meander bend, where the converging flows are nearly parallel to one another upon entering the confluence. A large helical cell imparted from upstream flow curvature in the main river occupies most of the downstream channel for prevailing low momentum-flux ratio conditions and a weak counter-rotating cell forms during infrequent tributary-dominant flow events. Bed morphology remains relatively stable and does not exhibit extensive scour that often occurs at confluences with concordant beds
S=1 kagom\'e Ising model with triquadratic interactions, single-ion anisotropy and magnetic field: exact phase diagrams
We consider a S=1 kagom\'e Ising model with triquadratic interactions around
each triangular face of the kagom\'e lattice, single-ion anisotropy and an
applied magnetic field. A mapping establishes an equivalence between the
magnetic canonical partition function of the model and the grand canonical
partition function of a kagom\'e lattice-gas model with localized
three-particle interactions. Since exact phase diagrams are known for
condensation in the one-parameter lattice-gas model, the mapping directly
provides the corresponding exact phase diagrams of the three-parameter S=1
Ising model. As anisotropy competes with interactions, results include the
appearance of confluent singularities effecting changes in the topology of the
phase diagrams, phase boundary curves (magnetic field vs temperature) with
purely positive or negative slopes as well as intermediate cases showing
nonmonotonicity, and coexistence curves (magnetization vs temperature) with
varying shapes and orientations, in some instances entrapping a homogeneous
phase.Comment: 14 pages plus 11 figures; to be published in Physica
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