1,323 research outputs found
Complexity of ITL model checking: some well-behaved fragments of the interval logic HS
Model checking has been successfully used in many computer science fields,
including artificial intelligence, theoretical computer science, and databases.
Most of the proposed solutions make use of classical, point-based temporal
logics, while little work has been done in the interval temporal logic setting.
Recently, a non-elementary model checking algorithm for Halpern and Shoham's
modal logic of time intervals HS over finite Kripke structures (under the
homogeneity assumption) and an EXPSPACE model checking procedure for two
meaningful fragments of it have been proposed. In this paper, we show that more
efficient model checking procedures can be developed for some expressive enough
fragments of HS
Checking Interval Properties of Computations
Model checking is a powerful method widely explored in formal verification.
Given a model of a system, e.g., a Kripke structure, and a formula specifying
its expected behaviour, one can verify whether the system meets the behaviour
by checking the formula against the model.
Classically, system behaviour is expressed by a formula of a temporal logic,
such as LTL and the like. These logics are "point-wise" interpreted, as they
describe how the system evolves state-by-state. However, there are relevant
properties, such as those constraining the temporal relations between pairs of
temporally extended events or involving temporal aggregations, which are
inherently "interval-based", and thus asking for an interval temporal logic.
In this paper, we give a formalization of the model checking problem in an
interval logic setting. First, we provide an interpretation of formulas of
Halpern and Shoham's interval temporal logic HS over finite Kripke structures,
which allows one to check interval properties of computations. Then, we prove
that the model checking problem for HS against finite Kripke structures is
decidable by a suitable small model theorem, and we provide a lower bound to
its computational complexity.Comment: In Journal: Acta Informatica, Springer Berlin Heidelber, 201
Strictly Positive Definite Kernels on a Product of Spheres II
We present, among other things, a necessary and sufficient condition for the
strict positive definiteness of an isotropic and positive definite kernel on
the cartesian product of a circle and a higher dimensional sphere. The result
complements similar results previously obtained for strict positive
definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169]
and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016),
286-301, arXiv:1505.03695]
Effect of assortative mixing in the second-order Kuramoto model
In this paper we analyze the second-order Kuramoto model presenting a
positive correlation between the heterogeneity of the connections and the
natural frequencies in scale-free networks. We numerically show that
discontinuous transitions emerge not just in disassortative but also in
assortative networks, in contrast with the first-order model. We also find that
the effect of assortativity on network synchronization can be compensated by
adjusting the phase damping. Our results show that it is possible to control
collective behavior of damped Kuramoto oscillators by tuning the network
structure or by adjusting the dissipation related to the phases movement.Comment: 7 pages, 6 figures. In press in Physical Review
Low-dimensional behavior of Kuramoto model with inertia in complex networks
Low-dimensional behavior of large systems of globally coupled oscillators has
been intensively investigated since the introduction of the Ott-Antonsen
ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order
Kuramoto models in complex networks. With an additional inertia term, we find a
low-dimensional behavior similar to the first-order Kuramoto model, derive a
self-consistent equation and seek the time-dependent derivation of the order
parameter. Numerical simulations are also conducted to verify our analytical
results.Comment: 6 figure
Spectra of random networks in the weak clustering regime
The asymptotic behaviour of dynamical processes in networks can be expressed
as a function of spectral properties of the corresponding adjacency and
Laplacian matrices. Although many theoretical results are known for the spectra
of traditional configuration models, networks generated through these models
fail to describe many topological features of real-world networks, in
particular non-null values of the clustering coefficient. Here we study effects
of cycles of order three (triangles) in network spectra. By using recent
advances in random matrix theory, we determine the spectral distribution of the
network adjacency matrix as a function of the average number of triangles
attached to each node for networks without modular structure and degree-degree
correlations. Implications to network dynamics are discussed. Our findings can
shed light in the study of how particular kinds of subgraphs influence network
dynamics
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