10,717 research outputs found
The statistical mechanics of turbo codes
The "turbo codes", recently proposed by Berrou et. al. are written as a
disordered spin Hamiltonian. It is shown that there is a threshold Theta such
that for signal to noise ratios v^2 / w^2 > Theta, the error probability per
bit vanishes in the thermodynamic limit, i.e. the limit of infinitly long
sequences. The value of the threshold has been computed for two particular
turbo codes. It is found that it depends on the code. These results are
compared with numerical simulations.Comment: 23 pages, 6 figures: Fig.2 has been replaced (in the preceding
version it was identical to Fig.1
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
Temporalized logics and automata for time granularity
Suitable extensions of the monadic second-order theory of k successors have
been proposed in the literature to capture the notion of time granularity. In
this paper, we provide the monadic second-order theories of downward unbounded
layered structures, which are infinitely refinable structures consisting of a
coarsest domain and an infinite number of finer and finer domains, and of
upward unbounded layered structures, which consist of a finest domain and an
infinite number of coarser and coarser domains, with expressively complete and
elementarily decidable temporal logic counterparts.
We obtain such a result in two steps. First, we define a new class of
combined automata, called temporalized automata, which can be proved to be the
automata-theoretic counterpart of temporalized logics, and show that relevant
properties, such as closure under Boolean operations, decidability, and
expressive equivalence with respect to temporal logics, transfer from component
automata to temporalized ones. Then, we exploit the correspondence between
temporalized logics and automata to reduce the task of finding the temporal
logic counterparts of the given theories of time granularity to the easier one
of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym:
TPLP Category: Paper for Special Issue (Verification and Computational Logic)
Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September
200
Begin, After, and Later: a Maximal Decidable Interval Temporal Logic
Interval temporal logics (ITLs) are logics for reasoning about temporal
statements expressed over intervals, i.e., periods of time. The most famous ITL
studied so far is Halpern and Shoham's HS, which is the logic of the thirteen
Allen's interval relations. Unfortunately, HS and most of its fragments have an
undecidable satisfiability problem. This discouraged the research in this area
until recently, when a number non-trivial decidable ITLs have been discovered.
This paper is a contribution towards the complete classification of all
different fragments of HS. We consider different combinations of the interval
relations Begins, After, Later and their inverses Abar, Bbar, and Lbar. We know
from previous works that the combination ABBbarAbar is decidable only when
finite domains are considered (and undecidable elsewhere), and that ABBbar is
decidable over the natural numbers. We extend these results by showing that
decidability of ABBar can be further extended to capture the language
ABBbarLbar, which lays in between ABBar and ABBbarAbar, and that turns out to
be maximal w.r.t decidability over strongly discrete linear orders (e.g. finite
orders, the naturals, the integers). We also prove that the proposed decision
procedure is optimal with respect to the complexity class
Retrieving information from a noisy "knowledge network"
We address the problem of retrieving information from a noisy version of the
``knowledge networks'' introduced by Maslov and Zhang. We map this problem onto
a disordered statistical mechanics model, which opens the door to many
analytical and numerical approaches. We give the replica symmetric solution,
compare with numerical simulations, and finally discuss an application to real
datas from the United States Senate.Comment: 10 pages, 4 figures. Writing of the last section improved; version
accepted in JSTA
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
Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality
We consider a family of vector fields defined in some bounded domain of R^p,
and we assume that they satisfy Hormander's rank condition of some step r, and
that their coefficients have r-1 continuous derivatives. We extend to this
nonsmooth context some results which are well-known for smooth Hormander's
vector fields, namely: some basic properties of the distance induced by the
vector fields, the doubling condition, Chow's connectivity theorem, and, under
the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's
inequality. By known results, these facts also imply a Sobolev embedding. All
these tools allow to draw some consequences about second order differential
operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous
version) changed. Some references adde
Investigation of dominant hydrological processes in a tropical catchment in a monsoonal climate via the downward approach
International audienceThis study explores the dominant processes that may be responsible for the observed streamflow response in Seventeen Mile Creek, a tropical catchment located in a monsoonal climate in Northern Territory, Australia. The hydrology of this vast region of Australia is little understood due to the low level of information and gauging that is available. Any insights that can be gained from the few well gauged catchments that exist can be valuable for predictions and water resource assessments in other poorly gauged or ungauged catchments in the region. To this end, the available rainfall and runoff data from Seventeen Mile Creek catchment are analyzed through the systematic and progressive development and testing of rainfall-runoff models of increasing complexity, by following the "downward" or "top-down" approach. At the end a multiple bucket model (4 buckets in parallel) is developed. Modelling results suggest that the catchment's soils and the landscape in general have a high storage capacity, generating a significant fraction of delayed runoff, whereas saturation excess overland flow occurs only after heavy rainfall events. The sensitivity analyses carried out with the model with regard to soil depth and temporal rainfall variability reveal that total runoff from the catchment is more sensitive to rainfall variations than to soil depth variations, whereas the partitioning into individual components of runoff appears to be more influenced by soil depth variations. The catchment exhibits considerable inter-annual variability in runoff volumes and the greatest determinant of this variability turns out to be the seasonality of the climate, the timing of the wet season, and temporal patterns of the rainfall. The water balance is also affected by the underlying geology, nature of the soils and the landforms, and the type, density and dynamics of vegetation, although, information pertaining to these is lacking
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