8,879 research outputs found

    Complexity of ITL model checking: some well-behaved fragments of the interval logic HS

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    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

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    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

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    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"

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    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

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    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

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    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

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    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

    Hydrology of the Po River: looking for changing patterns in river discharge

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    Abstract. Scientists and public administrators are devoting increasing attention to the Po River, in Italy, in view of concerns related to the impact of increasing urbanisation and exploitation of water resources. A better understanding of the hydrological regime of the river is necessary to improve water resources management and flood protection. In particular, the analysis of the effects of hydrological and climatic change is crucial for planning sustainable development and economic growth. An extremely interesting issue is to inspect to what extent river flows can be naturally affected by the occurrence of long periods of water abundance or scarcity, which can be erroneously interpreted as irreversible changes due to human impact. In fact, drought and flood periods alternatively occurred in the recent past in the form of long-term fluctuations. This paper presents advanced graphical and analytical methods to gain a better understanding of the temporal distribution of the Po River discharge. In particular, we present an analysis of river flow variability and persistence properties, to gain a better understanding of natural patterns, and in particular long-term changes, which may affect the future flood risk and availability of water resources
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