Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)

We consider the problem of verifying liveness for systems with a finite, but unbounded, number of processes, commonly known as parameterised systems. Typical examples of such systems include distributed protocols (e.g. for the dining philosopher problem). Unlike the case of verifying safety, proving liveness is still considered extremely challenging, especially in the presence of randomness in the system. In this paper we consider liveness under arbitrary (including unfair) schedulers, which is often considered a desirable property in the literature of self-stabilising systems. We introduce an automatic method of proving liveness for randomised parameterised systems under arbitrary schedulers. Viewing liveness as a two-player reachability game (between Scheduler and Process), our method is a CEGAR approach that synthesises a progress relation for Process that can be symbolically represented as a finite-state automaton. The method is incremental and exploits both Angluin-style L*-learning and SAT-solvers. Our experiments show that our algorithm is able to prove liveness automatically for well-known randomised distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon Protocol). To the best of our knowledge, this is the first fully-automatic method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape

Decidability and Complexity of Tree Share Formulas

Fractional share models are used to reason about how multiple actors share ownership of resources. We examine the decidability and complexity of reasoning over the "tree share" model of Dockins et al. using first-order logic, or fragments thereof. We pinpoint a connection between the basic operations on trees union, intersection, and complement and countable atomless Boolean algebras, allowing us to obtain decidability with the precise complexity of both first-order and existential theories over the tree share model with the aforementioned operations. We establish a connection between the multiplication operation on trees and the theory of word equations, allowing us to derive the decidability of its existential theory and the undecidability of its full first-order theory. We prove that the full first-order theory over the model with both the Boolean operations and the restricted multiplication operation (with constants on the right hand side) is decidable via an embedding to tree-automatic structures

A model study of the effects of climatic precipitation changes on ground temperatures

Temperature changes at the Earth surface propagate into the subsurface and leave a thermal signature in the underlying soil and rock. Inversions of subsurface temperature measurements yield reconstructions of ground surface temperature (GST) histories that provide estimates of climatic changes. A question remaining in the interpretation of reconstructed GST histories is the extent to which GST changes reflect changes principally in surface air temperature (SAT), or whether other factors may be significant. Here we use a Land Surface Processes (LSP) model to examine the influence of precipitation changes on GST and subsurface temperature and moisture fields on annual to decadal timescales. We model soil and vegetation conditions representative of a prairie region in the southern Great Plains of North America and force the model with meteorological data synthesized from a typical year in the region. Model responses are observed after changes in the amount of daily precipitation, the intensity and frequency of daily precipitation, and the diurnal and seasonal timing of precipitation. We show that: (1) increasing daily precipitation cools mean annual GST, (2) increasing the intensity and reducing the frequency of daily precipitation, while holding the annual amount of precipitation constant, cools mean annual GST, and (3) shifting maximum precipitation to occur in the warmest months cools mean annual GST. We compare modeled results to observed precipitation changes during the 20th century and conclude that the observed precipitation changes would cause only small changes to GST within the modeled region, on the order of 0.1 K or less

The Influence of Soil Moisture Upon the Geothermal Climate Signal

Estimates of regional climate warming over the past few hundred years are being obtained from profiles of borehole temperature versus depth. The assumptions in recovering mean annual Surface Air Temperature (SAT) are that the relationship between the Ground Surface Temperature (GST) and the temperature-depth profile is purely conductive, and that SAT is uniquely coupled to GST. While these assumptions have been demonstrated to be approximately valid, they ignore the role of moisture transport in soil between soil and atmosphere. In this study we examine the influence of climatic changes in precipitation upon mean annual GST with climatic SAT held constant. We use the most recent version of our Prairie SVAT model for a set of 80 years simulations. Our findings are 10 increasing precipitation reduces mean annual GST, 2) phasing maximum precipitation to occur during the warmest months reduces mean annual GST, and 3) increasing the variance of precipitation reduces mean annual GST. The amplitudes of the effects are small but potentially not insignificant fractions of the geothermal climate signal. One of the long-term objectives of this investigation is to use global EOS SAT and remotely sensed soil moisture to link region-specific, geothermal climate signal histories to evolution of regional climate

Comparing Lumped and Distributed Model in Hydrological Services - Impacts of Climate Change - a Case Study in Taiwan

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive