Fragments of ML Decidable by Nested Data Class Memory Automata

The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a "bad variable" construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at most 1 with free variables of order at most 2, and identify two subfragments of this for which we show observational equivalence to be decidable. The first subfragment consists of those terms in which the P-pointers in the game semantic representation are determined by the underlying sequence of moves. The second subfragment consists of terms in which the O-pointers of moves corresponding to free variables in the game semantic representation are determined by the underlying moves. These results are shown using a reduction to a form of automata over data words in which the data values have a tree-structure, reflecting the tree-structure of the threads in the game semantic plays. In addition we show that observational equivalence is undecidable at every third- or higher-order type, every second-order type which takes at least two first-order arguments, and every second-order type (of arity greater than one) that has a first-order argument which is not the final argument

Bisimilarity of Pushdown Systems is Nonelementary

Given two pushdown systems, the bisimilarity problem asks whether they are bisimilar. While this problem is known to be decidable our main result states that it is nonelementary, improving EXPTIME-hardness, which was the previously best known lower bound for this problem. Our lower bound result holds for normed pushdown systems as well

Asymmetric distances for approximate differential privacy

Differential privacy is a widely studied notion of privacy for various models of computation, based on measuring differences between probability distributions. We consider (epsilon,delta)-differential privacy in the setting of labelled Markov chains. For a given epsilon, the parameter delta can be captured by a variant of the total variation distance, which we call lv_{alpha} (where alpha = e^{epsilon}). First we study lv_{alpha} directly, showing that it cannot be computed exactly. However, the associated approximation problem turns out to be in PSPACE and #P-hard. Next we introduce a new bisimilarity distance for bounding lv_{alpha} from above, which provides a tighter bound than previously known distances while remaining computable with the same complexity (polynomial time with an NP oracle). We also propose an alternative bound that can be computed in polynomial time. Finally, we illustrate the distances on case studies

Stability of an MHD shear flow with a piecewise linear velocity profile

In this paper we present the results of the stability analysis of a simple shear flow of an incompressible fluid with a piecewise linear velocity profile in the presence of a magnetic field. In the flow, a finite transitional magnetic-free layer with a linear velocity profile is sandwiched by two semi-infinite regions. One of these regions is magnetic-free and the flow velocity in the region is constant. The other region is magnetic and the fluid in it is quiescent. The magnetic field is constant and parallel to the flow in the transitional layer. The fluid density is constant both in the magnetic as well as the magnetic-free regions, while it has a jump-type discontinuity at the boundary between the transitional layer and the magnetic region. The effect of gravity is included in the model, and it is assumed that the lighter fluid is overlaying the heavier one, thus no Rayleigh-Taylor instability is present. The dispersion equation governing the normal-mode stability of the flow is derived and its properties are analysed. We study stability of two cases: (i) magnetic-free flow in the presence of gravity, and (ii) magnetic flow without gravity. In the first case, the flow stability is controlled by the Rayleigh number, R. In the second case, the control parameter is the inverse squared Alfvénic Mach number, H . Stability of a particular monochromatic perturbation also depends on its dimensionless wavenumber α. We combine the analytical and numerical approaches to obtain the neutral stability curves in the (α,R)-plane in the case of the magnetic-free flow, and in the (α,H)-plane in the case of the magnetic flow. The dependence of the instability increment on R in the first case, and on H in the second case is treated. We apply the results of the analysis to the stability of a strongly subsonic portion of the heliopause. Our main conclusion is as follows: The inclusion of a transitional layer near the heliopause into the model increases by an order of magnitude the strength of the interstellar magnetic field required to stabilize this portion of the heliopause in comparison with the corresponding stabilizing strength of the magnetic field required when modelling the heliopause as a tangential discontinuity

Higher-order linearisability

Linearisability is a central notion for verifying concurrent libraries: a library is proven correct if its operational history can be rearranged into a sequential one that satisfies a given specification. Until now, linearisability has been examined for libraries in which method arguments and method results were of ground type. In this paper we extend linearisability to the general higher-order setting, where methods of arbitrary type can be passed as arguments and returned as values, and establish its soundness

10252 Executive Summary -- Game Semantics and Program Verification

The seminar took place from 20th until 25th June 2010. Its primary aim was to foster interaction between researchers working on modelling programs/proofs using games and the verification community. The meeting brought together 28 researchers from eight different countries, both junior and senior, for a systematic assessment of what the two areas have to offer to one another, critical evaluation of what has been achieved so far, with a view to establishing common research goals for the future

10252 Abstracts Collection -- Game Semantics and Program Verification

From 20th to 25th June 2010, the Dagstuhl Seminar "Game Semantics and Program Verification\u27\u27 was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Fragments of ML decidable by nested data class memory automata

The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a “bad variable” construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at most 1 with free variables of order at most 2, and identify two subfragments of this for which we show observational equivalence to be decidable. The first subfragment, RMLP−Str2⊢1, consists of those terms in which the P-pointers in the game semantic representation are determined by the underlying sequence of moves. The second subfragment consists of terms in which the O-pointers of moves corresponding to free variables in the game semantic representation are determined by the underlying moves. These results are shown using a reduction to a form of automata over data words in which the data values have a tree-structure, reflecting the tree-structure of the threads in the game semantic plays. In addition we show that observational equivalence is undecidable at every third- or higher-order type, every second-order type which takes at least two first-order arguments, and every second-order type (of arity greater than one) that has a first-order argument which is not the final argument

Propagating transverse waves in soft X-ray coronal jets

Aims. The theoretical model for magnetohydrodynamic (MHD) modes guided by a field-aligned plasma cylinder with a steady flow is adapted to interpret transverse waves observed in solar coronal hot jets, discovered with Hinode/XRT in terms of fast magnetoacoustic kink modes. Methods. Dispersion relations for linear magnetoacoustic perturbations of a plasma jet of constant cross-section surrounded by static magnetised plasma are used to determine the phase and group speeds of guided transverse waves and their relationship with the physical parameters of the jet and the background plasma. The structure of the perturbations in the macroscopic parameters of the plasma inside and outside the jet, and the phase relations between them are also established. Results. We obtained a convenient expansion for the long wave-length limit of the phase and group speeds and have shown that transverse waves observed in soft-X-ray solar coronal jets are adequately described in terms of fast magnetoacoustic kink modes by a magnetic cylinder model, which includes the effect of a steady flow. In the observationally determined range of parameters, the waves are not found to be subject to either the Kelvin-Helmholtz instability or the negative energy wave instability, and hence they are likely to be excited at the source of the jet

Density of States and Conductivity of Granular Metal or Array of Quantum Dots

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in the a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.Comment: 13 pages, 15 figures. Some misprints are fixed. Some figures are dropped. Some small changes are given to improve the organizatio