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

On the Complexity of the Equivalence Problem for Probabilistic Automata

Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test based on polynomial identity testing outperformed deterministic algorithms. In this paper we show that polynomial identity testing yields efficient algorithms for various generalisations of the equivalence problem. First, we provide a randomized NC procedure that also outputs a counterexample trace in case of inequivalence. Second, we show how to check for equivalence two probabilistic automata with (cumulative) rewards. Our algorithm runs in deterministic polynomial time, if the number of reward counters is fixed. Finally we show that the equivalence problem for probabilistic visibly pushdown automata is logspace equivalent to the Arithmetic Circuit Identity Testing problem, which is to decide whether a polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape

Contextual equivalence for state and control via nested data

We consider contextual equivalence in an ML-like language, where contexts have access to both general references and continuations. We show that in a finitary setting, i.e. when the base types are finite and there is no recursion, the problem is decidable for all programs with first-order references and continuations, assuming they have continuation- and reference-free interfaces. This is the best one can hope for in this case, because the addition of references to functions, to continuations or to references makes the problem undecidable. The result is notable since, unlike earlier work in the area, we need not impose any restrictions on type-theoretic order or the use of first-order references inside terms. In particular, the programs concerned can generate unbounded heaps. Our decidability argument relies on recasting the corresponding fully abstract trace semantics of terms as instances of automata with a decidable equivalence problem. The automata used for this purpose belong to the family of automata over infinite alphabets (aka data automata), where the infinite alphabet (dataset) has the shape of a forest

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

Saturating automata for game semantics

Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition that program moves (P-moves) may depend only on moves made by the environment (O-moves). We propose an automata model over an infinite alphabet, called saturating automata, for which all accepted languages are guaranteed to satisfy a closure property mimicking saturation. We show how to translate the finitary fragment of Idealized Concurrent Algol (FICA) into saturating automata, confirming their suitability for modelling higher-order concurrency. Moreover, we find that, for terms in normal form, the resultant automaton has linearly many transitions and states with respect to term size, and can be constructed in polynomial time. This is in contrast to earlier attempts at finding automata-theoretic models of FICA, which did not guarantee saturation and involved an exponential blow-up during translation, even for normal forms.Comment: Presented at MFPS 202

Numerical Simulations of Mass Loading in the Solar Wind Interaction with Venus

Numerical simulations are performed in the framework of nonlinear two-dimensional magnetohydrodynamics to investigate the influence of mass loading on the solar wind interaction with Venus. The principal physical features of the interaction of the solar wind with the atmosphere of Venus are presented. The formation of the bow shock, the magnetic barrier, and the magnetotail are some typical features of the interaction. The deceleration of the solar wind due to the mass loading near Venus is an additional feature. The effect of the mass loading is to push the shock farther outward from the planet. The influence of different values of the magnetic field strength on plasma evolution is considered

3D numerical simulations of propagating two-fluid, torsional Alfv\'en waves and heating of a partially-ionized solar chromosphere

We present a new insight into the propagation, attenuation and dissipation of two-fluid, torsional Alfv\'en waves in the context of heating of the lower solar atmosphere. By means of numerical simulations of the partially-ionized plasma, we solve the set of two-fluid equations for ion plus electron and neutral fluids in three-dimensional (3D) Cartesian geometry. We implement initially a current-free magnetic field configuration, corresponding to a magnetic flux-tube that is rooted in the solar photosphere and expands into the chromosphere and corona. We put the lower boundary of our simulation region in the low chromosphere, where ions and neutrals begin to decouple, and implement there a monochromatic driver that directly generates Alfv\'en waves with a wave period of 30 s. As the ion-neutral drift increases with height, the two-fluid effects become more significant and the energy carried by both Alfv\'en and magneto-acoustic waves can be thermalized in the process of ion-neutral collisions there. In fact, we observe a significant increase in plasma temperature along the magnetic flux-tube. In conclusion, the two-fluid torsional Alfv\'en waves can potentially play a role in the heating of the solar chromosphere.Comment: 10 pages, 7 figure

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

Exact Bayesian Inference on Discrete Models via Probability Generating Functions: A Probabilistic Programming Approach

We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to many discrete inference problems, even with infinite support and continuous priors. To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on events. Our key tool is probability generating functions: they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments. Our inference method is provably correct, fully automated and uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra. Our experiments show that its performance on a range of real-world examples is competitive with approximate Monte Carlo methods, while avoiding approximation errors