Ana Sokolova

Probabilistic automata : system types, parallel composition and comparison

We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models. We overview probabilistic systems with discrete probabilities only. The expressiveness order used to built the hierarchy is defined via the existence of mappings between the corresponding system types that preserve and reflect bisimilarity. Additionally, we discuss parallel composition for the presented types of systems, augmenting the map of probabilistic automata with closedness under this compositional operator.

A hierarchy of probabilistic system types

Abstract We arrange various types of probabilistic transition systems studied in the literature in an expressiveness hierarchy. The expressiveness criterion is the existence of an embedding of systems of the one class into those of the other. An embedding here is a system transformation which preserves and reflects bisimilarity. To facilitate the task, we define the classes of systems and the corresponding notion of bisimilarity coalgebraically and use the new technical result that an embedding arises from a natural transformation with injective components between the two coalgebra functors under consideration. Moreover, we argue that coalgebraic bisimilarity, on which we base our results, coincides with the concrete notions proposed in the literature for the different system classes, exemplified by a detailed proof for the case of general Segala-type systems.

Probabilistic systems coalgebraically

We survey the work on both discrete and continuous-space probabilistic systems as coalgebras, starting with how probabilistic systems are modeled as coalgebras and followed by a discussion of their bisimilarity and behavioral equivalence, mentioning results that follow from the coalgebraic treatment of probabilistic systems. It is interesting to note that, for different reasons, for both discrete and continuous probabilistic systems it may be more convenient to work with behavioral equivalence than with bisimilarity.

Exemplaric Expressivity of Modal Logics

This article investigates expressivity of modal logics for transition systems, multitransition systems, Markov chains and Markov processes, as coalgebras of the powerset, finitely supported multiset, finitely supported distribution and measure functor, respectively. Expressivity means that logically indistinguishable states, satisfying the same formulas, are behaviourally indistinguishable. The investigation is based on the framework of dual adjunctions between spaces and logics and focuses on a crucial injectivity property. The approach is generic both in the choice of systems and modalities, and in the choice of a ‘base logic’. Most of these expressivity results are already known, but the applicability of the uniform setting of dual adjunctions to these particular examples is what constitutes the contribution of the article.

Trace Semantics via Determinization

This paper takes a fresh look at the topic of trace semantics in the theory of coalgebras. The first development of coalgebraic trace semantics used final coalgebras in Kleisli categories, stemming from an initial algebra in the underlying category. This approach requires some non-trivial assumptions, like dcpo enrichment, which do not always hold, even in cases where one can reasonably speak of traces (like for weighted automata). More recently, it has been noticed that trace semantics can also arise by first performing a determinization construction. In this paper, we develop a systematic approach, in which the two approaches correspond to different orders of composing a functor and a monad, and accordingly, to different distributive laws. The relevant final coalgebra that gives rise to trace semantics does not live in a Kleisli category, but more generally, in a category of Eilenberg-Moore algebras. In order to exploit its finality, we identify an extension operation, that changes the state space of a coalgebra into a free algebra, which abstractly captures determinization of automata. Notably, we show that the two different views on trace semantics are equivalent, in the examples where both approaches are applicable.

Information hiding in probabilistic concurrent systems

Information hiding is a general concept which refers to the goal of preventing an adversary to infer secret information from the observables. Anonymity and Information Flow are examples of this notion. We study the problem of information hiding in systems characterized by the presence of randomization and concurrency. It is well known that the raising of nondeterminism, due to the possible interleavings and interactions of the parallel components, can cause unintended information leaks. One way to solve this problem is to fix the strategy of the scheduler beforehand. In this work, we propose a milder restriction on the schedulers, and we define the notion of strong (probabilistic) information hiding under various notions of observables. Furthermore, we propose a method, based on the notion of automorphism, to verify that a system satisfies the property of strong information hiding, namely strong anonymity or no-interference, depending on the context.

Distributed queues in shared memory: multicore performance and scalability through quantitative relaxation

A prominent remedy to multicore scalability issues in concurrent data structure implementations is to relax the sequential specification of the data structure. We present distributed queues (DQ), a new family of relaxed concurrent queue implementations. DQs implement relaxed queues with linearizable emptiness check and either configurable or bounded out-of-order behavior or pool behavior. Our experiments show that DQs outperform and outscale in micro- and macrobenchmarks all strict and relaxed queue as well as pool implementations that we considered.

The Logical Execution Time Paradigm

Since its introduction in 2000 in the time-triggered programming language Giotto, the Logical Execution Time (LET) paradigm has evolved from a highly controversial idea to a well-understood principle of real-time programming. This chapter provides an easy-to-read overview of LET programming languages and runtime systems as well as some LET-inspired models of computation. The presentation is intuitive, by example, citing the relevant literature including more formal treatment of the material for reference.

Performance, scalability, and semantics of concurrent FIFO queues

We introduce the notion of a k-FIFO queue which may dequeue elements out of FIFO order up to a constant k≥0. Retrieving the oldest element from the queue may require up to k+1 dequeue operations (bounded lateness), which may return elements not younger than the k+1 oldest elements in the queue (bounded age) or nothing even if there are elements in the queue. A k-FIFO queue is starvation-free for finite k where k+1 is what we call the worst-case semantical deviation (WCSD) of the queue from a regular FIFO queue. The WCSD bounds the actual semantical deviation (ASD) of a k-FIFO queue from a regular FIFO queue when applied to a given workload. Intuitively, the ASD keeps track of the number of dequeue operations necessary to return oldest elements and the age of dequeued elements. We show that a number of existing concurrent algorithms implement k-FIFO queues whose WCSD are determined by configurable constants independent from any workload. We then introduce so-called Scal queues, which implement k-FIFO queues with generally larger, workload-dependent as well as unbounded WCSD. Since ASD cannot be obtained without prohibitive overhead we have developed a tool that computes lower bounds on ASD from time-stamped runs. Our micro- and macrobenchmarks on a state-of-the-art 40-core multiprocessor machine show that Scal queues, as an immediate consequence of their weaker WCSD, outperform and outscale existing implementations at the expense of moderately increased lower bounds on ASD.

Trace semantics via determinization

This paper takes a fresh look at the topic of trace semantics in the theory of coalgebras. In the last few years, two approaches, somewhat incomparable at first sight, captured successfully in a coalgebraic setting trace semantics for various types of transition systems. The first development of coalgebraic trace semantics used final coalgebras in Kleisli categories and required some non-trivial assumptions, which do not always hold, even in cases where one can reasonably speak of traces (like for weighted automata). The second development stemmed from the observation that trace semantics can also arise by performing a determinization construction and used final coalgebras in Eilenberg-Moore categories. In this paper, we develop a systematic study in which the two approaches can be studied and compared. Notably, we show that the two different views on trace semantics are equivalent, in the examples where both approaches are applicable.