A Hierarchy of Scheduler Classes for Stochastic Automata

Stochastic automata are a formal compositional model for concurrent stochastic timed systems, with general distributions and non-deterministic choices. Measures of interest are defined over schedulers that resolve the nondeterminism. In this paper we investigate the power of various theoretically and practically motivated classes of schedulers, considering the classic complete-information view and a restriction to non-prophetic schedulers. We prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic reachability. We find that, unlike Markovian formalisms, stochastic automata distinguish most classes even in this basic setting. Verification and strategy synthesis methods thus face a tradeoff between powerful and efficient classes. Using lightweight scheduler sampling, we explore this tradeoff and demonstrate the concept of a useful approximative verification technique for stochastic automata

Lightweight Statistical Model Checking in Nondeterministic Continuous Time

Lightweight scheduler sampling brings statistical model checking to nondeterministic formalisms with undiscounted properties, in constant memory. Its direct application to continuous-time models is rendered ineffective by their dense concrete state spaces and the need to consider continuous input for optimal decisions. In this paper we describe the challenges and state of the art in applying lightweight scheduler sampling to three continuous-time formalisms: After a review of recent work on exploiting discrete abstractions for probabilistic timed automata, we discuss scheduler sampling for Markov automata and apply it on two case studies. We provide further insights into the tradeoffs between scheduler classes for stochastic automata. Throughout, we present extended experiments and new visualisations of the distribution of schedulers.</p

Do Homicide Perpetrators Have Higher Rates of Delayed-Suicide Than the Other Offenders? Data from a Sample of the Inmate Population in Italy

Homicide-suicide can be defined as homicide followed by the suicide of the perpetrator shortly afterward. In the so-called "homicide-delayed suicide", homicide and suicide occur but within a wide and not strictly defined timeframe. This study analyzes data concerning the suicide of 667 inmates in Italy between 2002 and 2015, considering homicide perpetrators compared to all offenders. The analyses revealed that inmates who had committed homicide were more likely to commit suicide (71% versus 45%; chi 2 = 10.952, p = 0.001) and the odds of suicide increase concerning 1.58 times among homicide perpetrators. The time-to-suicide interval after homicide ranges between 0 to 9.125 days (mean = 1.687,9; SD = 2.303,1). Moreover, the intimate-homicide offenders who committed suicide had a significantly shorter survival time after the offense than did the other non-intimate offenders who died by suicide (t test, t = -3.56, df = 90, p = 0.001). The link between homicide and higher suicide risk in homicide perpetrators should be highlighted because of all the homicide offenders passing through the criminal justice system. Superior knowledge about the path of homicide-delayed suicide will be of particular use to professionals in evaluating and treating homicide inmates. © 2022 by the authors

Optimal infinite scheduling for multi-priced timed automata

This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal non-terminating schedules for such double-priced timed automata is computable. This is done by a reduction of the problem to the determination of optimal mean-cycles in finite graphs with weighted edges. This reduction is obtained by introducing the so-called corner-point abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems

Buried volcanic structures in the Gulf of Naples (Southern Tyrrhenian Sea, Italy) resulting from high resolution magnetic survey and seismic profiling

In this paper we present a correlation between volcanic structures and magnetic anomalies in the Gulf of Naples (Southern Tyrrhenian Sea) based on high resolution magnetic profiling. A densely spaced grid of magnetic profiles coupled with multichannel seismics (seismic source Watergun 15 cubic inch) was recorded in the Gulf of Naples, representing an active volcanic area during the Late Quaternary (volcanic centers of Somma-Vesuvius, Phlegraean Fields and Ischia and Procida islands). The dataset was collected during the oceanographic cruise GMS00-05 which took place during October-November 2000 in the South Tyrrhenian Sea onboard of the R/V Urania (National Research Council, Italy). Shallow volcanic structures in the subsurface of the gulf were recognized by seismo-stratigraphic analysis of high resolution profiles; the volcanic nature of some of these structures was inferred identifying the magnetic anomalies on a high resolution magnetic anomaly map of the gulf. Even if qualitative, the correlations between seismic and magnetic profiles allow us to better assess the geological structure of the Gulf of Naples

MoDeST: a compositional modeling formalism for hard and softly timed systems

This paper presents Modest (MOdeling and DEscription language for Stochastic Timed systems), a formalism that is aimed to support (i) the modular description of reactive system's behaviour while covering both (ii) functional and (iii) nonfunctional system aspects such as timing and quality-of-service constraints in a single specification. The language contains features such as simple and structured data types, structuring mechanisms like parallel composition and abstraction, means to control the granularity of assignments, exception handling, and non-deterministic and random branching and timing. Modest can be viewed as an overarching notation for a wide spectrum of models, ranging from labeled transition systems, to timed automata (and probabilistic variants thereof) as well as prominent stochastic processes such as (generalized semi-)Markov chains and decision processes. The paper describes the design rationales and details of the syntax and semantics

Distribution-based bisimulation for labelled Markov processes

In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based bisimulations, our distribution bisimulation is weaker, but corresponds more closely to linear properties. We construct a logic and a metric to describe our distribution bisimulation and discuss linearity, continuity and compositional properties.Comment: Accepted by FORMATS 201

Characterising Probabilistic Processes Logically

In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mu-calculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae.Comment: 18 page

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far