22 research outputs found
Productivity equation and the m distributions of information processing in workflows
This research investigates an equation of productivity for workflows
regarding its robustness towards the definition of workflows as probabilistic
distributions. The equation was formulated across its derivations through a
theoretical framework about information theory, probabilities and complex
adaptive systems. By defining the productivity equation for organism-object
interactions, workflows mathematical derivations can be predicted and monitored
without strict empirical methods and allows workflow flexibility for
organism-object environments.Comment: 6 pages, 0 figure
Analysis of Non-Linear Probabilistic Hybrid Systems
This paper shows how to compute, for probabilistic hybrid systems, the clock
approximation and linear phase-portrait approximation that have been proposed
for non probabilistic processes by Henzinger et al. The techniques permit to
define a rectangular probabilistic process from a non rectangular one, hence
allowing the model-checking of any class of systems. Clock approximation, which
applies under some restrictions, aims at replacing a non rectangular variable
by a clock variable. Linear phase-approximation applies without restriction and
yields an approximation that simulates the original process. The conditions
that we need for probabilistic processes are the same as those for the classic
case.Comment: In Proceedings QAPL 2011, arXiv:1107.074
An Overview of Modest Models and Tools for Real Stochastic Timed Systems
We depend on the safe, reliable, and timely operation of cyber-physical
systems ranging from smart grids to avionics components. Many of them involve
time-dependent behaviours and are subject to randomness. Modelling languages
and verification tools thus need to support these quantitative aspects. In my
invited presentation at MARS 2022, I gave an introduction to quantitative
verification using the Modest modelling language and the Modest Toolset, and
highlighted three recent case studies with increasing demands on model
expressiveness and tool capabilities: A case of power supply noise in a
network-on-chip modelled as a Markov chain; a case of message routing in
satellite constellations that uses Markov decision processes with distributed
information; and a case of optimising an attack on Bitcoin via Markov automata
model checking. This paper summarises the presentation.Comment: In Proceedings MARS 2022, arXiv:2203.0929
Extending Hybrid CSP with Probability and Stochasticity
Probabilistic and stochastic behavior are omnipresent in computer controlled
systems, in particular, so-called safety-critical hybrid systems, because of
fundamental properties of nature, uncertain environments, or simplifications to
overcome complexity. Tightly intertwining discrete, continuous and stochastic
dynamics complicates modelling, analysis and verification of stochastic hybrid
systems (SHSs). In the literature, this issue has been extensively
investigated, but unfortunately it still remains challenging as no promising
general solutions are available yet. In this paper, we give our effort by
proposing a general compositional approach for modelling and verification of
SHSs. First, we extend Hybrid CSP (HCSP), a very expressive and process
algebra-like formal modeling language for hybrid systems, by introducing
probability and stochasticity to model SHSs, which is called stochastic HCSP
(SHCSP). To this end, ordinary differential equations (ODEs) are generalized by
stochastic differential equations (SDEs) and non-deterministic choice is
replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) to
specify and reason about SHCSP processes. We demonstrate our approach by an
example from real-world.Comment: The conference version of this paper is accepted by SETTA 201
Comparing Two Approaches to Include Stochasticity in Hybrid Automata
Different stochastic extensions of hybrid automata have been proposed in the
past, with unclear expressivity relations between them. To structure and relate
these modeling languages, in this paper we formalize two alternative approaches
to extend hybrid automata with stochastic choices of discrete events and their
time points. The first approach, which we call decomposed scheduling, adds
stochasticity via stochastic races, choosing random time points for the
possible discrete events and executing a winner with an earliest time. In
contrast, composed scheduling first samples the time point of the next event
and then the event to be executed at the sampled time point. We relate the two
approaches regarding their expressivity and categorize available stochastic
extensions of hybrid automata from the literature.Comment: This paper is accepted for publication (without appendix) in the
Proceedings of the 2023 International Conference on Quantitative Evaluation
of Systems (QEST). The appendix was part of the submission and provides
additional material which is not included in the QEST publicatio
Exact and Approximate Abstraction for Classes of Stochastic Hybrid Systems
A stochastic hybrid system contains a collection of interacting discrete and continuous components, subject to random behaviour. The formal verification of a stochastic hybrid system often comprises a method for the generation of a finite-state probabilistic system which either represents exactly the behaviour of the stochastic hybrid system, or which approximates conservatively its behaviour. We extend such abstraction-based formal verification of stochastic hybrid systems in two ways. Firstly, we generalise previous results by showing how bisimulation-based abstractions of non-probabilistic hybrid automata can be lifted to the setting of probabilistic hybrid automata, a subclass of stochastic hybrid systems in which probabilistic choices can be made with respect to finite, discrete alternatives only. Secondly, we consider the problem of obtaining approximate abstractions for discrete-time stochastic systems in which there are continuous probabilistic choices with regard to the slopes of certain system variables. We restrict our attention to the subclass of such systems in which the approximate abstraction of such a system, obtained using the previously developed techniques of Fraenzle et al., results in a probabilistic rectangular hybrid automaton, from which in turn a finite-state probabilistic system can be obtained. We illustrate this technique with an example, using the probabilistic model checking tool PRISM
Maximizing Reachability Probabilities in Rectangular Automata with Random Clocks
This paper proposes an algorithm to maximize reachability probabilities for
rectangular automata with random clocks via a history-dependent prophetic
scheduler. This model class incorporates time-induced nondeterminism on
discrete behavior and nondeterminism in the dynamic behavior. After computing
reachable state sets via a forward flowpipe construction, we use backward
refinement to compute maximum reachability probabilities. The feasibility of
the presented approach is illustrated on a scalable model