861 research outputs found
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
Quantitative model checking of continuous-time Markov chains against timed automata specifications
We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are\ud
accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations
Stochastic Timed Automata
A stochastic timed automaton is a purely stochastic process defined on a
timed automaton, in which both delays and discrete choices are made randomly.
We study the almost-sure model-checking problem for this model, that is, given
a stochastic timed automaton A and a property , we want to decide whether
A satisfies with probability 1. In this paper, we identify several
classes of automata and of properties for which this can be decided. The proof
relies on the construction of a finite abstraction, called the thick graph,
that we interpret as a finite Markov chain, and for which we can decide the
almost-sure model-checking problem. Correctness of the abstraction holds when
automata are almost-surely fair, which we show, is the case for two large
classes of systems, single- clock automata and so-called weak-reactive
automata. Techniques employed in this article gather tools from real-time
verification and probabilistic verification, as well as topological games
played on timed automata.Comment: 40 pages + appendi
Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)
The B\"uchi non-emptiness problem for timed automata refers to deciding if a
given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting
condition. The standard solution to this problem involves adding an auxiliary
clock to take care of the non-Zenoness. In this paper, it is shown that this
simple transformation may sometimes result in an exponential blowup. A
construction avoiding this blowup is proposed. It is also shown that in many
cases, non-Zenoness can be ascertained without extra construction. An
on-the-fly algorithm for the non-emptiness problem, using non-Zenoness
construction only when required, is proposed. Experiments carried out with a
prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV
2010; Formal Methods in System Design, 201
Model checking embedded system designs
We survey the basic principles behind the application of model checking to controller verification and synthesis. A promising development is the area of guided model checking, in which the state space search strategy of the model checking algorithm can be influenced to visit more interesting sets of states first. In particular, we discuss how model checking can be combined with heuristic cost functions to guide search strategies. Finally, we list a number of current research developments, especially in the area of reachability analysis for optimal control and related issues
Verification and control of partially observable probabilistic systems
We present automated techniques for the verification and control of partially observable, probabilistic systems for both discrete and dense models of time. For the discrete-time case, we formally model these systems using partially observable Markov decision processes; for dense time, we propose an extension of probabilistic timed automata in which local states are partially visible to an observer or controller. We give probabilistic temporal logics that can express a range of quantitative properties of these models, relating to the probability of an eventâs occurrence or the expected value of a reward measure. We then propose techniques to either verify that such a property holds or synthesise a controller for the model which makes it true. Our approach is based on a grid-based abstraction of the uncountable belief space induced by partial observability and, for dense-time models, an integer discretisation of real-time behaviour. The former is necessarily approximate since the underlying problem is undecidable, however we show how both lower and upper bounds on numerical results can be generated. We illustrate the effectiveness of the approach by implementing it in the PRISM model checker and applying it to several case studies from the domains of task and network scheduling, computer security and planning
- âŠ