481 research outputs found
Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs
Verification of PCTL properties of MDPs with convex uncertainties has been
investigated recently by Puggelli et al. However, model checking algorithms
typically suffer from state space explosion. In this paper, we address
probabilistic bisimulation to reduce the size of such an MDPs while preserving
PCTL properties it satisfies. We discuss different interpretations of
uncertainty in the models which are studied in the literature and that result
in two different definitions of bisimulations. We give algorithms to compute
the quotients of these bisimulations in time polynomial in the size of the
model and exponential in the uncertain branching. Finally, we show by a case
study that large models in practice can have small branching and that a
substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Probabilistic regular graphs
Deterministic graph grammars generate regular graphs, that form a structural
extension of configuration graphs of pushdown systems. In this paper, we study
a probabilistic extension of regular graphs obtained by labelling the terminal
arcs of the graph grammars by probabilities. Stochastic properties of these
graphs are expressed using PCTL, a probabilistic extension of computation tree
logic. We present here an algorithm to perform approximate verification of PCTL
formulae. Moreover, we prove that the exact model-checking problem for PCTL on
probabilistic regular graphs is undecidable, unless restricting to qualitative
properties. Our results generalise those of EKM06, on probabilistic pushdown
automata, using similar methods combined with graph grammars techniques.Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Negotiating the Probabilistic Satisfaction of Temporal Logic Motion Specifications
We propose a human-supervised control synthesis method for a stochastic
Dubins vehicle such that the probability of satisfying a specification given as
a formula in a fragment of Probabilistic Computational Tree Logic (PCTL) over a
set of environmental properties is maximized. Under some mild assumptions, we
construct a finite approximation for the motion of the vehicle in the form of a
tree-structured Markov Decision Process (MDP). We introduce an efficient
algorithm, which exploits the tree structure of the MDP, for synthesizing a
control policy that maximizes the probability of satisfaction. For the proposed
PCTL fragment, we define the specification update rules that guarantee the
increase (or decrease) of the satisfaction probability. We introduce an
incremental algorithm for synthesizing an updated MDP control policy that
reuses the initial solution. The initial specification can be updated, using
the rules, until the supervisor is satisfied with both the updated
specification and the corresponding satisfaction probability. We propose an
offline and an online application of this method.Comment: 9 pages, 4 figures; The results in this paper were presented without
proofs in IEEE/RSJ International Conference on Intelligent Robots and Systems
November 3-7, 2013 at Tokyo Big Sight, Japa
Probabilistic Plan Synthesis for Coupled Multi-Agent Systems
This paper presents a fully automated procedure for controller synthesis for
multi-agent systems under the presence of uncertainties. We model the motion of
each of the agents in the environment as a Markov Decision Process (MDP)
and we assign to each agent one individual high-level formula given in
Probabilistic Computational Tree Logic (PCTL). Each agent may need to
collaborate with other agents in order to achieve a task. The collaboration is
imposed by sharing actions between the agents. We aim to design local control
policies such that each agent satisfies its individual PCTL formula. The
proposed algorithm builds on clustering the agents, MDP products construction
and controller policies design. We show that our approach has better
computational complexity than the centralized case, which traditionally suffers
from very high computational demands.Comment: IFAC WC 2017, Toulouse, Franc
Automated Experiment Design for Data-Efficient Verification of Parametric Markov Decision Processes
We present a new method for statistical verification of quantitative
properties over a partially unknown system with actions, utilising a
parameterised model (in this work, a parametric Markov decision process) and
data collected from experiments performed on the underlying system. We obtain
the confidence that the underlying system satisfies a given property, and show
that the method uses data efficiently and thus is robust to the amount of data
available. These characteristics are achieved by firstly exploiting parameter
synthesis to establish a feasible set of parameters for which the underlying
system will satisfy the property; secondly, by actively synthesising
experiments to increase amount of information in the collected data that is
relevant to the property; and finally propagating this information over the
model parameters, obtaining a confidence that reflects our belief whether or
not the system parameters lie in the feasible set, thereby solving the
verification problem.Comment: QEST 2017, 18 pages, 7 figure
Lukasiewicz mu-Calculus
We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations
Robust Probabilistic Temporal Logics
We robustify PCTL and PCTL*, the most important specification languages for
probabilistic systems, and show that robustness does not increase the
complexity of the model-checking problems
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