644 research outputs found
Parametric LTL on Markov Chains
This paper is concerned with the verification of finite Markov chains against
parametrized LTL (pLTL) formulas. In pLTL, the until-modality is equipped with
a bound that contains variables; e.g., asserts that
holds within time steps, where is a variable on natural
numbers. The central problem studied in this paper is to determine the set of
parameter valuations for which the probability to
satisfy pLTL-formula in a Markov chain meets a given threshold , where is a comparison on reals and a probability. As for pLTL
determining the emptiness of is undecidable, we consider
several logic fragments. We consider parametric reachability properties, a
sub-logic of pLTL restricted to next and , parametric B\"uchi
properties and finally, a maximal subclass of pLTL for which emptiness of is decidable.Comment: TCS Track B 201
Accelerating Parametric Probabilistic Verification
We present a novel method for computing reachability probabilities of
parametric discrete-time Markov chains whose transition probabilities are
fractions of polynomials over a set of parameters. Our algorithm is based on
two key ingredients: a graph decomposition into strongly connected subgraphs
combined with a novel factorization strategy for polynomials. Experimental
evaluations show that these approaches can lead to a speed-up of up to several
orders of magnitude in comparison to existing approache
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
Reachability in Parametric Interval Markov Chains using Constraints
Parametric Interval Markov Chains (pIMCs) are a specification formalism that
extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into
account imprecision in the transition probability values: transitions in pIMCs
are labeled with parametric intervals of probabilities. In this work, we study
the difference between pIMCs and other Markov Chain abstractions models and
investigate the two usual semantics for IMCs: once-and-for-all and
at-every-step. In particular, we prove that both semantics agree on the
maximal/minimal reachability probabilities of a given IMC. We then investigate
solutions to several parameter synthesis problems in the context of pIMCs --
consistency, qualitative reachability and quantitative reachability -- that
rely on constraint encodings. Finally, we propose a prototype implementation of
our constraint encodings with promising results
Data-driven and Model-based Verification: a Bayesian Identification Approach
This work develops a measurement-driven and model-based formal verification
approach, applicable to systems with partly unknown dynamics. We provide a
principled method, grounded on reachability analysis and on Bayesian inference,
to compute the confidence that a physical system driven by external inputs and
accessed under noisy measurements, verifies a temporal logic property. A case
study is discussed, where we investigate the bounded- and unbounded-time safety
of a partly unknown linear time invariant system
Lazy Probabilistic Model Checking without Determinisation
The bottleneck in the quantitative analysis of Markov chains and Markov
decision processes against specifications given in LTL or as some form of
nondeterministic B\"uchi automata is the inclusion of a determinisation step of
the automaton under consideration. In this paper, we show that full
determinisation can be avoided: subset and breakpoint constructions suffice. We
have implemented our approach---both explicit and symbolic versions---in a
prototype tool. Our experiments show that our prototype can compete with mature
tools like PRISM.Comment: 38 pages. Updated version for introducing the following changes: -
general improvement on paper presentation; - extension of the approach to
avoid full determinisation; - added proofs for such an extension; - added
case studies; - updated old case studies to reflect the added extensio
Counterexample Generation in Probabilistic Model Checking
Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol
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