28 research outputs found
On Quantitative Software Verification
International audienceSoftware verification has made great progress in recent years, resulting in several tools capable of working directly from source code, for example, SLAM and Astree. Typical properties that can be verified are expressed as Boolean assertions or temporal logic properties, and include whether the program eventually terminates, or the executions never violate a safety property. The underlying techniques crucially rely on the ability to extract from programs, using compiler tools and predicate abstraction, finite-state abstract models, which are then iteratively refined to either demonstrate the violation of a safety property (e.g. a buffer overflow) or guarantee the absence of such faults. An established method to achieve this automatically executes an abstraction-refinement loop guided by counterexample traces [1]
An expectation transformer approach to predicate abstraction and data independence for probabilistic programs
In this paper we revisit the well-known technique of predicate abstraction to
characterise performance attributes of system models incorporating probability.
We recast the theory using expectation transformers, and identify transformer
properties which correspond to abstractions that yield nevertheless exact bound
on the performance of infinite state probabilistic systems. In addition, we
extend the developed technique to the special case of "data independent"
programs incorporating probability. Finally, we demonstrate the subtleness of
the extended technique by using the PRISM model checking tool to analyse an
infinite state protocol, obtaining exact bounds on its performance
Formal analysis techniques for gossiping protocols
We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them
Model checking Quantitative Linear Time Logic
This paper considers QLtl, a quantitative analagon of Ltl and presents algorithms for model checking QLtl over quantitative versions of Kripke structures and Markov chains
Abstract Interpretation for Probabilistic Termination of Biological Systems
In a previous paper the authors applied the Abstract Interpretation approach
for approximating the probabilistic semantics of biological systems, modeled
specifically using the Chemical Ground Form calculus. The methodology is based
on the idea of representing a set of experiments, which differ only for the
initial concentrations, by abstracting the multiplicity of reagents present in
a solution, using intervals. In this paper, we refine the approach in order to
address probabilistic termination properties. More in details, we introduce a
refinement of the abstract LTS semantics and we abstract the probabilistic
semantics using a variant of Interval Markov Chains. The abstract probabilistic
model safely approximates a set of concrete experiments and reports
conservative lower and upper bounds for probabilistic termination
Refinement sensitive formal semantics of state machines with persistent choice
Modeling languages usually support two kinds of nondeterminism, an external one for interactions of a system with its environment, and one that stems from under-specification as familiar in models of behavioral requirements. Both forms of nondeterminism are resolvable by composing a system with an environment model and by refining under-specified behavior (respectively). Modeling languages usually dont support nondeterminism that is persistent in that neither the composition with an environment nor refinements of under-specification will resolve it. Persistent nondeterminism is used, e.g., for modeling faulty systems. We present a formal semantics for UML state machines enriched with an operator persistent choice that models persistent nondeterminism. This semantics is based on abstract models - μ-automata with a novel refinement relation - and a sound three-valued satisfaction relation for properties expressed in the μ-calculus. © 2009 Elsevier B.V. All rights reserved
A linear process algebraic format for probabilistic systems with data
This paper presents a novel linear process algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar techniques for traditional process algebras with data, and — more importantly — treats data and data-dependent probabilistic choice in a fully symbolic manner, paving the way to the symbolic analysis of parameterised probabilistic systems
Approximating Euclidean by Imprecise Markov Decision Processes
Euclidean Markov decision processes are a powerful tool for modeling control
problems under uncertainty over continuous domains. Finite state imprecise,
Markov decision processes can be used to approximate the behavior of these
infinite models. In this paper we address two questions: first, we investigate
what kind of approximation guarantees are obtained when the Euclidean process
is approximated by finite state approximations induced by increasingly fine
partitions of the continuous state space. We show that for cost functions over
finite time horizons the approximations become arbitrarily precise. Second, we
use imprecise Markov decision process approximations as a tool to analyse and
validate cost functions and strategies obtained by reinforcement learning. We
find that, on the one hand, our new theoretical results validate basic design
choices of a previously proposed reinforcement learning approach. On the other
hand, the imprecise Markov decision process approximations reveal some
inaccuracies in the learned cost functions