2,989 research outputs found
Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games
Probabilistic model checking for stochastic games enables formal verification
of systems that comprise competing or collaborating entities operating in a
stochastic environment. Despite good progress in the area, existing approaches
focus on zero-sum goals and cannot reason about scenarios where entities are
endowed with different objectives. In this paper, we propose probabilistic
model checking techniques for concurrent stochastic games based on Nash
equilibria. We extend the temporal logic rPATL (probabilistic alternating-time
temporal logic with rewards) to allow reasoning about players with distinct
quantitative goals, which capture either the probability of an event occurring
or a reward measure. We present algorithms to synthesise strategies that are
subgame perfect social welfare optimal Nash equilibria, i.e., where there is no
incentive for any players to unilaterally change their strategy in any state of
the game, whilst the combined probabilities or rewards are maximised. We
implement our techniques in the PRISM-games tool and apply them to several case
studies, including network protocols and robot navigation, showing the benefits
compared to existing approaches
Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes
Interval Markov decision processes (IMDPs) generalise classical MDPs by
having interval-valued transition probabilities. They provide a powerful
modelling tool for probabilistic systems with an additional variation or
uncertainty that prevents the knowledge of the exact transition probabilities.
In this paper, we consider the problem of multi-objective robust strategy
synthesis for interval MDPs, where the aim is to find a robust strategy that
guarantees the satisfaction of multiple properties at the same time in face of
the transition probability uncertainty. We first show that this problem is
PSPACE-hard. Then, we provide a value iteration-based decision algorithm to
approximate the Pareto set of achievable points. We finally demonstrate the
practical effectiveness of our proposed approaches by applying them on several
case studies using a prototypical tool.Comment: This article is a full version of a paper accepted to the Conference
on Quantitative Evaluation of SysTems (QEST) 201
Probabilistic Model Checking for Energy Analysis in Software Product Lines
In a software product line (SPL), a collection of software products is
defined by their commonalities in terms of features rather than explicitly
specifying all products one-by-one. Several verification techniques were
adapted to establish temporal properties of SPLs. Symbolic and family-based
model checking have been proven to be successful for tackling the combinatorial
blow-up arising when reasoning about several feature combinations. However,
most formal verification approaches for SPLs presented in the literature focus
on the static SPLs, where the features of a product are fixed and cannot be
changed during runtime. This is in contrast to dynamic SPLs, allowing to adapt
feature combinations of a product dynamically after deployment. The main
contribution of the paper is a compositional modeling framework for dynamic
SPLs, which supports probabilistic and nondeterministic choices and allows for
quantitative analysis. We specify the feature changes during runtime within an
automata-based coordination component, enabling to reason over strategies how
to trigger dynamic feature changes for optimizing various quantitative
objectives, e.g., energy or monetary costs and reliability. For our framework
there is a natural and conceptually simple translation into the input language
of the prominent probabilistic model checker PRISM. This facilitates the
application of PRISM's powerful symbolic engine to the operational behavior of
dynamic SPLs and their family-based analysis against various quantitative
queries. We demonstrate feasibility of our approach by a case study issuing an
energy-aware bonding network device.Comment: 14 pages, 11 figure
Decidability Results for Multi-objective Stochastic Games
We study stochastic two-player turn-based games in which the objective of one
player is to ensure several infinite-horizon total reward objectives, while the
other player attempts to spoil at least one of the objectives. The games have
previously been shown not to be determined, and an approximation algorithm for
computing a Pareto curve has been given. The major drawback of the existing
algorithm is that it needs to compute Pareto curves for finite horizon
objectives (for increasing length of the horizon), and the size of these Pareto
curves can grow unboundedly, even when the infinite-horizon Pareto curve is
small. By adapting existing results, we first give an algorithm that computes
the Pareto curve for determined games. Then, as the main result of the paper,
we show that for the natural class of stopping games and when there are two
reward objectives, the problem of deciding whether a player can ensure
satisfaction of the objectives with given thresholds is decidable. The result
relies on intricate and novel proof which shows that the Pareto curves contain
only finitely many points. As a consequence, we get that the two-objective
discounted-reward problem for unrestricted class of stochastic games is
decidable.Comment: 35 page
Permissive Controller Synthesis for Probabilistic Systems
We propose novel controller synthesis techniques for probabilistic systems
modelled using stochastic two-player games: one player acts as a controller,
the second represents its environment, and probability is used to capture
uncertainty arising due to, for example, unreliable sensors or faulty system
components. Our aim is to generate robust controllers that are resilient to
unexpected system changes at runtime, and flexible enough to be adapted if
additional constraints need to be imposed. We develop a permissive controller
synthesis framework, which generates multi-strategies for the controller,
offering a choice of control actions to take at each time step. We formalise
the notion of permissivity using penalties, which are incurred each time a
possible control action is disallowed by a multi-strategy. Permissive
controller synthesis aims to generate a multi-strategy that minimises these
penalties, whilst guaranteeing the satisfaction of a specified system property.
We establish several key results about the optimality of multi-strategies and
the complexity of synthesising them. Then, we develop methods to perform
permissive controller synthesis using mixed integer linear programming and
illustrate their effectiveness on a selection of case studies
PRISM-games:Verification and Strategy Synthesis for Stochastic Multi-player Games with Multiple Objectives
PRISM-games is a tool for modelling, verification and strategy synthesis for stochastic multi-player games. These allow models to incorporate both probability, to represent uncertainty, unreliability or randomisation, and game-theoretic aspects, for systems where different entities have opposing objectives. Applications include autonomous transport, security protocols, energy management systems and many more. We provide a detailed overview of the PRISM-games tool, including its modelling and property specification formalisms, and its underlying architecture and implementation. In particular, we discuss some of its key features, which include multi-objective and compositional approaches to verification and strategy synthesis. We also discuss the scalability and efficiency of the tool and give an overview of some of the case studies to which it has been applied
Verification of Open Interactive Markov Chains
Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation. For this we embed the IMC into a game that is played with the environment. We devise algorithms that enable us to derive bounds on reachability probabilities that are assured to hold in any composition context
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