Results 11  20
of
54
Computational Methods for Reachability Analysis of Stochastic Hybrid
 Systems, Hybrid Systems: Computation and Control 2006 LNCS 3927
, 2006
"... Abstract. Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing algorithms for reachability analysis is challen ..."
Abstract

Cited by 25 (8 self)
 Add to MetaCart
(Show Context)
Abstract. Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing algorithms for reachability analysis is challenging because of the interaction between the discrete and continuous stochastic dynamics. In this paper, we propose a probabilistic method for reachability analysis based on discrete approximations. The contribution of the paper is twofold. First, we show that reachability can be characterized as a viscosity solution of a system of coupled HamiltonJacobiBellman equations. Second, we present a numerical method for computing the solution based on discrete approximations and we show that this solution converges to the one for the original system as the discretization becomes finer. Finally, we illustrate the approach with a navigation benchmark that has been proposed for hybrid system verification. 1
A gamebased abstractionrefinement framework for
 Markov Decision Processes. Formal Methods in System Design 36(3):246–280
, 2010
"... In the field of model checking, abstraction refinement has proved to be an extremely successful methodology for combating the statespace explosion problem. However, little practical progress has been made in the setting of probabilistic verification. In this paper we present a novel abstractionr ..."
Abstract

Cited by 22 (15 self)
 Add to MetaCart
In the field of model checking, abstraction refinement has proved to be an extremely successful methodology for combating the statespace explosion problem. However, little practical progress has been made in the setting of probabilistic verification. In this paper we present a novel abstractionrefinement framework for Markov decision processes (MDPs), which are widely used for modelling and verifying systems that exhibit both probabilistic and nondeterministic behaviour. Our framework comprises an abstraction approach based on stochastic twoplayer games, two refinement methods and an efficient algorithm for the abstractionrefinement loop. The key idea behind the abstraction approach is to maintain a separation between nondeterminism present in the original MDP and nondeterminism introduced during the abstraction process, each type being represented by a different player in the game. Crucially, this allows lower and upper bounds to be computed for the values of reachability properties of the MDP. These give a quantitative measure of the quality of the abstraction and form the basis of the corresponding refinement methods. We describe a prototype implementation of our framework and present experimental results demonstrating automatic generation of compact, yet precise, abstractions for a large selection of realworld case studies. 1
Play to test
 In FATES’05
, 2005
"... Abstract. Testing tasks can be viewed (and organized!) as games against nature. We study reachability games in the context of testing. Such games are ubiquitous. A single industrial test suite may involve many instances of a reachability game. Hence the importance of optimal or near optimal strategi ..."
Abstract

Cited by 19 (9 self)
 Add to MetaCart
(Show Context)
Abstract. Testing tasks can be viewed (and organized!) as games against nature. We study reachability games in the context of testing. Such games are ubiquitous. A single industrial test suite may involve many instances of a reachability game. Hence the importance of optimal or near optimal strategies for reachability games. One can use linear programming or the value iteration method of Markov decision process theory to find optimal strategies. Both methods have been implemented in an industrial modelbased testing tool, Spec Explorer, developed at Microsoft Research. 1
An Introduction to Probabilistic Automata
 Bulletin of the European Association for Theoretical Computer Science
, 2002
"... This paper provides an elementary introduction to the probabilistic automaton (PA) model, which has been developed by Segala. We describe how distributed systems with discrete probabilities can be modeled and analyzed by means of PAs. We explain how the basic concepts for the analysis of nonproba ..."
Abstract

Cited by 19 (0 self)
 Add to MetaCart
(Show Context)
This paper provides an elementary introduction to the probabilistic automaton (PA) model, which has been developed by Segala. We describe how distributed systems with discrete probabilities can be modeled and analyzed by means of PAs. We explain how the basic concepts for the analysis of nonprobabilistic automata can be extended to probabilistic systems. In particular, we treat the parallel composition operator on PAs, the semantics of a PA as a set of trace distributions, an extension of the PA model with time and simulation relations for PAs. Finally, we give an overview of various other state based models that are used for the analysis of probabilistic systems.
A.: Automatic verification of competitive stochastic systems
, 2011
"... Abstract. We present automatic verification techniques for the modelling and analysis of probabilistic systems that incorporate competitive behaviour. These systems are modelled as turnbased stochastic multiplayer games, in which the players can either collaborate or compete in order to achieve a p ..."
Abstract

Cited by 17 (12 self)
 Add to MetaCart
(Show Context)
Abstract. We present automatic verification techniques for the modelling and analysis of probabilistic systems that incorporate competitive behaviour. These systems are modelled as turnbased stochastic multiplayer games, in which the players can either collaborate or compete in order to achieve a particular goal. We define a temporal logic called rPATL for expressing quantitative properties of stochastic multiplayer games. This logic allows us to reason about the collective ability of a set of players to achieve a goal relating to the probability of an event’s occurrence or the expected amount of cost/reward accumulated. We give a model checking algorithm for verifying properties expressed in this logic and implement the techniques in a probabilistic model checker, based on the PRISM tool. We demonstrate the applicability and efficiency of our methods by deploying them to analyse and detect potential weaknesses in a variety of large case studies, including algorithms for energy management and collective decision making for autonomous systems. 1
Results on the quantitative µcalculus qMµ
 ACM Transactions on Computational Logic
"... Abstract. The µcalculus is a powerful tool for specifying and verifying transition systems, including those with both demonic (universal) and angelic (existential) choice; its quantitative generalisation qMµ [17,29,9] extends that to probabilistic choice. We show here that for a finitestate system ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
(Show Context)
Abstract. The µcalculus is a powerful tool for specifying and verifying transition systems, including those with both demonic (universal) and angelic (existential) choice; its quantitative generalisation qMµ [17,29,9] extends that to probabilistic choice. We show here that for a finitestate system the logical interpretation of qMµ, via fixedpoints in a domain of realvalued functions into [0,1], is equivalent to an operational interpretation given as a turnbased gambling game between two players. The equivalence sets qMµ on a par with the standard µcalculus, in that it too can benefit from a solid interface linking the logical and operational frameworks. The logical interpretation provides direct access to axioms, laws and metatheorems. The operational, game based interpretation aids the intuition and continues in the more general context to provide a surprisingly practical specification tool — meeting for example Vardi’s challenge to “figure out the meaning of AF AX p ” as a branchingtime formula. A corollary of our proofs is an extension of Everett’s singlynested games result in the finite turnbased case: we prove welldefinedness of the minimax value, and existence of fixed memoriless strategies, for all qMµ games/formulae, of arbitrary (including alternating) nesting structure. 1
Computational Methods for Verification of Stochastic Hybrid Systems
 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS  PART A
, 2008
"... Stochastic hybrid system (SHS) models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing sound computational methods for verification is ch ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
Stochastic hybrid system (SHS) models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing sound computational methods for verification is challenging because of the interaction between the discrete and the continuous stochastic dynamics. In this paper, we propose a probabilistic method for verification of SHSs based on discrete approximations focusing on reachability and safety problems. We show that reachability and safety can be characterized as a viscosity solution of a system of coupled Hamilton–Jacobi–Bellman equations. We present a numerical algorithm for computing the solution based on discrete approximations that are derived using finitedifference methods. An advantage of the method is that the solution converges to the one for the original system as the discretization becomes finer. We also prove that the algorithm is polynomial in the number of states of the discrete approximation. Finally, we illustrate the approach with two benchmarks: a navigation and a room heater example, which have been proposed for hybrid system verification.
From Fairness to Chance
 In Proceedings, Probabilistic Methods in Verification (PROBMIV'98
, 1999
"... Fairness is a mathematical abstraction used in the modeling of a wide range of phenomena, including concurrency, scheduling, and probability. In this paper, we study fairness in the context of probabilistic systems, and we introduce probabilistic fairness, a novel notion of fairness that is itself d ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
(Show Context)
Fairness is a mathematical abstraction used in the modeling of a wide range of phenomena, including concurrency, scheduling, and probability. In this paper, we study fairness in the context of probabilistic systems, and we introduce probabilistic fairness, a novel notion of fairness that is itself defined in terms of probability. The definition of probabilistic fairness makes it invariant with respect to synchronous composition, and facilitates the design of modelchecking algorithms for quantitative properties of probabilistic systems. We compare probabilistic fairness with other notions of fairness for probabilistic systems, and we provide algorithms that solve the verification problem for various classes of probabilistic properties on finitestate systems with fairness. 1 Introduction The use of formal methods for the analysis and verification of systems requires a mathematical model of the system being studied. Many system models include nondeterminism, which enables the represen...
/ Quantitative Timed Analysis of Interactive Markov Chains
"... Abstract. This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1 2player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering formalisms such as AADL and ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
(Show Context)
Abstract. This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1 2player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering formalisms such as AADL and dynamic fault trees. We provide algorithms for determining the extremal expected time of reaching a set of states, and the longrun average of time spent in a set of states. The prototypical tool Imca supports these algorithms as well as the synthesis of εoptimal piecewise constant timed policies for timed reachability objectives. Two case studies show the feasibility and scalability of the algorithms. 1
State explosion in almostsure probabilistic reachability
, 2007
"... We show that the problem of reaching a state set with probability 1 in probabilisticnondeterministic systems operating in parallel is EXPTIMEcomplete. We then show that this probabilistic reachability problem is EXPTIMEcomplete also for probabilistic timed automata. Key words: probabilistic system ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
(Show Context)
We show that the problem of reaching a state set with probability 1 in probabilisticnondeterministic systems operating in parallel is EXPTIMEcomplete. We then show that this probabilistic reachability problem is EXPTIMEcomplete also for probabilistic timed automata. Key words: probabilistic systems, model checking, computational complexity, formal methods, timed automata 1