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27
On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative ..."
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Cited by 107 (25 self)
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Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
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 ..."
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Cited by 17 (12 self)
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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
Randomness for free
 CoRR
"... Abstract. We consider twoplayer zerosum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partialobservation (both players have partial view o ..."
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Cited by 14 (13 self)
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Abstract. We consider twoplayer zerosum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partialobservation (both players have partial view of the game); (b) onesided completeobservation (one player has complete observation); and (c) completeobservation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (players interact simultaneously); and (b) turnbased (players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. We present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function (probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games. 1
PartialObservation Stochastic Games: How to Win when Belief Fails
, 2011
"... Abstract. In twoplayer finitestate stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitely many rounds and ..."
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Cited by 12 (6 self)
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Abstract. In twoplayer finitestate stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almostsurely (i.e., with probability 1) or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be onesided with either (a) player 1, or (b) player 2 having partial observation (andtheotherplayerhasperfect observation),or twosided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization
What is Decidable about Partially Observable Markov Decision Processes with omegaRegular Objectives
, 2013
"... We consider partially observable Markov decision processes (POMDPs) with ωregular conditions specified as parity objectives. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. pos ..."
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Cited by 10 (7 self)
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We consider partially observable Markov decision processes (POMDPs) with ωregular conditions specified as parity objectives. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal EXPTIMEcomplete complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finitememory strategies. We also establish optimal (exponential) memory bounds.
Formalizing and reasoning about quality
, 2012
"... Abstract. Traditional formal methods are based on a Boolean satisfaction notion: a reactive system satisfies, or not, a given specification. We generalize formal methods to also address the quality of systems. As an adequate specification formalism we introduce the linear temporal logic LTL[F]. The ..."
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Cited by 9 (6 self)
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Abstract. Traditional formal methods are based on a Boolean satisfaction notion: a reactive system satisfies, or not, a given specification. We generalize formal methods to also address the quality of systems. As an adequate specification formalism we introduce the linear temporal logic LTL[F]. The satisfaction value of an LTL[F] formula is a number between 0 and 1, describing the quality of the satisfaction. The logic generalizes traditional LTL by augmenting it with a (parameterized) set F of arbitrary functions over the interval [0, 1]. For example, F may contain the maximum or minimum between the satisfaction values of subformulas, their product, and their average. The classical decision problems in formal methods, such as satisfiability, model checking, and synthesis, are generalized to search and optimization problems in the quantitative setting. For example, model checking asks for the quality in which a specification is satisfied, and synthesis returns a system satisfying the specification with the highest quality. Reasoning about quality gives rise to other natural questions, like the distance between specifications. We formalize these basic questions and study them for LTL[F]. By extending the automatatheoretic approach for LTL to a setting that takes quality into an account, we are able to solve the above problems and show that reasoning about LTL[F] has roughly the same complexity as reasoning about traditional LTL. 1
Bridging boolean and quantitative synthesis using smoothed proof search
, 2014
"... We present a new technique for parameter synthesis under boolean and quantitative objectives. The input to the technique is a “sketch” — a program with missing numerical parameters — and a probabilistic assumption about the program’s inputs. The goal is to automatically synthesize values for the p ..."
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Cited by 9 (3 self)
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We present a new technique for parameter synthesis under boolean and quantitative objectives. The input to the technique is a “sketch” — a program with missing numerical parameters — and a probabilistic assumption about the program’s inputs. The goal is to automatically synthesize values for the parameters such that the resulting program satisfies: (1) a boolean specification, which states that the program must meet certain assertions, and (2) a quantitative specification, which assigns a real valued rating to every program and which the synthesizer is expected to optimize. Our method — called smoothed proof search — reduces this task to a sequence of unconstrained smooth optimization problems that are then solved numerically. By iteratively solving these problems, we obtain parameter values that get closer and closer to meeting the boolean specification; at the limit, we obtain values that provably meet the specification. The approximations are computed using a new notion of smoothing for program abstractions, where an abstract transformer is approximated by a function that is continuous according to a metric over abstract states. We present a prototype implementation of our synthesis procedure, and experimental results on two benchmarks from the embedded control domain. The experiments demonstrate the benefits of smoothed proof search over an approach that does not meet the boolean and quantitative synthesis goals simultaneously.
Automated verification and strategy synthesis for probabilistic systems
"... Probabilistic model checking is an automated technique to verify whether a probabilistic system, e.g., a distributed network protocol which can exhibit failures, satisfies a temporal logic property, for example, “the minimum probability of the network recovering from a fault in a given time period ..."
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Cited by 7 (1 self)
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Probabilistic model checking is an automated technique to verify whether a probabilistic system, e.g., a distributed network protocol which can exhibit failures, satisfies a temporal logic property, for example, “the minimum probability of the network recovering from a fault in a given time period is above 0.98”. Dually, we can also synthesise, from a model and a property specification, a strategy for controlling the system in order to satisfy or optimise the property, but this aspect has received less attention to date. In this paper, we give an overview of methods for automated verification and strategy synthesis for probabilistic systems. Primarily, we focus on the model of Markov decision processes and use property specifications based on probabilistic LTL and expected reward objectives. We also describe how to apply multiobjective model checking to investigate tradeoffs between several properties, and extensions to stochastic multiplayer games. The paper concludes with a summary of future challenges in this area.
R.: QUASY: Quantitative Synthesis Tool
 TACAS 2011. LNCS
, 2011
"... Abstract. We present the tool QUASY, a quantitative synthesis tool. QUASY takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. The user can choose be ..."
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Cited by 6 (2 self)
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Abstract. We present the tool QUASY, a quantitative synthesis tool. QUASY takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. The user can choose between a system that satisfies and optimizes the specifications (a) under all possible environment behaviors or (b) under the mostlikely environment behaviors given as a probability distribution on the possible input sequences. QUASY solves these two quantitative synthesis problems by reduction to instances of 2player games and Markov Decision Processes (MDPs) with quantitative winning objectives. QUASY can also be seen as a game solver for quantitative games. Most notable, it can solve lexicographic meanpayoff games with2players, MDPs with meanpayoff objectives, and ergodic MDPs with meanpayoff parity objectives. 1