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36
Counterexample generation in probabilistic model checking
 IEEE TRANS. ON SOFTWARE ENGINEERING
, 2009
"... 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 formulas in discretetime Markov chains. Finding the strongest evidence (i.e., the most prob ..."
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Cited by 32 (9 self)
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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 formulas in discretetime Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) untilformula is shown to be reducible to a singlesource (hopconstrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) kshortest (hopconstrained) 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.
Sliding window abstraction for infinite Markov chains
 In Proc. CAV, volume 5643 of LNCS
, 2009
"... Abstract. We present an onthefly abstraction technique for infinitestate continuoustime Markov chains. We consider Markov chains that are specified by a finite set of transition classes. Such models naturally represent biochemical reactions and therefore play an important role in the stochastic ..."
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Cited by 22 (8 self)
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Abstract. We present an onthefly abstraction technique for infinitestate continuoustime Markov chains. We consider Markov chains that are specified by a finite set of transition classes. Such models naturally represent biochemical reactions and therefore play an important role in the stochastic modeling of biological systems. We approximate the transient probability distributions at various time instances by solving a sequence of dynamically constructed abstract models, each depending on the previous one. Each abstract model is a finite Markov chain that represents the behavior of the original, infinite chain during a specific time interval. Our approach provides complete information about probability distributions, not just about individual parameters like the mean. The error of each abstraction can be computed, and the precision of the abstraction refined when desired. We implemented the algorithm and demonstrate its usefulness and efficiency on several case studies from systems biology. 1
Formal Analysis Techniques for Gossiping Protocols
 ACM SIGOPS Oper. Syst. Rev.
, 2007
"... 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 the ..."
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Cited by 15 (4 self)
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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.
Compositional design methodology with constraint Markov chains
 in: International Conference on Quantitative Evaluation of Systems, QEST, IEEE Computer Society
"... Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a specification theory. We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on ..."
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Cited by 14 (7 self)
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Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a specification theory. We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on probability distributions and thus generalize prior abstractions such as Interval MCs. Linear (polynomial) constraints suffice for closure under conjunction (respectively parallel composition). This is the first specification theory for MCs with such closure properties. We discuss its relation to simpler operators for known languages such as probabilistic process algebra. Despite the generality, all operators and relations are computable. I.
TimeBounded Model Checking of InfiniteState ContinuousTime Markov Chains
"... The design of complex concurrent systems often involves intricate performance and dependability considerations. Continuoustime Markov chains (CTMCs) are widely used models for concurrent system designs making it possible to model check such properties. In this paper, we focus on probabilistic timin ..."
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Cited by 13 (3 self)
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The design of complex concurrent systems often involves intricate performance and dependability considerations. Continuoustime Markov chains (CTMCs) are widely used models for concurrent system designs making it possible to model check such properties. In this paper, we focus on probabilistic timing properties of infinitestate CTMCs, expressible in continuous stochastic logic (CSL). Such properties comprise important dependability measures, such as timed probabilistic reachability, performability, survivability, and various availability measures like instantaneous availabilities, conditional instantaneous availabilities and interval availabilities. Conventional model checkers explore the given model exhaustively which is not always possible either due to state explosion or because the model is infinite. This paper presents a method that only explores the infinite (or prohibitively large) model up to a finite depth, with the depth bound being computed onthefly. We provide experimental evidence showing that our method is effective.
INFAMY: An infinitestate Markov model checker
 In CAV
, 2009
"... Abstract. The design of complex concurrent systems often involves intricate performance and dependability considerations. Continuoustime Markov chains (CTMCs) are a widely used modeling formalism, where performance and dependability properties are analyzable by model checking. We present INFAMY, a ..."
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Cited by 9 (1 self)
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Abstract. The design of complex concurrent systems often involves intricate performance and dependability considerations. Continuoustime Markov chains (CTMCs) are a widely used modeling formalism, where performance and dependability properties are analyzable by model checking. We present INFAMY, a model checker for arbitrarily structured infinitestate CTMCs. It checks probabilistic timing properties expressible in continuous stochastic logic (CSL). Conventional model checkers explore the given model exhaustively, which is often costly, due to state explosion, and impossible if the model is infinite. INFAMY only explores the model up to a finite depth, with the depth bound being computed onthefly. The computation of depth bounds is configurable to adapt to the characteristics of different classes of models. 1 Introducing INFAMY Continuoustime Markov chains (CTMCs) are widely used in performance and dependability analysis and biological modeling. Properties are typically specified in continuous stochastic logic (CSL) [1], a logic inspired by CTL. In CSL, the until operator is equipped with a time interval to express properties such as: “The probability to reach a goal within 2 hours while maintaining a probability of at least 0.5 of communicating ( ( periodically (every five minutes) with a base station, is at least 0.9 ” via P≥0.9 P≥0.5✸≤5communicate) U ≤120 goal). CSL model checking amounts to analysis of the transient (timedependent) probability vectors [1], typically carried out by uniformization, where the transient probability is expressed by a weighted infinite sum (weights are given by a Poisson process). The standard methodology in CSL model checking is to truncate the infinite sum up to some prespecified accuracy [2]. Outside the model checking arena, ideas have been developed [3,4,5] which not only truncate the infinite sum, but also the matrix representing the system, which admits transient analysis of CTMCs with large or even infinite state spaces, provided they are given implicitly in a This work is supported by the NWODFG bilateral project VOSS, by the DFG as
Advances and Challenges of Probabilistic Model Checking
 48TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL AND COMPUTING (2010) 16911698
, 2010
"... Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many domains: probabilistic behaviour may arise, for example, due to failures of unreliable components, communication across los ..."
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Cited by 8 (0 self)
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Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many domains: probabilistic behaviour may arise, for example, due to failures of unreliable components, communication across lossy media, or through the use of randomisation in distributed protocols. In this paper, we give a short overview of probabilistic model checking and of PRISM (www.prismmodelchecker.org), currently the leading software tool in this area. We then mention some of the limitations of these techniques, describe some of the advances that are being made to overcome them, and outline key challenges that remain in this research area.
Relative Performance Evaluation and
 Project Selection, 30 JOURNAL OF ACCOUNTING RESEARCH
, 1984
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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Cited by 7 (0 self)
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
A linear processalgebraic format with data for probabilistic automata
, 2011
"... This paper presents a novel linear processalgebraic 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 te ..."
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Cited by 6 (4 self)
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This paper presents a novel linear processalgebraic 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 datadependent probabilistic choice in a fully symbolic manner, leading to the symbolic analysis of parameterised probabilistic systems. We discuss several reduction techniques that can easily be applied to our models. A validation of our approach on two benchmark leader election protocols shows reductions of more than an order of magnitude.
Least upper bounds for probability measures and their applications to abstractions
, 2008
"... Abstraction is a key technique to combat the state space explosion problem in model checking probabilistic systems. In this paper we present new ways to abstract Discrete Time Markov Chains (DTMCs), Markov Decision Processes (MDPs), and Continuous Time Markov Chains (CTMCs). The main advantage of o ..."
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Cited by 5 (1 self)
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Abstraction is a key technique to combat the state space explosion problem in model checking probabilistic systems. In this paper we present new ways to abstract Discrete Time Markov Chains (DTMCs), Markov Decision Processes (MDPs), and Continuous Time Markov Chains (CTMCs). The main advantage of our abstractions is that they result in abstract models that are purely probabilistic, which maybe more amenable to automatic analysis than models with both nondeterministic and probabilistic steps that typically arise from previously known abstraction techniques. A key technical tool, developed in this paper, is the construction of least upper bounds for any collection of probability measures. This upper bound construction may be of independent interest that could be useful in the abstract interpretation and static analysis of probabilistic programs.