Results 11  20
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73
Symbolic and parametric model checking of discretetime markov Chains
 In Proc. of ICTAC’04, Springer LNCS 3407
, 2004
"... daws at cs.ru.nl Abstract. We present a languagetheoretic approach to symbolic model checking of PCTL over discretetime Markov chains. The probability with which a path formula is satisfied is represented by a regular expression. A recursive evaluation of the regular expression yields an exact rat ..."
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Cited by 32 (0 self)
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daws at cs.ru.nl Abstract. We present a languagetheoretic approach to symbolic model checking of PCTL over discretetime Markov chains. The probability with which a path formula is satisfied is represented by a regular expression. A recursive evaluation of the regular expression yields an exact rational value when transition probabilities are rational, and rational functions when some probabilities are left unspecified as parameters of the system. This allows for parametric model checking by evaluating the regular expression for different parameter values, for instance, to study the influence of a lossy channel in the overall reliability of a randomized protocol. 1
K.: Rapture: A tool for verifying Markov Decision Processes
 University Brno
, 2002
"... Abstract. We present a tool that performs verification of quantified reachability properties over Markov decision processes (or probabilistic transition system). The originality of the tool is to provide two reduction techniques that limit the state space explosion problem: automatic abstraction an ..."
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Cited by 29 (3 self)
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Abstract. We present a tool that performs verification of quantified reachability properties over Markov decision processes (or probabilistic transition system). The originality of the tool is to provide two reduction techniques that limit the state space explosion problem: automatic abstraction and refinement algorithms, and a socalled essential states reduction. We present several casestudies to illustrate the usefulness of these techniques. 1
Automatic Verification of the IEEE1394 Root Contention Protocol with KRONOS and PRISM
 SOFTWARE TOOLS FOR TECHNOLOGY TRANSFER
"... We report on the automatic verification of timed probabilistic properties of the IEEE 1394 root contention protocol combining two existing tools: the realtime modelchecker Kronos and the probabilistic modelchecker Prism. The system is modelled as a probabilistic timed automaton. We first use Kro ..."
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Cited by 27 (10 self)
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We report on the automatic verification of timed probabilistic properties of the IEEE 1394 root contention protocol combining two existing tools: the realtime modelchecker Kronos and the probabilistic modelchecker Prism. The system is modelled as a probabilistic timed automaton. We first use Kronos to perform a symbolic forward reachability analysis to generate the set of states that are reachable with nonzero probability from the initial state, and before the deadline expires. We then encode this information as a Markov decision process to be analyzed with Prism. We apply this technique to compute the minimal probability of a leader being elected before a deadline, for different deadlines, and study how this minimal probability is influenced by using a biased coin and considering different wire lengths.
Magnifyinglens abstraction for Markov decision processes
 In CAV
, 2007
"... Abstract. We present a novel abstraction technique which allows the analysis of reachability and safety properties of Markov decision processes with very large state spaces. The technique, called magnifyinglens abstraction, (MLA) copes with the stateexplosion problem by partitioning the statespac ..."
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Cited by 25 (1 self)
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Abstract. We present a novel abstraction technique which allows the analysis of reachability and safety properties of Markov decision processes with very large state spaces. The technique, called magnifyinglens abstraction, (MLA) copes with the stateexplosion problem by partitioning the statespace into regions, and by computing upper and lower bounds for reachability and safety properties on the regions, rather than on the states. To compute these bounds, MLA iterates over the regions, considering the concrete states of each region in turn, as if one were sliding across the abstraction a magnifying lens which allowed viewing the concrete states. The algorithm adaptively refines the regions, using smaller regions where more detail is needed, until the difference between upper and lower bounds is smaller than a specified accuracy. We provide experimental results on three case studies illustrating that MLA can provide accurate answers, with savings in memory requirements. 1
Abstraction refinement for probabilistic software
 Proc. 10th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI’09), volume 5403 of LNCS
, 2009
"... Abstract. We present a methodology and implementation for verifying ANSIC programs that exhibit probabilistic behaviour, such as failures or randomisation. We use abstractionrefinement techniques that represent probabilistic programs as Markov decision processes and their abstractions as stochasti ..."
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Cited by 23 (7 self)
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Abstract. We present a methodology and implementation for verifying ANSIC programs that exhibit probabilistic behaviour, such as failures or randomisation. We use abstractionrefinement techniques that represent probabilistic programs as Markov decision processes and their abstractions as stochastic twoplayer games. Our techniques target quantitative properties of software such as “the maximum probability of filetransfer failure ” or “the minimum expected number of loop iterations ” and the abstractions we construct yield lower and upper bounds on these properties, which then guide the refinement process. We build upon stateoftheart techniques and tools, using SATbased predicate abstraction, symbolic implementations of probabilistic model checking and components from GOTOCC, SATABS and PRISM. Experimental results show that our approach performs very well in practice, successfully verifying actual networking software whose complexity is significantly beyond the scope of existing probabilistic verification tools. 1
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
Verifying Randomized Byzantine Agreement
 Proc. Formal Techniques for Networked and Distributed Systems (FORTE’02), volume 2529 of LNCS
, 2002
"... Distributed systems increasingly rely on faulttolerant and secure authorization services. An essential primitive used to implement such services is the Byzantine agreement protocol for achieving agreement among n parties even if t parties (t < n=3) are corrupt and behave maliciously. We desc ..."
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Cited by 22 (9 self)
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Distributed systems increasingly rely on faulttolerant and secure authorization services. An essential primitive used to implement such services is the Byzantine agreement protocol for achieving agreement among n parties even if t parties (t < n=3) are corrupt and behave maliciously. We describe our experience verifying the randomized protocol ABBA (Asynchronous Binary Byzantine Agreement) of Cachin, Kursawe and Shoup [5], a practical protocol that incorporates modern thresholdcryptographic techniques and forms a core of powerful asynchronous broadcast protocols [4]. The protocol is ecient (runs in constant expected time), optimal (it tolerates the maximum number of corrupted parties) and provably secure (in the random oracle model). We model the protocol in Cadence SMV, replacing the coin tosses with nondeterministic choice, and provide a proof of the protocol correctness for all n under the assumption that the cryptographic primitives are correct.
Symbolic Representations and Analysis of Large Probabilistic Systems
 In Validation of Stochastic Systems
, 2004
"... Abstract. This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting highlevel structure and regularity in the models to which they are applied, increasing the size of the stat ..."
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Cited by 19 (2 self)
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Abstract. This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting highlevel structure and regularity in the models to which they are applied, increasing the size of the state spaces which can be tackled. In general, this is done by using data structures which provide compact storage but which are still efficient to manipulate, usually based on binary decision diagrams (BDDs) or their extensions. In this paper we focus on BDDs, multivalued decision diagrams (MDDs), multiterminal binary decision diagrams (MTBDDs) and matrix diagrams. 1
On Automated Verification of Probabilistic Programs
, 2007
"... We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over nite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, whic ..."
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Cited by 14 (7 self)
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We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over nite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, which we call apex, for this language, based on game semantics. We illustrate our approach with three nontrivial case studies: (i) Herman's selfstabilisation algorithm; (ii) an analysis of the average shape of binary search trees obtained by certain sequences of random insertions and deletions; and (iii) the problem of anonymity in the Dining Cryptographers protocol. In particular, we record an exponential speedup in the latter over stateoftheart competing approaches.
Analysing randomized distributed algorithms
 Validation of Stochastic Systems
, 2004
"... Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, thi ..."
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Cited by 13 (2 self)
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Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, this comes at a cost: the analysis of such systems become very complex, particularly in the context of distributed computation. This arises through the interplay between probability and nondeterminism. To prove a randomized distributed algorithm correct one usually involves two levels: classical, assertionbased reasoning, and a probabilistic analysis based on a suitable probability space on computations. In this paper we describe a number of approaches which allows us to verify the correctness of randomized distributed algorithms. 1