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12
Generic trace semantics via coinduction
 Logical Methods in Comp. Sci
, 2007
"... Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace ..."
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Cited by 17 (6 self)
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Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace
Observing Branching Structure through Probabilistic Contexts
 SIAM J. Comput
"... Abstract. Probabilistic automata (PAs) constitute a general framework for modeling and analyzing discrete event systems that exhibit both nondeterministic and probabilistic behavior, such as distributed algorithms and network protocols. The behavior of PAs is commonly defined using schedulers (also ..."
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Cited by 13 (2 self)
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Abstract. Probabilistic automata (PAs) constitute a general framework for modeling and analyzing discrete event systems that exhibit both nondeterministic and probabilistic behavior, such as distributed algorithms and network protocols. The behavior of PAs is commonly defined using schedulers (also called adversaries or strategies), which resolve all nondeterministic choices based on past history. From the resulting purely probabilistic structures, trace distributions can be extracted, whose intent is to capture the observable behavior of a PA. However, when PAs are composed via an (asynchronous) parallel composition operator, a global scheduler may establish strong correlations between the behavior of system components and, for example, resolve nondeterministic choices in one PA based on the outcome of probabilistic choices in the other. It is well known that, as a result of this, the (lineartime) trace distribution precongruence is not compositional for PAs. In his 1995 Ph.D. thesis, Segala has shown that the (branchingtime) probabilistic simulation preorder is compositional for PAs. In this paper, we establish that the simulation preorder is, in fact, the coarsest refinement of the trace distribution preorder that is compositional. We prove our characterization result by providing (1) a context of a given PA A, called the tester, which may announce the state of A to the outside world, and (2) a specific global scheduler, called the observer, which ensures that the state information that is announced is actually correct. Now when another PA B is composed with the tester, it may generate the same external behavior as the observer only when it is able to simulate A in the sense that whenever A goes to some state s, B can go to a corresponding state u, from which it may generate the same external behavior. Our result shows that probabilistic contexts together with global schedulers are able to exhibit the branching structure of PAs.
Generic forward and backward simulations
 International Conference on Concurrency Theory (CONCUR 2006), volume 4137 of Lect. Notes Comp. Sci
, 2006
"... Abstract. The technique of forward/backward simulations has been applied successfuly in many distributed and concurrent applications. In this paper, however, we claim that the technique can actually have more genericity and mathematical clarity. We do so by identifying forward/backward simulations a ..."
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Cited by 11 (3 self)
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Abstract. The technique of forward/backward simulations has been applied successfuly in many distributed and concurrent applications. In this paper, however, we claim that the technique can actually have more genericity and mathematical clarity. We do so by identifying forward/backward simulations as lax/oplax morphisms of coalgebras. Starting from this observation, we present a systematic study of this generic notion of simulations. It is meant to be a generic version of the study by Lynch and Vaandrager, covering both nondeterministic and probabilistic systems. In particular we prove soundness and completeness results with respect to trace inclusion: the proof is by coinduction using the generic theory of traces developed by Jacobs, Sokolova and the author. By suitably instantiating our generic framework, one obtains the appropriate definition of forward/backward simulations for various kinds of systems, for which soundness and completeness come for free. 1
Automated Verification Techniques for Probabilistic Systems
"... Abstract. This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to ..."
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Cited by 10 (7 self)
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Abstract. This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to analyse a wide range of their properties, including specifications in the temporal logics PCTL and LTL, probabilistic safety properties and cost or rewardbased measures. We also discuss multiobjective probabilistic model checking, used to analyse tradeoffs between several different quantitative properties. Applications of the techniques in this tutorial include performance and dependability analysis of networked systems, communication protocols and randomised distributed algorithms. Since such systems often comprise several components operating in parallel, we also cover techniques for compositional modelling and verification of multicomponent probabilistic systems. Finally, we describe three large case studies which illustrate practical applications of the various methods discussed in the tutorial. 1
Modeling Radio Networks
"... Abstract. We describe a modeling framework and collection of foundational composition results for the study of probabilistic distributed algorithms in synchronous radio networks. Though the radio setting has been studied extensively by the distributed algorithms community, their results rely on info ..."
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Cited by 5 (4 self)
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Abstract. We describe a modeling framework and collection of foundational composition results for the study of probabilistic distributed algorithms in synchronous radio networks. Though the radio setting has been studied extensively by the distributed algorithms community, their results rely on informal descriptions of the channel behavior and therefore lack easy comparability and are prone to error caused by definition subtleties. Our framework rectifies these issues by providing: (1) a method to precisely describe a radio channel as a probabilistic automaton; (2) a mathematical notion of implementing one channel using another channel, allowing for direct comparisons of channel strengths and a natural decomposition of problems into implementing a more powerful channel and solving the problem on the powerful channel; (3) a mathematical definition of a problem and solving a problem; (4) a pair of composition results that simplify the tasks of proving properties about channel implementation algorithms and combining problems with channel implementations.
Probabilistic anonymity via coalgebraic simulations
 European Symposium on Programming (ESOP 2007), volume 4421 of Lect. Notes Comp. Sci
, 2007
"... Abstract. There is a growing concern on anonymity and privacy on the Internet, resulting in lots of work on formalization and verification of anonymity. Especially, importance of probabilistic aspect of anonymity is claimed recently by many authors. Among them are Bhargava and Palamidessi who presen ..."
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Cited by 5 (2 self)
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Abstract. There is a growing concern on anonymity and privacy on the Internet, resulting in lots of work on formalization and verification of anonymity. Especially, importance of probabilistic aspect of anonymity is claimed recently by many authors. Among them are Bhargava and Palamidessi who present the definition of probabilistic anonymity for which, however, proof methods are not yet elaborated. In this paper we introduce a simulationbased proof method for probabilistic anonymity. It is a probabilistic adaptation of the method by Kawabe et al. for nondeterministic anonymity: anonymity of a protocol is proved by finding out a forward/backward simulation between certain automata. For the jump from nondeterminism to probability we fully exploit a generic, coalgebraic theory of traces and simulations developed by Hasuo and others. In particular, an appropriate notion of probabilistic simulations is obtained by instantiating a generic definition with suitable parameters. 1
Quantitative Model Checking Revisited: neither Decidable nor Approximable ⋆
"... Abstract. Quantitative model checking computes the probability values of a given property quantifying over all possible schedulers. It turns out that maximum and minimum probabilities calculated in such a way are overestimations on models of distributed systems in which components are loosely couple ..."
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Cited by 5 (1 self)
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Abstract. Quantitative model checking computes the probability values of a given property quantifying over all possible schedulers. It turns out that maximum and minimum probabilities calculated in such a way are overestimations on models of distributed systems in which components are loosely coupled and share little information with each other (and hence arbitrary schedulers may result too powerful). Therefore, we focus on the quantitative model checking problem restricted to distributed schedulers that are obtained only as a combination of local schedulers (i.e. the schedulers of each component) and show that this problem is undecidable. In fact, we show that there is no algorithm that can compute an approximation to the maximum probability of reaching a state within a given bound when restricted to distributed schedulers. 1
Proving Approximate Implementations for Probabilistic I/O Automata?? Abstract
, 2006
"... In this paper we introduce the notion of approximate implementations for Probabilistic I/O Automata (PIOA) and develop methods for proving such relationships. We employ a task structure on the locally controlled actions and a task scheduler to resolve nondeterminism. The interaction between a schedu ..."
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Cited by 2 (0 self)
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In this paper we introduce the notion of approximate implementations for Probabilistic I/O Automata (PIOA) and develop methods for proving such relationships. We employ a task structure on the locally controlled actions and a task scheduler to resolve nondeterminism. The interaction between a scheduler and an automaton gives rise to a trace distribution—a probability distribution over the set of traces. We define a PIOA to be a (discounted) approximate implementation of another PIOA if the set of trace distributions produced by the first is close to that of the latter, where closeness is measured by the (resp. discounted) uniform metric over trace distributions. We propose simulation functions for proving approximate implementations corresponding to each of the above types of approximate implementation relations. Since our notion of similarity of traces is based on a metric on trace distributions, we do not require the state spaces nor the space of external actions of the automata to be metric spaces. We discuss applications of approximate implementations to verification of probabilistic safety and termination.
Tracebased Semantics for Probabilistic Timed I/O Automata Submitted for review. Full version http://theory.lcs.mit.edu/ ∼mitras/ research/PTIOA06full.pdf
"... Abstract. We propose the Probabilistic Timed I/O Automaton (PTIOA) framework for modelling and analyzing discretely communicating probabilistic hybrid systems. State transition of a PTIOA can be nondeterministic or probabilistic. Probabilistic choices can be based on continuous distributions. Contin ..."
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Cited by 1 (1 self)
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Abstract. We propose the Probabilistic Timed I/O Automaton (PTIOA) framework for modelling and analyzing discretely communicating probabilistic hybrid systems. State transition of a PTIOA can be nondeterministic or probabilistic. Probabilistic choices can be based on continuous distributions. Continuous evolution of a PTIOA is purely nondeterministic. PTIOAs can communicate through shared actions. By supporting external nondeterminism, the framework allows us to model arbitrary interleaving of concurrently executing automata. The framework generalizes several previously studied automata models of its class. We develop the tracebased semantics for PTIOAs which involves measure theoretic constructions on the space of executions of the automata. We introduce a new notion of external behavior for PTIOAs and show that PTIOAs have simple compositionality properties with respect this external behavior. 1
Model Checking Concurrent Programs with Nondeterminism and Randomization
"... For concurrent probabilistic programs having processlevel nondeterminism, it is often necessary to restrict the class of schedulers that resolve nondeterminism to obtain sound and precise model checking algorithms. In this paper, we introduce two classes of schedulers called view consistent and loc ..."
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For concurrent probabilistic programs having processlevel nondeterminism, it is often necessary to restrict the class of schedulers that resolve nondeterminism to obtain sound and precise model checking algorithms. In this paper, we introduce two classes of schedulers called view consistent and locally Markovian schedulers and consider the model checking problem of concurrent, probabilistic programs under these alternate semantics. Specifically, given a Büchi automaton Spec, a threshold x ∈ [0, 1], and a concurrent program P, the model checking problem asks if the measure of computations of P that satisfy Spec is at least x, under all view consistent (or locally Markovian) schedulers. We give precise complexity results for the model checking problem (for different classes of Büchi automata specifications) and contrast it with the complexity under the standard semantics that considers all schedulers. Digital Object Identifier 10.4230/LIPIcs.FSTTCS.2010.364 1