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Partial Order Techniques for Distributed Discrete Event Systems: why you can’t avoid using them
, 2007
"... Monitoring or diagnosis of large scale distributed Discrete Event Systems with asynchronous communication is a demanding task. Ensuring that the methods developed for Discrete Event Systems properly scale up to such systems is a challenge. In this paper we explain why the use of partial orders canno ..."
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Cited by 15 (1 self)
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Monitoring or diagnosis of large scale distributed Discrete Event Systems with asynchronous communication is a demanding task. Ensuring that the methods developed for Discrete Event Systems properly scale up to such systems is a challenge. In this paper we explain why the use of partial orders cannot be avoided in order to achieve this objective. To support this claim, we try to push classical techniques (parallel composition of automata and languages) to their limits and we eventually discover that partial order models arise at some point. We focus on online techniques, where a key difficulty is the choice of proper data structures to represent the set of all runs of a distributed system, in a modular way. We discuss the use of previously known structures such as execution trees and unfoldings. We propose a novel and more compact data structure called “trellis”. Then, we show how all the above data structures can be used in performing distributed monitoring and diagnosis. The techniques reported here were used in an industrial context for fault management and alarm correlation in telecommunications networks. This paper is an extended and improved version of the plenary address that was given by the second author at WODES’2006.
Types of Asynchronous Diagnosability and the RevealsRelation in Occurrence Nets
"... We consider asynchronous diagnosis in (safe) Petri net models of distributed systems, using the partial order semantics of occurrence net unfoldings. Both the observability and diagnosability properties will appear in two different forms, depending on the semantics chosen: strong observability and ..."
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Cited by 12 (10 self)
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We consider asynchronous diagnosis in (safe) Petri net models of distributed systems, using the partial order semantics of occurrence net unfoldings. Both the observability and diagnosability properties will appear in two different forms, depending on the semantics chosen: strong observability and diagnosability are the classical notions from the state machine model and correspond to interleaving semantics in Petri nets. By contrast, the weak form is linked to characteristics of nonsequential processes, and requires an asynchronous progress assumption on those processes. We give algebraic characterizations for both types, and give verification methods. The study of weak diagnosability leads us to the analysis of a relation in occurrence nets, first presented in [15]: given the occurrence of some event a that reveals b, the occurrence of b is inevitable. Then b may already have occurred, be concurrent to, or even in the future of a. We show that the revealsrelation can be effectively computed recursively for each pair, a suitable finite prefix of bounded depth is sufficient, and show its use in asynchronous diagnosis. Based on this relation, a decomposition of the Petri net unfolding into facets is defined, yielding an abstraction technique that preserves and reflects maximal partially ordered runs.
Distributed probabilistic and quantum strategies
 Submitted LICS
"... Abstract—Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copycat strategies as identities. A higherorder probabilistic pr ..."
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Abstract—Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copycat strategies as identities. A higherorder probabilistic process language reminiscent of Milner’s CCS is interpreted within probabilistic strategies. Probabilistic games extend to games with payoff and games of imperfect information. W.r.t. new definitions of quantum event structures, it is shown how consistent parts of a quantum event structure are automatically probabilistic event structures, and so possess a probability measure. This gives a nontraditional take on the consistenthistories approach to quantum theory. The paper concludes with an extension to quantum strategies. I.
On the origin of events: branching cells as stubborn sets
"... In prime event structures with binary conflicts (pesbc)³ a branching cell [1] is a subset of events closed under downward causality and immediate conflict relations. This means that no event outside the branching cell can be in conflict with or enable any event inside the branching cell. It bears a ..."
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In prime event structures with binary conflicts (pesbc)³ a branching cell [1] is a subset of events closed under downward causality and immediate conflict relations. This means that no event outside the branching cell can be in conflict with or enable any event inside the branching cell. It bears a strong resemblance to stubborn sets, a partial order reduction method on transition systems. A stubborn set (at a given state) is a subset of actions such that no execution consisting entirely of actions outside the stubborn set can be in conflict with or enable actions that are inside the stubborn set. A rigorous study of the relationship between the two ideas, however, is not straightforward due to the facts that 1) stubborn sets utilise sophisticated causality and conflict relations that invalidate the stability and coherence of event structures [18], 2) without stability it becomes very difficult to define concepts like prefixes and branching cells, which prerequire a clear notion of causality, and 3) it is challenging to devise a technique for identifying ‘proper’ subsets of transitions as ‘events ’ such that the induced eventbased system captures exactly the causality and conflict information needed by stubborn sets. In this paper we give a solution to the problems by providing an unfolding of labelled transition systems into configuration structures, a more general structure supporting orcausality and finite conflict. We show that the branching cell definition can be extended to configuration structures and that each branching cell in the unfolding is a longlived stubborn set, such that no matter how the system evolves, what remains of the branching cell is always a stubborn set.
MFPS 2013 Distributed Probabilistic Strategies
"... Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copycat strategies as identities. A higherorder probabilistic process lan ..."
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Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copycat strategies as identities. A higherorder probabilistic process language reminiscent of Milner’s CCS is interpreted within probabilistic strategies. W.r.t. a new definition of quantum event structure, it is shown how consistent parts of a quantum event structure are automatically probabilistic event structures, and so possess a probability measure. This gives a nontraditional take on the consistenthistories approach to quantum theory. It leads to an extension to quantum strategies. Probabilistic games extend to games with payoff, symmetry and games of imperfect information. 1
Order algebras: a quantitative model of interaction
, 2010
"... Abstract. A quantitative model of concurrent interaction in introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential nondeterminism in synchronisation. This algebraic structure is shown to provide faithful inte ..."
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Abstract. A quantitative model of concurrent interaction in introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential nondeterminism in synchronisation. This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational (in the sense that the internal workings of processes are ignored) and noninterleaving. Constructions on algebras and their subspaces enjoy a good structure that make them (nearly) a model of differential linear logic, showing that the underlying approach to the representation of nondeterminism as linear
s’ Distributed Markov Chains
"... Abstract. The formal verification of large probabilistic models is important and challenging. Exploiting the concurrency that is often present is one way to address this problem. Here we study a restricted class of asynchronous distributed probabilistic systems in which the synchronizations determ ..."
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Abstract. The formal verification of large probabilistic models is important and challenging. Exploiting the concurrency that is often present is one way to address this problem. Here we study a restricted class of asynchronous distributed probabilistic systems in which the synchronizations determine the probability distribution for the next moves of the participating agents. The key restriction we impose is that the synchronizations are deterministic, in the sense that any two simultaneously enabled synchronizations must involve disjoint sets of agents. As a result, this network of agents can be viewed as a succinct and distributed presentation of a large global Markov chain. A rich class of Markov chains can be represented this way. We define an interleaved semantics for our model in terms of the local synchronization actions. The network structure induces an independence relation on these actions, which, in turn, induces an equivalence relation over the interleaved runs in the usual way. We construct a natural probability measure over these equivalence classes of runs by exploiting Mazurkiewicz trace theory and the probability measure space of the associated global Markov chain. It turns out that verification of our model, called DMCs (distributed Markov chains), can often be efficiently carried out by exploiting the partial order nature of the interleaved semantics. To demonstrate this, we develop a statistical model checking (SMC) procedure and use it to verify two large distributed probabilistic networks. 1