Results 1  10
of
15
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 ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
(Show Context)
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.
Probabilistic trueconcurrency models: branching cells and distributed probabilities, in "Information and Computation
, 2006
"... This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finit ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite. Locally finite event structures exhibit “finite confusion”; in particular, under some mild condition, confusionfree event structures are locally finite. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite substructures capturing the choices performed while scanning a maximal configuration. A probabilistic event structure (p.e.s.) is a pair (E, P), where E is a prime event structure and P is a probability on the space of maximal configurations of E. We introduce the new class of distributed probabilities for p.e.s.: distributed probabilities are such that random choices in
The (True) Concurrent Markov Property and Some Applications to Markov Nets
"... Abstract. We study probabilistic safe Petri nets, a probabilistic extension of safe Petri nets interpreted under the trueconcurrent semantics. In particular, the likelihood of processes is defined on partial orders, not on firing sequences. We focus on memoryless probabilistic nets: we give a defin ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
(Show Context)
Abstract. We study probabilistic safe Petri nets, a probabilistic extension of safe Petri nets interpreted under the trueconcurrent semantics. In particular, the likelihood of processes is defined on partial orders, not on firing sequences. We focus on memoryless probabilistic nets: we give a definition for such systems, that we call Markov nets, and we study their properties. We show that several tools from Markov chains theory can be adapted to this trueconcurrent framework. In particular, we introduce stopping operators that generalize stopping times, in a more convenient fashion than other extensions previously proposed. A Strong Markov Property holds in the concurrency framework. We show that the Concurrent Strong Markov property is the key ingredient for studying the dynamics of Markov nets. In particular we introduce some elements of a recurrence theory for nets, through the study of renewal operators. Due to the concurrency properties of Petri nets, Markov nets have global and local renewal operators, whereas both coincide for sequential systems. 1
Trueconcurrency probabilistic models Branching cells and distributed probabilities for event structures
, 2006
"... ..."
Trueconcurrency Probabilistic Models: Markov Nets and a Law of Large Numbers
, 2005
"... We introduce the model of Markov nets, a probabilistic extension of safe Petri nets under the trueconcurrency semantics. This model builds upon our previous work on probabilistic event structures. We use the notion of branching cell for event structures and show that the latter provides the adequa ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
We introduce the model of Markov nets, a probabilistic extension of safe Petri nets under the trueconcurrency semantics. This model builds upon our previous work on probabilistic event structures. We use the notion of branching cell for event structures and show that the latter provides the adequate notion of local state, for nets. We prove a Law of Large Numbers (LLN) for Markov nets—this constitutes the main contribution of the paper. This LLN allows characterizing in a quantitative way the asymptotic behavior of Markov nets.
Typed event Structures and the πcalculus
 In Proc. MFPS’06
, 2006
"... Abstract. We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. It is a generalisation of confluence to systems that allow nondeterminism. Ours is the first typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the πcalculi with internal mobility. The semantics we provide is the first event structure semantics of the πcalculus and generalises Winskel’s original event structure semantics of CCS. 1
A Cartesian Closed Category of Event Structures with Quotients
, 2006
"... We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural notion of quotient event structure is defined within it. We study in particular the topological space of maximal configurations of quotient event structures. We introduce the compress ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural notion of quotient event structure is defined within it. We study in particular the topological space of maximal configurations of quotient event structures. We introduce the compression of event structures as an example of quotient: the compression of an event structure E is a minimal event structure with the same space of maximal configurations as E.
Law and Partial Order  Nonsequential Behaviour and Probability in Asynchronous Systems
, 2008
"... ..."
Concurrency, σalgebras, and probabilistic fairness
"... We extend previous constructions of probabilities for a prime event structure E by allowing arbitrary confusion. Our study builds on results related to fairness in event structures that are of interest per se. Executions of E are captured by the set Ω of maximal configurations. We show that the inf ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We extend previous constructions of probabilities for a prime event structure E by allowing arbitrary confusion. Our study builds on results related to fairness in event structures that are of interest per se. Executions of E are captured by the set Ω of maximal configurations. We show that the information collected by observing only fair executions of E is confined in some σalgebra F0, contained in the Borel σalgebra F of Ω. Equality F0 = F holds when confusion is finite (formally, for the class of locally finite event structures), but inclusion F0 ⊆ F is strict in general. We show the existence of an increasing chain F0 ⊆ F1 ⊆ F2 ⊆... of subσalgebras of F that capture the information collected when observing executions of increasing unfairness. We show that, if the event structure unfolds a 1safe net, then unfairness remains quantitatively bounded, that is, the above chain reaches F in finitely many steps. The construction of probabilities typically relies on a Kolmogorov extension argument. Such arguments can achieve the construction of probabilities on the σalgebra F0 only, while one is interested in probabilities defined on the entire Borel σalgebra F. We prove that, when the event structure unfolds a 1safe net, then unfair executions all belong to some set of F0 of zero probability. Whence F0 = F modulo 0 always holds, whereas F0 ̸ = F in general. This yields a new construction of Markovian probabilistic nets, carrying a natural interpretation that “unfair executions possess zero probability”.
Author manuscript, published in "International Conference on Theory and Applications of Petri Nets, Miami: ÉtatsUnis d'Amérique (2005)" The (True) Concurrent Markov Property and Some Applications to Markov Nets
, 2009
"... Abstract. We study probabilistic safe Petri nets, a probabilistic extension of safe Petri nets interpreted under the trueconcurrent semantics. In particular, the likelihood of processes is defined on partial orders, not on firing sequences. We focus on memoryless probabilistic nets: we give a defin ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We study probabilistic safe Petri nets, a probabilistic extension of safe Petri nets interpreted under the trueconcurrent semantics. In particular, the likelihood of processes is defined on partial orders, not on firing sequences. We focus on memoryless probabilistic nets: we give a definition for such systems, that we call Markov nets, and we study their properties. We show that several tools from Markov chains theory can be adapted to this trueconcurrent framework. In particular, we introduce stopping operators that generalize stopping times, in a more convenient fashion than other extensions previously proposed. A Strong Markov Property holds in the concurrency framework. We show that the Concurrent Strong Markov property is the key ingredient for studying the dynamics of Markov nets. In particular we introduce some elements of a recurrence theory for nets, through the study of renewal operators. Due to the concurrency properties of Petri nets, Markov nets have global and local renewal operators, whereas both coincide for sequential systems. 1