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Computation in Networks of Passively Mobile FiniteState Sensors
 Distributed Computing
, 2004
"... We explore the computational power of networks of small resourcelimited mobile agents. We define two new models of computation based on pairwise interactions of finitestate agents in populations of finite but unbounded size. With a fairness condition on interactions, we define the concept of stabl ..."
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Cited by 71 (15 self)
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We explore the computational power of networks of small resourcelimited mobile agents. We define two new models of computation based on pairwise interactions of finitestate agents in populations of finite but unbounded size. With a fairness condition on interactions, we define the concept of stable computation of a function or predicate, and give protocols that stably compute functions in a class including Boolean combinations of thresholdk, parity, majority, and simple arithmetic. We prove that all stably computable predicates are in NL. With uniform random sampling of pairs to interact, we define the model of conjugating automata and show that any counter machine with O(1) counters of capacity O(n) can be simulated with high probability by a protocol in a population of size n. We prove that all predicates computable with high probability in this model are in P #RL.
Markov Nets: Probabilistic Models for distributed and concurrent systems
 IEEE Transactions on Automatic Control
, 2001
"... For distributed systems, i.e. large networked complex systems, there is a drastic difference between a local view and knowledge of the system, and its global view. Distributed systems have local state and time, but do not possess global state and time in the usual sense. In this paper, motivated by ..."
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Cited by 33 (16 self)
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For distributed systems, i.e. large networked complex systems, there is a drastic difference between a local view and knowledge of the system, and its global view. Distributed systems have local state and time, but do not possess global state and time in the usual sense. In this paper, motivated by the monitoring of distributed systems and in particular of telecommunications networks, we develop Markov nets as an extension of Markov chains and hidden Markov models (Hmm) for distributed and concurrent systems. By a concurrent system, we mean a system in which components may evolve independently, with sparse synchronizations. We follow a socalled true concurrency approach, in which neither global state nor global linear time are available. Instead, we use only local states in combination with a partial order model of time. Our basic mathematical tool is that of Petri net unfoldings. Keywords : discrete event systems, stochastic Petri nets, unfoldings. 1 Motivations Distributed network...
Branching cells as local states for event structures and nets: Probabilistic applications
 In Proceedings of 8th FoSSaCS, volume 3441 of LNCS
, 2005
"... Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is ..."
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Cited by 16 (9 self)
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Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is to bring an interpretation of branching cells as a right notion of “local state”, for concurrent systems. We illustrate the above claim through applications to probabilistic concurrent models. In this respect, our results extends in part previous work by VaraccaVölzerWinskel on probabilistic confusion free event structures. We propose a construction for probabilities over socalled locally finite event structures that makes concurrent processes probabilistically independent—simply attach a dice to each branching cell; dices attached to concurrent branching cells are thrown independently. Furthermore, we provide a true concurrency generalization of Markov chains, called Markov nets. Unlike in existing variants of stochastic Petri nets, our approach randomizes Mazurkiewicz traces, not firing sequences. We show in this context the Law of Large Numbers (LLN), which confirms that branching cells deserve the status of local state. Our study was motivated by the stochastic modeling of fault propagation and alarm correlation in telecommunications networks and services. It provides the foundations for probabilistic diagnosis, as well as the statistical distributed learning of such models. 1
Urn Automata
, 2003
"... Urn automata are a new class of automata consisting of an input tape, a finitestate controller, and an urn containing tokens with a finite set of colors, where the finitestate controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the comput ..."
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Cited by 13 (11 self)
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Urn automata are a new class of automata consisting of an input tape, a finitestate controller, and an urn containing tokens with a finite set of colors, where the finitestate controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the computational power of urn automata, showing that an urn automaton with O(f(n)) tokens can, with high probability, simulate a probabilistic Turing machine using O(log f(n)) space and vice versa, as well as giving several technical results showing that the computational power of urn automata is not a#ected by variations in parameters such as the size of the state space, the number of tokens sampled per step, and so forth. Motivated by problems in distributed computing, we consider a special class of urn automata called pairing automata that model systems of finitestate machines that interact through random pairwise encounters.
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 ..."
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Cited by 7 (4 self)
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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
"... ..."
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 ..."
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Cited by 5 (1 self)
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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
Probability, Nondeterminism and Concurrency: Two Denotational Models for Probabilistic Computation
 PHD THESIS, UNIV. AARHUS, 2003. BRICS DISSERTATION SERIES
, 2003
"... Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particular t ..."
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Cited by 5 (1 self)
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Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particular there is no categorical distributive law between them. We introduce the powerdomain of indexed valuations which modifies the usual probabilistic powerdomain to take more detailed account of where probabilistic choices are made. We show the existence of a distributive law between the powerdomain of indexed valuations and the nondeterministic powerdomain. By means of an equational theory we give an alternative characterisation of indexed valuations and the distributive law. We study the relation between valuations and indexed valuations. Finally we use indexed valuations to give a semantics to a programming language. This semantics reveals the computational intuition lying behind the mathematics. In the second part of the thesis we provide an operational reading of continuous valuations on certain domains (the distributive concrete domains of Kahn and Plotkin) through the model of probabilistic event structures. Event structures are a model for concurrent computation that account for causal relations between events. We propose a way of adding probabilities to confusion free event structures, defining the notion of probabilistic event structure. This leads to various ideas of a run for probabilistic event structures. We show a confluence theorem for such runs. Configurations of a confusion free event structure form a distributive concrete domain. We give a representation theorem which characterises completely the powerdomain of valuations of such concrete domains in terms of prob...
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 ..."
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Cited by 5 (0 self)
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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.
Probabilistic πCalculus and Event Structures
"... This paper proposes two semantics of a probabilistic variant of the πcalculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of nondeterministic p ..."
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Cited by 2 (2 self)
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This paper proposes two semantics of a probabilistic variant of the πcalculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of nondeterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed πcalculus.