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44
Concurrent strategies
 In LICS’11. IEEE Computer Society
, 2011
"... Abstract—A bicategory of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, en ..."
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Cited by 22 (8 self)
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Abstract—A bicategory of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate. I.
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 15 (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
The Winning Ways of Concurrent Games
"... Abstract—A bicategory of concurrent games, where nondeterministic strategies are formalized as certain maps of event structures, was introduced recently. This paper studies an extension of concurrent games by winning conditions, specifying players ’ objectives. The introduction of winning conditions ..."
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Cited by 11 (4 self)
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Abstract—A bicategory of concurrent games, where nondeterministic strategies are formalized as certain maps of event structures, was introduced recently. This paper studies an extension of concurrent games by winning conditions, specifying players ’ objectives. The introduction of winning conditions raises the question of whether such games are determined, that is, if one of the players has a winning strategy. This paper gives a positive answer to this question when the games are wellfounded and satisfy a structural property, racefreedom, which prevents one player from interfering with the moves available to the other. Uncovering the conditions under which concurrent games with winning conditions are determined opens up the possibility of further applications of concurrent games in areas such as logic and verification, where both winning conditions and determinacy are most needed. A concurrentgame semantics for predicate calculus is provided as an illustration. I.
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 10 (3 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
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 8 (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
"... ..."
An Algorithm for Exact Satisfiability Analysed with the Number of Clauses as Parameter
, 2004
"... We give an algorithm for Exact Satisfiability with polynomial space usage and a time bound of poly(L) m!, where m is the number of clauses and L is the length of the formula. Skjernaa has given an algorithm for Exact Satisfiability with time bound poly(L) but using exponential space. We ..."
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Cited by 7 (0 self)
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We give an algorithm for Exact Satisfiability with polynomial space usage and a time bound of poly(L) m!, where m is the number of clauses and L is the length of the formula. Skjernaa has given an algorithm for Exact Satisfiability with time bound poly(L) but using exponential space. We leave the following problem open: Is there an algorithm for Exact Satisfiability using only polynomial space with a time bound of c , where c is a constant and m is the number of clauses?
Events, Causality and Symmetry
, 2008
"... The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences ..."
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Cited by 6 (2 self)
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The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences, actual and potential, are discussed.
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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Cited by 6 (4 self)
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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.
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 6 (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.