Claudine Picaronny - Academia.edu (original) (raw)

Papers by Claudine Picaronny

Research paper thumbnail of Determinate Probabilistic Timed Automata As Markov Chains with Parametric Costs

We consider probabilistic systems modeled under the form of a special class of probabilistic time... more We consider probabilistic systems modeled under the form of a special class of probabilistic timed automata. Such automata have "no choice": - when the automaton arrives at a node, the time at which it will leave it is determined; - when the automaton leaves the node, there is just one distribution of target nodes. In the paper, we give a

Research paper thumbnail of Rapport de stage Analyse de stabilit e d'algorithmes distribu es probabilistes

Research paper thumbnail of Accepting Zeno words: a way towards timed refinements

Acta Informatica, 1997

. Timed models were introduced to describe the behaviors ofreal-time systems and they were usuall... more . Timed models were introduced to describe the behaviors ofreal-time systems and they were usually required to produce only executionswith divergent sequences of times. However, some physical phenomena,as the movements of a damped oscillator, can be representedby convergent executions, producing Zeno words in a natural way. Moreover,time can progress if such an infinite execution can be followed byother ones.Therefore, in

Research paper thumbnail of A Well-Structured Framework for Analysing Petri Nets Extensions

Transition systems defined from recursive functions INp! INpare introduced and named WSN,or well-... more Transition systems defined from recursive functions INp! INpare introduced and named WSN,or well-structured nets. Such "minimally Petri net-like" transition systems sit conveniently betweenPetri net extensions and general transition systems. In a first part, we study decidability propertiesof WSN classes obtained by imposing natural restrictions to their defining functions, with respectto termination, to coverability, and to four variants of the boundedness

Research paper thumbnail of Accepting Zeno words without making time stand still

Lecture Notes in Computer Science, 1997

Timed models were introduced to describe the behaviors of real-time systems and, up to now, they ... more Timed models were introduced to describe the behaviors of real-time systems and, up to now, they were usually required to produce only executions with divergent sequences of times. However, some physical phenomena, as the movements of a damped oscillator, can be represented by convergent executions, producing Zeno words in a natural way. Moreover, time can progress if such an execution can be followed by other ones. We extend the definition of timed automata, allowing to generate sequences of infinite convergent executions, while keeping good properties for the verification of systems: emptiness is still decidable. We introduce a new notion of refinement for timed systems, in which actions are replaced by recognizable Zeno languages and we prove that the corresponding class of languages is the closure of the usual one under refinement.

Research paper thumbnail of Randomized Dining Philosophers without Fairness Assumption

IFIP International Conference on Theoretical Computer Science, 2002

We consider Lehmann-Rabin's randomized solution to the well-known problem of the dining philo... more We consider Lehmann-Rabin's randomized solution to the well-known problem of the dining philosophers. Up to now, such an analysis has always required a "fairness" assumption on the scheduler: if a philosopher is continuously hungry then he must eventually be scheduled. In contrast here, we modify the algorithm in order to get rid of the fairness assumption. We claim that the

Research paper thumbnail of Coupling and Importance Sampling for Statistical Model Checking

Lecture Notes in Computer Science, 2012

Research paper thumbnail of Computing Expected Absorption Times for Parametric Determinate Probabilistic Timed Automata

2008 Fifth International Conference on Quantitative Evaluation of Systems

We consider a variant of probabilistic timed automata called parametric determinate probabilistic... more We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automaton's nodes, and it is possible to remain at a node only for a given amount of time. The residence time within a node may be given in terms of a parameter, and hence we do not assume that its concrete value is known. We claim that, often in practice, the maximal expected time to reach a given absorbing node of a probabilistic timed automaton can be captured using a parametric determinate probabilistic timed automaton. We give a method for computing the expected time for a parametric determinate probabilistic timed automaton to reach an absorbing node. The method consists in constructing a variant of a Markov chain with costs (where the costs correspond to durations), and is parametric in the sense that the expected absorption time is computed as a function of the model's parameters. The complexity of the analysis is independent from the maximal constant bounding the values of the clocks, and is polynomial in the number of edges of the original parametric determinate probabilistic timed automaton.

Research paper thumbnail of Randomized Finite-state Distributed Algorithms As Markov Chains

Distributed Computing, 2001

Research paper thumbnail of Practical Applications of Probabilistic Model Checking to Communication Protocols

Formal Methods for Industrial Critical Systems, 2012

relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approache... more relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approaches to the implementation of probabilistic model checking, namely those based on numerical computation and those based on discrete-event simulation. Using results from the two tools PRISM and APMC, we summarise the advantages, disadvantages and trade-offs associated with these techniques.

Research paper thumbnail of Probabilistic Model Checking of the CSMA/CD Protocol Using PRISM and APMC

Electronic Notes in Theoretical Computer Science, 2005

Carrier Sense Multiple Access/Collision Detection (CSMA/CD) is the protocol for carrier transmiss... more Carrier Sense Multiple Access/Collision Detection (CSMA/CD) is the protocol for carrier transmission access in Ethernet networks (international standard IEEE 802.3). On Ethernet, any Network Interface Card (NIC) can try to send a packet in a channel at any time. If another NIC tries to send a packet at the same time, a collision is said to occur and the packets are discarded. The CSMA/CD protocol was designed to avoid this problem, more precisely to allow a NIC to send its packet without collision. This is done by way of a randomized exponential backoff process. In this paper, we analyse the correctness of the CSMA/CD protocol, using techniques from probabilistic model checking and approximate probabilistic model checking. The tools that we use are PRISM and APMC. Moreover, we provide a quantitative analysis of some CSMA/CD properties.

Research paper thumbnail of Coupling and self-stabilization

Distributed Computing, 2006

A randomized self-stabilizing algorithm A is an algorithm that, whatever the initial configuratio... more A randomized self-stabilizing algorithm A is an algorithm that, whatever the initial configuration is, reaches a set L of legal configurations in finite time with probability 1. The proof of convergence towards L is generally done by exhibiting a potential function ϕ, which measures the "vertical" distance of any configuration to L, such that ϕ decreases with non-null probability at each step of A. We propose here a method, based on the notion of coupling, which makes use of a "horizontal" distance δ between any pair of configurations, such that δ decreases in expectation at each step of A. In contrast with classical methods, our coupling method does not require the knowledge of L. In addition to the proof of convergence, the method allows us to assess the convergence rate according to two different measures. Proofs produced by the method are often simpler or give better upper bounds than their classical counterparts, as examplified here on Herman's mutual exclusion and Iterated Prisoner's Dilemma algorithms in the case of cyclic graphs.

Research paper thumbnail of Accepting Zeno words: a way toward timed refinements

Acta Informatica, 2000

. Timed models were introduced to describe the behaviors ofreal-time systems and they were usuall... more . Timed models were introduced to describe the behaviors ofreal-time systems and they were usually required to produce only executionswith divergent sequences of times. However, when some physicalphenomena are represented by convergent executions, Zeno words appearin a natural way. Moreover, time can progress if such an infiniteexecution can be followed by other ones.Therefore, in a first part, we extend the definition of timed automata,allowing to generate sequences of infinite...

Research paper thumbnail of A well-structured framework for analysing petri net extensions

Information and Computation, 2004

Transition systems de ned from recursive functions IN p ! IN p are introduced and named WSN, or w... more Transition systems de ned from recursive functions IN p ! IN p are introduced and named WSN, or well-structured nets. Such \minimally Petri net-like" transition systems sit conveniently between Petri net extensions and general transition systems. In a rst part, we study decidability properties of WSN classes obtained by imposing natural restrictions to their de ning functions, with respect to termination, to coverability, and to four variants of the boundedness problem. We are able to answer optimally almost all the questions which arise, thus gaining much insight into old and new generalized Petri net decidability results. In a second part, we specialize our analysis to WSN de ned from a ne functions. Such a ne WSN elegantly encompass most Petri net extensions studied in the litterature. Again, we study decidability properties of natural classes of a ne WSN with respect to six computational problems. In particular, we develop a nontrivial algorithm computing limits of iterated nonnegative a ne functions, in order to decide the path-place variant of the boundedness problem for the relevant a ne WSN. Undecidability results are scattered throughout the paper, concerning, for example, extending the domain of a recursive function from IN p to (IN f!g) p .

Research paper thumbnail of Determinate Probabilistic Timed Automata As Markov Chains with Parametric Costs

We consider probabilistic systems modeled under the form of a special class of probabilistic time... more We consider probabilistic systems modeled under the form of a special class of probabilistic timed automata. Such automata have "no choice": - when the automaton arrives at a node, the time at which it will leave it is determined; - when the automaton leaves the node, there is just one distribution of target nodes. In the paper, we give a

Research paper thumbnail of Rapport de stage Analyse de stabilit e d'algorithmes distribu es probabilistes

Research paper thumbnail of Accepting Zeno words: a way towards timed refinements

Acta Informatica, 1997

. Timed models were introduced to describe the behaviors ofreal-time systems and they were usuall... more . Timed models were introduced to describe the behaviors ofreal-time systems and they were usually required to produce only executionswith divergent sequences of times. However, some physical phenomena,as the movements of a damped oscillator, can be representedby convergent executions, producing Zeno words in a natural way. Moreover,time can progress if such an infinite execution can be followed byother ones.Therefore, in

Research paper thumbnail of A Well-Structured Framework for Analysing Petri Nets Extensions

Transition systems defined from recursive functions INp! INpare introduced and named WSN,or well-... more Transition systems defined from recursive functions INp! INpare introduced and named WSN,or well-structured nets. Such "minimally Petri net-like" transition systems sit conveniently betweenPetri net extensions and general transition systems. In a first part, we study decidability propertiesof WSN classes obtained by imposing natural restrictions to their defining functions, with respectto termination, to coverability, and to four variants of the boundedness

Research paper thumbnail of Accepting Zeno words without making time stand still

Lecture Notes in Computer Science, 1997

Timed models were introduced to describe the behaviors of real-time systems and, up to now, they ... more Timed models were introduced to describe the behaviors of real-time systems and, up to now, they were usually required to produce only executions with divergent sequences of times. However, some physical phenomena, as the movements of a damped oscillator, can be represented by convergent executions, producing Zeno words in a natural way. Moreover, time can progress if such an execution can be followed by other ones. We extend the definition of timed automata, allowing to generate sequences of infinite convergent executions, while keeping good properties for the verification of systems: emptiness is still decidable. We introduce a new notion of refinement for timed systems, in which actions are replaced by recognizable Zeno languages and we prove that the corresponding class of languages is the closure of the usual one under refinement.

Research paper thumbnail of Randomized Dining Philosophers without Fairness Assumption

IFIP International Conference on Theoretical Computer Science, 2002

We consider Lehmann-Rabin's randomized solution to the well-known problem of the dining philo... more We consider Lehmann-Rabin's randomized solution to the well-known problem of the dining philosophers. Up to now, such an analysis has always required a "fairness" assumption on the scheduler: if a philosopher is continuously hungry then he must eventually be scheduled. In contrast here, we modify the algorithm in order to get rid of the fairness assumption. We claim that the

Research paper thumbnail of Coupling and Importance Sampling for Statistical Model Checking

Lecture Notes in Computer Science, 2012

Research paper thumbnail of Computing Expected Absorption Times for Parametric Determinate Probabilistic Timed Automata

2008 Fifth International Conference on Quantitative Evaluation of Systems

We consider a variant of probabilistic timed automata called parametric determinate probabilistic... more We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automaton's nodes, and it is possible to remain at a node only for a given amount of time. The residence time within a node may be given in terms of a parameter, and hence we do not assume that its concrete value is known. We claim that, often in practice, the maximal expected time to reach a given absorbing node of a probabilistic timed automaton can be captured using a parametric determinate probabilistic timed automaton. We give a method for computing the expected time for a parametric determinate probabilistic timed automaton to reach an absorbing node. The method consists in constructing a variant of a Markov chain with costs (where the costs correspond to durations), and is parametric in the sense that the expected absorption time is computed as a function of the model's parameters. The complexity of the analysis is independent from the maximal constant bounding the values of the clocks, and is polynomial in the number of edges of the original parametric determinate probabilistic timed automaton.

Research paper thumbnail of Randomized Finite-state Distributed Algorithms As Markov Chains

Distributed Computing, 2001

Research paper thumbnail of Practical Applications of Probabilistic Model Checking to Communication Protocols

Formal Methods for Industrial Critical Systems, 2012

relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approache... more relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approaches to the implementation of probabilistic model checking, namely those based on numerical computation and those based on discrete-event simulation. Using results from the two tools PRISM and APMC, we summarise the advantages, disadvantages and trade-offs associated with these techniques.

Research paper thumbnail of Probabilistic Model Checking of the CSMA/CD Protocol Using PRISM and APMC

Electronic Notes in Theoretical Computer Science, 2005

Carrier Sense Multiple Access/Collision Detection (CSMA/CD) is the protocol for carrier transmiss... more Carrier Sense Multiple Access/Collision Detection (CSMA/CD) is the protocol for carrier transmission access in Ethernet networks (international standard IEEE 802.3). On Ethernet, any Network Interface Card (NIC) can try to send a packet in a channel at any time. If another NIC tries to send a packet at the same time, a collision is said to occur and the packets are discarded. The CSMA/CD protocol was designed to avoid this problem, more precisely to allow a NIC to send its packet without collision. This is done by way of a randomized exponential backoff process. In this paper, we analyse the correctness of the CSMA/CD protocol, using techniques from probabilistic model checking and approximate probabilistic model checking. The tools that we use are PRISM and APMC. Moreover, we provide a quantitative analysis of some CSMA/CD properties.

Research paper thumbnail of Coupling and self-stabilization

Distributed Computing, 2006

A randomized self-stabilizing algorithm A is an algorithm that, whatever the initial configuratio... more A randomized self-stabilizing algorithm A is an algorithm that, whatever the initial configuration is, reaches a set L of legal configurations in finite time with probability 1. The proof of convergence towards L is generally done by exhibiting a potential function ϕ, which measures the "vertical" distance of any configuration to L, such that ϕ decreases with non-null probability at each step of A. We propose here a method, based on the notion of coupling, which makes use of a "horizontal" distance δ between any pair of configurations, such that δ decreases in expectation at each step of A. In contrast with classical methods, our coupling method does not require the knowledge of L. In addition to the proof of convergence, the method allows us to assess the convergence rate according to two different measures. Proofs produced by the method are often simpler or give better upper bounds than their classical counterparts, as examplified here on Herman's mutual exclusion and Iterated Prisoner's Dilemma algorithms in the case of cyclic graphs.

Research paper thumbnail of Accepting Zeno words: a way toward timed refinements

Acta Informatica, 2000

. Timed models were introduced to describe the behaviors ofreal-time systems and they were usuall... more . Timed models were introduced to describe the behaviors ofreal-time systems and they were usually required to produce only executionswith divergent sequences of times. However, when some physicalphenomena are represented by convergent executions, Zeno words appearin a natural way. Moreover, time can progress if such an infiniteexecution can be followed by other ones.Therefore, in a first part, we extend the definition of timed automata,allowing to generate sequences of infinite...

Research paper thumbnail of A well-structured framework for analysing petri net extensions

Information and Computation, 2004

Transition systems de ned from recursive functions IN p ! IN p are introduced and named WSN, or w... more Transition systems de ned from recursive functions IN p ! IN p are introduced and named WSN, or well-structured nets. Such \minimally Petri net-like" transition systems sit conveniently between Petri net extensions and general transition systems. In a rst part, we study decidability properties of WSN classes obtained by imposing natural restrictions to their de ning functions, with respect to termination, to coverability, and to four variants of the boundedness problem. We are able to answer optimally almost all the questions which arise, thus gaining much insight into old and new generalized Petri net decidability results. In a second part, we specialize our analysis to WSN de ned from a ne functions. Such a ne WSN elegantly encompass most Petri net extensions studied in the litterature. Again, we study decidability properties of natural classes of a ne WSN with respect to six computational problems. In particular, we develop a nontrivial algorithm computing limits of iterated nonnegative a ne functions, in order to decide the path-place variant of the boundedness problem for the relevant a ne WSN. Undecidability results are scattered throughout the paper, concerning, for example, extending the domain of a recursive function from IN p to (IN f!g) p .