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31
Comparison of the expressiveness of timed automata and time Petri nets
 IN PROC. FORMATS’05, VOL. 3829 OF LNCS
, 2005
"... In this paper we consider the model of Time Petri Nets (TPN) “à la Merlin” where a time interval is associated with the firing of a transition, but we extend it with open intervals. We also consider Timed Automata (TA) as defined by Alur & Dill. We investigate some questions related to expressi ..."
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Cited by 22 (9 self)
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In this paper we consider the model of Time Petri Nets (TPN) “à la Merlin” where a time interval is associated with the firing of a transition, but we extend it with open intervals. We also consider Timed Automata (TA) as defined by Alur & Dill. We investigate some questions related to expressiveness for these models: we study the impact of slight variations of semantics for TPN and we compare the expressive power of TA and TPN, with respect to both time language acceptance and weak time bisimilarity. We prove that TA and bounded TPNs (enlarged with strict constraints) are equivalent w.r.t. timed language equivalence, providing an efficient construction of a TPN equivalent to a TA. We then exhibit a TA A such that no TPN (even unbounded) is weakly bisimilar to A. Because of this last result, it is natural to try and identify the (strict) subclass of TA that is equivalent to TPN w.r.t. weak timed bisimilarity. Thus we give some further results: 1) we characterize the subclass TA − of TA that is equivalent to the original model of TPN as defined by Merlin, i.e. restricted to closed intervals, 2) we show that the associated membership problem for TA − is PSPACEcomplete and 3) we prove that the reachability problem for TA − is also PSPACEcomplete.
E.: StateDensity Functions over DBM Domains in the Analysis of NonMarkovian Models
 IEEE Trans. on SW Eng
, 2009
"... Abstract—Quantitative evaluation of models with generally distributed transitions requires the analysis of nonMarkovian processes that may be not isomorphic to their underlying untimed models and may include any number of concurrent nonexponential timers. The analysis of stochastic Time Petri Nets ..."
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Abstract—Quantitative evaluation of models with generally distributed transitions requires the analysis of nonMarkovian processes that may be not isomorphic to their underlying untimed models and may include any number of concurrent nonexponential timers. The analysis of stochastic Time Petri Nets (sTPNs) copes with the problem by covering the state space with stochastic classes, which extend the theory of Difference Bounds Matrix (DBM) with a state probability density function. As a core step, the analysis process requires symbolic manipulation of density functions supported over DBM domains. We characterize and engineer the critical steps of this derivation. We first show that the statedensity function accepts a continuous piecewise representation over a partition in DBMshaped subdomains. We then develop a closedform symbolic calculus of statedensity functions under the assumption that transitions in the sTPN model have expolynomial distributions over possibly bounded intervals. The calculus shows that within each subdomain, the statedensity function is a multivariate expolynomial function, and it makes explicit the way in which this form evolves and grows in complexity as the state accumulates memory through subsequent transitions. This enables an efficient implementation of the analysis process and provides the formal basis that supports the introduction of an imprecise analysis based on the approximation of statedensity functions through Bernstein Polynomials. The approximation attacks practical and theoretical limits in the applicability of stochastic state classes and devises a new approach to the analysis of nonMarkovian models, relying on approximations in the state space rather than in the structure of the model. Index Terms—Correctness verification, performance and dependability, quantitative evaluation, stochastic Time Petri nets, densetime statespace analysis, Difference Bounds Matrix, Markov Renewal Theory, approximate statespace representation, density function approximation, Bernstein polynomials. Ç 1
Using Stochastic State Classes in Quantitative Evaluation of DenseTime Reactive Systems
"... Abstract—In the verification of reactive systems with nondeterministic densely valued temporal parameters, the statespace can be covered through equivalence classes, each composed of a discrete logical location and a dense variety of clock valuations encoded as a Difference Bounds Matrix (DBM). The ..."
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Abstract—In the verification of reactive systems with nondeterministic densely valued temporal parameters, the statespace can be covered through equivalence classes, each composed of a discrete logical location and a dense variety of clock valuations encoded as a Difference Bounds Matrix (DBM). The reachability relation among such classes enables qualitative verification of properties pertaining events ordering and stimulus/response deadlines, but it does not provide any measure of probability for feasible behaviors. We extend DBM equivalence classes with a densityfunction which provides a measure for the probability of individual states. To this end, we extend Time Petri Nets by associating a probability densityfunction to the static firing interval of each nondeterministic transition. We then explain how this stochastic information induces a probability distribution for the states contained within a DBM class and how this probability evolves in the enumeration of the reachability relation among classes. This enables the construction of a stochastic transition system which supports correctness verification based on the theory of TPNs, provides a measure of probability for each feasible run, enables steadystate analysis based on Markov Renewal Theory. In so doing, we provide a means to identify feasible behaviors and to associate them with a measure of probability in models with multiple concurrent generally distributed nondeterministic timers.
When are timed automata weakly timed bisimilar to time Petri nets?
 25TH CONFERENCE ON FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE (FSTTCS 2005), HYDERABAD, INDIA LNCS
, 2005
"... In this paper, we compare Timed Automata (TA) and Time Petri Nets (TPN) with respect to weak timed bisimilarity. It is already known that the class of bounded TPNs is strictly included in the class of TA. It is thus natural to try and identify the subclass T A wtb of TA equivalent to some TPN for t ..."
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Cited by 12 (4 self)
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In this paper, we compare Timed Automata (TA) and Time Petri Nets (TPN) with respect to weak timed bisimilarity. It is already known that the class of bounded TPNs is strictly included in the class of TA. It is thus natural to try and identify the subclass T A wtb of TA equivalent to some TPN for the weak timed bisimulation relation. We give a characterization of this subclass and we show that the membership problem and the reachability problem for T A wtb are PSPACEcomplete. Furthermore we show that for a TA in T A wtb with integer constants, an equivalent TPN can be built with integer bounds but with a size exponential w.r.t. the original model. Surprisingly, using rational bounds yields a TPN whose size is linear.
Aggregated Stochastic State Classes in Quantitative Evaluation of nonMarkovian Stochastic Petri Nets
"... Abstract—The method of stochastic state classes provides a new approach for the analysis of nonMarkovian stochastic Petri Nets, which relies on the stochastic expansion of the graph of nondeterministic state classes based on Difference Bounds Matrix (DBM) which is usually employed in qualitative ve ..."
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Cited by 11 (5 self)
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Abstract—The method of stochastic state classes provides a new approach for the analysis of nonMarkovian stochastic Petri Nets, which relies on the stochastic expansion of the graph of nondeterministic state classes based on Difference Bounds Matrix (DBM) which is usually employed in qualitative verification. In so doing, the method is able to manage multiple concurrent nonexponential (GEN) transitions and largely extends the class of models that are amenable to quantitative evaluation. However, its application requires that every cycle in the graph of nondeterministic state classes visits at least a regeneration point where all GEN transitions are newly enabled. In particular, this rules out models whose nondeterministic class graph includes cycles within a Continuous Time Markov Chain (CTMC) subordinated to the activity period of one or more GEN transitions. In this paper, we propose an extension that overcomes this limitation by aggregating together classes that are reached through firings that do not change the enabling status of GEN transitions. This enlarges the class of models that can be analysed through the method of stochastic state classes and makes it become a proper extension of the class of models that satisfies the so called enabling restriction. Index Terms—nonMarkovian stochastic Petri nets, stochastic time Petri nets, steady state analysis, stochastic state classes.
Sirio: A framework for simulation and symbolic state space analysis of nonMarkovian models
 In 8st Int. Conf. on Quantitative Evaluation of Systems (QEST '11
, 2011
"... Abstract. Formal methods supporting development of safetycritical systems require tools that can be integrated within composed environments. Sirio is a framework for simulation and analysis of various timed extensions of Petri Nets, supporting correctness verification and quantitative evaluation ..."
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Abstract. Formal methods supporting development of safetycritical systems require tools that can be integrated within composed environments. Sirio is a framework for simulation and analysis of various timed extensions of Petri Nets, supporting correctness verification and quantitative evaluation of timed concurrent systems. As a characterizing trait, Sirio is expressly designed to support reuse and to facilitate extensions such as the definition of new reward measures, new variants of the analysis, and new models with a different semantics. We describe here the functional responsibilities and the SW architecture of the framework.
Symbolic Unfoldings for Networks of Timed Automata
, 2006
"... Abstract. In this paper we give a symbolic concurrent semantics for network of timed automata (NTA) in terms of extended symbolic nets. Extended symbolic nets are standard occurrence nets extended with read arcs and symbolic constraints on places and transitions. We prove that there is a complete fi ..."
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Abstract. In this paper we give a symbolic concurrent semantics for network of timed automata (NTA) in terms of extended symbolic nets. Extended symbolic nets are standard occurrence nets extended with read arcs and symbolic constraints on places and transitions. We prove that there is a complete finite prefix for any NTA that contains at least the information of the simulation graph of the NTA but keep explicit the notions of concurrency and causality of the network. 1
A ConcurrencyPreserving Translation from Time Petri Nets to Networks of Timed Automata
, 2010
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Formal methods for Systems Engineering behavior models
 IEEE Transactions on Industrial Informatics
, 2008
"... cesses, as usually implemented, rarely relies on formal methods such as model checking since such techniques, however powerful and mature, are deemed too complex for efficient use. This paper thus aims at improving the verification practice in SE design: considering the widelyused model of EFFBDs ( ..."
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Cited by 3 (0 self)
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cesses, as usually implemented, rarely relies on formal methods such as model checking since such techniques, however powerful and mature, are deemed too complex for efficient use. This paper thus aims at improving the verification practice in SE design: considering the widelyused model of EFFBDs (Enhanced Function Flow Block Diagrams), it formally establishes its syntax and behavioral semantics. It also proposes a structural translation of EFFBDs to transition time Petri nets (TPNs); this translation is then proved to preserve the behavioral semantics (i.e. timed bisimilarity). After proving results on the boundedness of the resulting TPNs, it was possible to extend a number of fundamental properties (such as the decidability of liveness, stateaccess, etc.) from bounded TPNs to socalled bounded EFFBDs. Finally, these results led to both implementing and integrating a formal verification tool within a development platform for system design for defense applications and in which the underlying complexity is totally concealed from the enduser. Index Terms—Systems Engineering, time Petri nets, embedded system design, formal verification, timed bisimulation.
Extended Timed Automata and Time Petri Nets
, 2006
"... Timed Automata (TA) and Time Petri Nets (TPN) are two wellestablished formal models for realtime systems. Recently, a linear transformation of TA to TPNs preserving reachability properties and timed languages has been proposed, which does however not extend to larger classes of TA which would allo ..."
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Timed Automata (TA) and Time Petri Nets (TPN) are two wellestablished formal models for realtime systems. Recently, a linear transformation of TA to TPNs preserving reachability properties and timed languages has been proposed, which does however not extend to larger classes of TA which would allow diagonal constraints or more general resets of clocks. Though these features do not add expressiveness, they yield exponentially more concise models. In this work, we propose two translations: one from extended TA to TPNs whose size is either linear or quadratic in the size of the original TA, depending on the features which are allowed; another one from a parallel composition of TA to TPNs, which is also linear. As a consequence, we get that TPNs are exponentially more concise than TA.