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22
Alternating Timed Automata
 In FOSSACS’05, volume 3441 of LNCS
, 2005
"... Abstract. A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations and which has an effective presentation. We prove th ..."
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Cited by 27 (3 self)
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Abstract. A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations and which has an effective presentation. We prove that the complexity of the emptiness problem for alternating timed automata with one clock is nonprimitive recursive. The proof gives also the same lower bound for the universality problem for nondeterministic timed automata with one clock. We investigate extension of the model with epsilontransitions and prove that emptiness is undecidable. Over infinite words, we show undecidability of the universality problem. 1
On the decidability and complexity of metric temporal logic over finite words
 Logical Methods in Computer Science
, 2007
"... Abstract. Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with nonprimitive recursive complexity. We also consider the modelchecking problem for MTL: whethe ..."
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Cited by 22 (2 self)
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Abstract. Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with nonprimitive recursive complexity. We also consider the modelchecking problem for MTL: whether all words accepted by a given AlurDill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL— which includes invariance and timebounded response properties—is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature. 1.
The Cost of Punctuality
, 2007
"... ... Metric Interval Temporal Logic (MITL) as a fragment of the realtime logic Metric Temporal Logic (MTL) in which exact or punctual timing constraints are banned. Their main result showed that model checking and satisfiability for MITL are both EXPSPACEComplete. Until recently, it was widely beli ..."
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Cited by 19 (9 self)
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... Metric Interval Temporal Logic (MITL) as a fragment of the realtime logic Metric Temporal Logic (MTL) in which exact or punctual timing constraints are banned. Their main result showed that model checking and satisfiability for MITL are both EXPSPACEComplete. Until recently, it was widely believed that admitting even the simplest punctual specifications in any lineartime temporal logic would automatically lead to undecidability. Although this was recently disproved, until now no punctual fragment of MTL was known to have even primitive recursive complexity (with certain decidable fragments having provably nonprimitive recursive complexity). In this paper we identify a ‘coflat ’ subset of MTL that is capable of expressing a large class of punctual specifications and for which model checking (although not satisfiability) has no complexity cost over MITL. Our logic is moreover qualitatively different from MITL in that it can express properties that are not timedregular. Correspondingly, our decision procedures do not involve translating formulas into finitestate automata, but rather into certain kinds of reversalbounded Turing machines. Using this translation we show that the model checking problem for our logic is EXPSPACEComplete
Timed Petri Nets and Timed Automata: On the Discriminating Power of Zeno Sequences
, 2006
"... Timed Petri nets and timed automata are two standard models for the analysis of realtime systems. In this paper, we prove that they are incomparable for the timed language equivalence. Thus we propose an extension of timed Petri nets with readarcs (RATdPN), whose coverability problem is decidabl ..."
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Cited by 10 (4 self)
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Timed Petri nets and timed automata are two standard models for the analysis of realtime systems. In this paper, we prove that they are incomparable for the timed language equivalence. Thus we propose an extension of timed Petri nets with readarcs (RATdPN), whose coverability problem is decidable. We also show that this model unifies timed Petri nets and timed automata. Then, we establish numerous expressiveness results and prove that zeno behaviours discriminate between several subclasses of RATdPNs. This has surprising consequences on timed automata, for instance on the power of nondeterministic clock resets.
Decision Problems for the Verification of RealTime Software
 In Proceedings of HSCC 06
, 2006
"... Abstract. We study two questions in the theory of timed automata concerning timed language inclusion of realtime programs modeled as timed pushdown automata in realtime specifications with just one clock. We show that if the specification B is modeled as a timed automaton with one clock, then the ..."
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Cited by 7 (0 self)
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Abstract. We study two questions in the theory of timed automata concerning timed language inclusion of realtime programs modeled as timed pushdown automata in realtime specifications with just one clock. We show that if the specification B is modeled as a timed automaton with one clock, then the language inclusion problem L(A) ` L(B) for a timed pushdown automaton A is decidable. On the other hand, we show that the universality problem of timed visibly pushdown automata with only one clock is undecidable. Thus there is no algorithm to check language inclusion of realtime programs for specifications given by visibly pushdown specifications with just one clock.
Model Checking Timed and Stochastic Properties with CSL^TA
, 2008
"... Markov chains are a wellknown stochastic process that provide a balance between being able to adequately model the system’s behavior and being able to afford the cost of the model solution. Systems can be modelled directly as Markov chains, or with a higherlevel formalism for which Markov chains r ..."
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Cited by 7 (3 self)
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Markov chains are a wellknown stochastic process that provide a balance between being able to adequately model the system’s behavior and being able to afford the cost of the model solution. Systems can be modelled directly as Markov chains, or with a higherlevel formalism for which Markov chains represent the underlying semantics. Markov chains are widely used to study the performance of computer and telecommunication systems. The definition of stochastic temporal logics like Continuous Stochastic Logic (CSL) and its variant asCSL, and of their modelchecking algorithms, allows a unified approach to the verification of systems, allowing the mix of performance evaluation and probabilistic verification. In this paper we present the stochastic logic CSL TA, which is more expressive than CSL and asCSL, and in which properties can be specified using automata (more precisely, timed automata with a single clock). The extension with respect to expressiveness allows the specification of properties referring to the probability of a finite sequence of timed events. A typical example is the responsiveness property “with probability at least 0.75, a message sent at time 0 by a system A will be received before time 5 by system B and the acknowledgment will be back at A before time 7”, a property that cannot be expressed in either CSL or asCSL. Furthermore, the choice of using automata rather than the classical temporal operators Next and Until should help in enlarging the accessibility of model checking to a larger public. We also present a modelchecking algorithm for CSL TA. 1
Controller synthesis for MTL specifications
 In Proc. 17th International Conference on Concurrency Theory (CONCUR’06
, 2006
"... Abstract. We consider the control problem for timed automata against specifications given as MTL formulas. The logic MTL is a lineartime timed temporal logic which extends LTL with timing constraints on modalities, and recently, its modelchecking has been proved decidable in several cases. We inve ..."
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Cited by 7 (2 self)
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Abstract. We consider the control problem for timed automata against specifications given as MTL formulas. The logic MTL is a lineartime timed temporal logic which extends LTL with timing constraints on modalities, and recently, its modelchecking has been proved decidable in several cases. We investigate these decidable fragments of MTL (full MTL when interpreted over finite timed words, and SafetyMTL when interpreted over infinite timed words), and prove two kinds of results. (1) We first prove that, contrary to modelchecking, the control problem is undecidable. Roughly, the computation of a lossy channel system could be encoded as a modelchecking problem, and we prove here that a perfect channel system can be encoded as a control problem. (2) We then prove that if we fix the resources of the controller (by resources we mean clocks and constants that the controller can use), the control problem becomes decidable. This decidability result relies on properties of well (and better) quasiorderings. 1
Undecidable problems about timed automata
 IN PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON FORMAL MODELING AND ANALYSIS OF TIMED SYSTEMS, FORMATS 2006
, 2006
"... We solve some decision problems for timed automata which were raised by S. Tripakis in [Tri04] and by E. Asarin in [Asa04]. In particular, we show that one cannot decide whether a given timed automaton is determinizable or whether the complement of a timed regular language is timed regular. We show ..."
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Cited by 6 (1 self)
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We solve some decision problems for timed automata which were raised by S. Tripakis in [Tri04] and by E. Asarin in [Asa04]. In particular, we show that one cannot decide whether a given timed automaton is determinizable or whether the complement of a timed regular language is timed regular. We show that the problem of the minimization of the number of clocks of a timed automaton is undecidable. It is also undecidable whether the shuffle of two timed regular languages is timed regular. We show that in the case of timed Büchi automata accepting infinite timed words some of these problems are Π 1 1hard, hence highly undecidable (located beyond the arithmetical hierarchy).
Formal Verification with Timed Automata and DEVS Models: a case study
"... Abstract. A methodology for the design of control systems that allows the formal verifications of its properties is presented, this is achieved using Timed Automata to describe the desired highlevel properties of the control to be designed, and DEVS for modeling the lowlevel implementation of the ..."
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Cited by 4 (0 self)
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Abstract. A methodology for the design of control systems that allows the formal verifications of its properties is presented, this is achieved using Timed Automata to describe the desired highlevel properties of the control to be designed, and DEVS for modeling the lowlevel implementation of the control. The formal verification problem consists in proving that the behaviour described by the DEVS model is contained in the one specified by the Timed Automaton, this is achieved through the concept of simulation relations between DEVS models and Timed Automata. Furthermore, using as an example a barrel filling system, the advantages and adequacy of this methodology are shown. A full description of the system is presented, as well as a safety property that the control to be implemented should meet, furthermore the implementation of the control as a DEVS model is given, and it is formally verified that it conforms the safety requirement using the methodology proposed. 1
CSL TA: an Expressive Logic for ContinuousTime Markov Chains
"... The stochastic temporal logic CSL can be used to describe formally properties of continuoustime Markov chains, and has been extended with expressions over states and actions to obtain the logic asCSL. However, properties referring to the probability of a finite sequence of timed events (such as “wi ..."
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Cited by 3 (3 self)
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The stochastic temporal logic CSL can be used to describe formally properties of continuoustime Markov chains, and has been extended with expressions over states and actions to obtain the logic asCSL. However, properties referring to the probability of a finite sequence of timed events (such as “with probability at least 0.75, the system will be in state set A at time 5, then in state set B at time 7, then in state set C at time 20”) cannot be expressed in either CSL or asCSL. With the aim of increasing the expressive power of temporal logics for continuoustime Markov chains, we introduce the logic CSL TA and its modelchecking algorithm. CSL TA extends CSL and asCSL by allowing the specification of timed properties through a deterministic oneclock timed automata. 1