Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Hybrid Systems, number 736 in LNCS, pages 179--208. Springer, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Zhou Chaochen, Director 01.8.1997 31.7.2001 Software Technology P.O. Box 3058 Macau On Checking Timed Automata for Abstract In this work, we address the problem of verifying a Timed Automaton for Duration Calculus formula in the form of Linear Duration Invariants. Accurate methods [14] seem not practical even for small examples. We present a conservative method for solving the problem that is based on linear programming techniques applied on an algebraic representation of Timed Automata. We also provide a translation procedure from Timed Automata to this sort of regular ....

....most widely used formalism to model real time systems. Linear Duration Invariants (LDI) is a fragment of Duration Calculus (DC) 6] Roughly speaking, Linear Duration Invariants express linear constraints on the accumulated time for the presence of system behaviours. They are fist presented in [14] where the reachability problem for a class of Hybrid Automata, the Integration Graphs is reduced to the verification of TA for a LDI. Our goal is to develop a technique to verify algorithmically the real time systems modelled by Timed Automaton for this kind of real time properties. ....

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Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Proceedings of Workshop on Theory of Hybrid Systems, number 736 in Lecture Notes in Computer Science, pages 179--208. Springer-Verlag, June 1992.

....checking timed automata w.r.t. some duration properties have been developed. These duration properties constrain the accumulated time during which certain predicates hold, and are represented formally by Duration Calculus formulas. A solution to the problem for the general case has been given in [8] using mixed integer and linear programming techniques. Since the mixed integer and linear programming techniques are complicated, many authors have searched for a simpler solution by restricting themselves to some special cases of the problem. It has been shown that by using the linear ....

Y.Kesten, A.Pnueli, J.Sifakis, and S.Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, number 736 in LNCS, pages 179--208, 1993. A Proof of Some Propositions Proposition 1 Let M be a timed automaton. Let D 1 , D 2 be DC formulas of the following

....may be physically plausible [22] The models studied in this paper are dynamical systems or hybrid systems. We call hlbrid systems that combine discrete and continuous dynamic. Sev eral formal definitions have been proposed in the literature [16, 21, 1, 20] Some undecidability results are known [9, 1, 11, 2], but only a small number of papers have been devoted to the study of hybrid systems as computational models: the work of Asarin, Maler and Pnuelli [4, 3] about Piecewise Constant Derivative systems and the work of Branicky [8] about simulation capabilities of Ordinary Differential Equations can ....

....proceed at n different rates. See [1, 2] for the definitions of the following special cases of linear hybrid systems: discrete systems, finite state systems, timed automata, multi rate timed systems, n rate time systems, integrator systems. Examples of linear hybrid systems can also be found in [9, 11, 16, 21, 20] We focus now on the computational power of linear hybrid systems. Thus, we study continuous systems that are not necessarily systems with continuous trajectories. Theorem 3.3 cannot be applied any more, and we obtain that now, dimension 2 is sufficient to get universality and super Turing ....

Y. Kesten, A. Pnuelli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems, Leer. Notes in Comp. Science, vol 736: 179-208, 1993. REFERENCES 36

....see below. To our experience, linear duration properties form an important class of Duration Calculus formulas in specifying requirements of real time systems, and the problem of checking a realReport time system for a linear duration property has attracted a great deal of attention (see, e.g. [10, 15, 12, 6]) A predicate D of the form (K1) is evaluated to true for a finite sequence of transitions oe iff whenever the length joej (the number of elements) of oe satisfies the premise t 1 joej t 2 , the durations of the state of the process satisfy the inequality q i M . A predicate D of the form ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179--208. Springer Verlag, 1994.

....themselves to a restricted class of systems and a restricted class of real time requirements. For the class of requirements written as linear duration invariants, i.e. linear constraints on the durations of the system states in the observation time interval, the problem has been considered in [1, 8, 3, 4]. In [1] the authors showed that for finitary timed automata, i.e. timed automata satisfying some restriction conditions, the problem can be solved using the mixed integer linear programming techniques. In [8, 3, 4] the authors show that with some restrictions on the models of real time ....

....a restricted class of systems and a restricted class of real time requirements. For the class of requirements written as linear duration invariants, i.e. linear constraints on the durations of the system states in the observation time interval, the problem has been considered in [1, 8, 3, 4] In [1], the authors showed that for finitary timed automata, i.e. timed automata satisfying some restriction conditions, the problem can be solved using the mixed integer linear programming techniques. In [8, 3, 4] the authors show that with some restrictions on the models of real time systems, the ....

[Article contains additional citation context not shown here]

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208. References 22

....considered the problem of checking whether a real time system whose behaviours could be represented by a timed regular expression, satisfies a Linear Duration Invariant. We have developed a technique to solve the problem using linear programming, and implemented this technique. In comparison to [6], our techique is simpler. However when we tried our tool on some small sized practical examples, we discovered that the tool could give answers in few hours or ran out of the computer memory. We reconsidered our technique and found that the size of the linear programming problem we have to solve ....

Y. Kesten, A. Pnueli, J Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179--208. Springer Verlag, 1994.

....to the trace of system locations, while linear duration invariants pay attention to the length of the observation intervals during of real time systems running. We have shown in this paper that veri cation of temporal duration properties is much simpler than that of linear duration invariants. In [8], the authors shows that the satisfaction problem of linear duration invariants for timed automata can be solved by mixed integer linear programming. In [4, 5, 11] we have restricted ourselves to study the problem of checking whether a real time system whose behaviours could be represented by a ....

....we have restricted ourselves to study the problem of checking whether a real time system whose behaviours could be represented by a timed regular expression, satis es a Linear Duration Invariant. We have developed a technique to solve the problem and implemented it as a tool. In comparison to [8], our technique is simpler because it uses only linear programming techniques. However, when we tried our tool on some small sized practical examples, we discovered that the tool could give answers in few hours or ran out of the computer memory. We reconsidered our technique and found that the ....

Y. Kesten, A. Pnueli, J Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179-208. Springer Verlag, 1994.

....numbers (T may be 1) For real time automata, an algorithm [2] has been presented for checking the correctness with respect to a linear duration invariant, which reduces the correctness problem to a finite set of very simple linear programming problems. On the other hand, it has been shown in [5] that the satisfaction problem of a linear duration invariant for a timed automaton can be solved by mixed integer linear programming. Since integer programming is more complex than linear programming, it would be interesting to extend the techniques in [2] to the class of timed automata. In this ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208.

....problems. This technique has been generalised for verifying a subset of timed automata by [4] and for verifying a parallel composition of real time automata by [12] This technique has also been generalised for verifying a subset of hybrid automata by [5] For timed automata, it has been shown in [14] that the problem can be solved but ones have to use the mixed integer and linear programming techniques, which are very complicated. In [1] an algorithm has been developed for checking durationbounded reachability which asks whether there is a run of an automaton from a start state to a target ....

Y.Kesten, A.Pnueli, J.Sifakis, and S.Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, number 736 in LNCS, pages 179--208, 1993.

....invariants s 4 ) 12 ; s 4 ) 1 : Now, the problem we are concerned in this paper can be formulated as follows. Given a hybrid automaton A, given a linear duration invariant D, decide efficiently whether A satisfy D. The problem has attracted a great deal of attention. In [6] the authors have solved the problem for a subclass of integration graph using mixed integer linear programming techniques which inherit very high complexity. In [4] the authors have solved the problem for a simple class of real time automata using linear programming techniques, which is well ....

....of linear hybrid automata the problem is still undecidable in general. HREs define a subclass of linear hybrid automata for which the problem can be solved efficiently. It should be noticed that the subclass defined by HREs is not comparable with the class of linear hybrid systems defined in [6]. Thus, theoretically the paper gives a new result for the decidability of the model checking problem. Currently, a model checking tool based on the algorithms presented in this paper and in our previous ones is being developed. Hopefully, the tool will display more clearly the advantages of our ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208.

....2 Oe 0 ) 4 Decidability of LIDL We rst introduce the notion of event recording integrator automata before considering decidability. Integrator Automata These are a sub class of hybrid automata where only clocks (whose rate is always 1) or integrators (whose rate is either 0 or 1) are used [10]. An Integrator Automaton AT is the tuple (Q; q 0 ; F; C; It has a nite set of states Q with initial state q 0 , an alphabet , a set of nal states F , a set of integrators (clocks) C and a transition relation . The transition relation has the type Q 2 C C [C f0; 1g] Q ....

Y. Kesten, A. Pnueli, J. Sifakis and S. Yovine, Integration graphs: A Class of Decidable Hybrid Systems, in Proc. Hybrid Systems, LNCS 736, Springer-Verlag, 1993.

....10 Pandya 4 Decidability of LIDL We first introduce the notion of event recording integrator automata before considering decidability. Integrator Automata These are a sub class of hybrid automata where only clocks (whose rate is always 1) or integrators (whose rate is either 0 or 1) are used [14]. An Integrator Automaton AT is the tuple (Q, #, q 0 , F, C, #) It has a finite set of states Q with initial state q 0 , an alphabet #, a set of final states F , a set of integrators (clocks) C and a transition relation #. The transition relation has the type # # Q # 2 C #C [C # ....

Kesten, Y., A. Pnueli, J. Sifakis and S. Yovine, Integration graphs: A Class of Decidable Hybrid Systems, in Proc. Hybrid Systems, LNCS 736, SpringerVerlag, 1993.

.... express the execution architecture along with the timing requirements and 5 Moreover, there are some subclasses of Hybrid Automata that are accurately expressible or conservatively expressible as a timed automaton (Non Zero Constant Slope, Non Zero Linear Hybrid System [64] Integration Graphs [54]) none of them suited for non fixed preemption modeling. 132 estimations of the system. These estimations are expressed as lower and upper bounds of the execution time of the functionalities in a dedicated environment (the computation requirement of the software) The designer would like to be ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. n Proceedings of Workshop on Theory of Hybrid Systems, pages 179--208, Lyngby, Denmark, June 1992. Lecture Notes in Computer Science 736, Springer-Verlag.

....on various restrictions on the form of the invariants, the guards, the activities etc. a score of variants and simplifications of the general model have been investigated, especially to obtain decidable and automatically checkable subclasses of the general definition (cf. for instance [1] 2] [6] [5] 8] The main line of research concentrated on model checking of finite abstractions of restricted subclasses of the general model. Besides the drawback of limited expressive power, fully automatic approaches suffer from the usual state space explosion problem, when dealing with the parallel ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Grossman et al. [4], pages 179--208.

....semi decidable for hybrid automata [ACH 95] and even in the decidable cases, the verification algorithms are not very efficient. For these reasons, the verification problem has been attacked from two directions. The first one is to obtain restricted, decidable classes of hybrid automata [KPSY93, PV94, HKPV95, BER94, BES93, HH95, Hen95, RR94, RR95] The second consists in using abstractions [HPR94] or compositionality and on the fly techniques [BGK 96] to accelerate reaching a result. Our current proposal lies in the first of these two directions, and it aims at obtaining ....

.... symbolic forward analysis algorithm of [ACH 95] But another serious problem arises: this algorithm is not guaranteed to terminate ever; indeed, properties of the form (ff) are only semi decidable on general hybrid automata, and undecidability is shown to affect even quite simple automata [KPSY93, HKPV95] This is no surprise, because hybrid automata, seen as machines, are extremely powerful (when compared to Turing or to n counter machines) However, some partial decidability results exist [KPSY93, PV94, HKPV95, BER94, BES93, HH95, Hen95] All consist in restricting (drastically) the ....

[Article contains additional citation context not shown here]

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs : a class of decidable hybrid systems. In Proc. Workshop on Theory of Hybrid Systems, LNCS, 1993.

....on various restrictions on the form of the invariants, the guards, the activities, etc. a score of variants and simplifications of the general model have been investigated, especially to obtain decidable and automatically checkable subclasses of the general definition (cf. for instance [1] 2] [15] [10] 22] The main line of research concentrated on model checking of finite abstractions of restricted subclasses of the general model. Besides the drawback of limited expressive power, fully automatic approaches suffer from the usual state space explosion problem, when dealing with the ....

....Depending on various restrictions on the form of the invariants, the guards, the activities etc. a score of variants and simplifications of this model have been investigated, especially to obtain decidable and automatically checkable subclasses of the general definition (cf. for instance [1] 2] [15] [10] 22] As in this paper we are concerned with formulating a proof method within a deductive framework, we will stick to the general definition. As mentioned before, a system s state can change in two ways: either by time delay or by discrete transitions. Hence there are two kinds of ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Grossman et al. [8], pages 179--208.

....may be physically plausible [22] The models studied in this paper are dynamical systems or hybrid systems. We call hybrid systems that combine discrete and continuous dynamic. Several formal definitions have been proposed in the literature [16, 21, 1, 20] Some undecidability results are known [9, 1, 11, 2], but only a small number of papers have been devoted to the study of hybrid systems as computational models: the work of Asarin, Maler and Pnuelli [4, 3] about Piecewise Constant Derivative systems and the work of Branicky [8] about simulation capabilities of Ordinary Differential Equations can ....

....proceed at n different rates. See [1, 2] for the definitions of the following special cases of linear hybrid systems: discrete systems, finite state systems, timed automata, multi rate timed systems, n rate time systems, integrator systems. Examples of linear hybrid systems can also be found in [9, 11, 16, 21, 20] We focus now on the computational power of linear hybrid systems. Thus, we study continuous systems that are not necessarily systems with continuous trajectories. Theorem 3.3 cannot be applied any more, and we obtain that now, dimension 2 is sufficient to get universality and super Turing ....

Y. Kesten, A. Pnuelli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems, Lect. Notes in Comp. Science, vol 736: 179-208, 1993.

....only in the supervisor. ffl The concept of invariants for specification of the closed loop continuous behaviour is not explicitly included in [3] 5. 2 Phase transition models Models based upon a phase transition structure havebeendeveloped by computer scientists, see e.g. 13] 15] 14] or [27]. Phase transition structures can be seen as an extension to statetransition graphs or discrete automata in that they besides a set of discrete variables also contain a set of continuous variables VD compare with our state vector x that change with time. The 13 system s state is an ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: A class of decidable hybrid systems. In R.L. Grossman, A. Nerode, A.P.Ravn, and H. Rischel, editors, Hybrid Systems, Lecture Notes in Computer Science 736, pages 179--208. Springer-Verlag, 1993.

....problems. This technique has been generalised for verifying a subset of timed automata in [6] and for verifying a parallel composition of real time automata in [12] This technique has also been generalised for verifying a subset of hybrid automata in [7] For timed automata, it has been shown in [14] that the problem can be solved but ones have to use the mixed integer and linear programming techniques, which are very complicated. In [1] an algorithm has been developed for checking duration bounded reachability which asks whether there is a run of an automaton from a start state to a target ....

Y.Kesten, A.Pnueli, J.Sifakis, and S.Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, number 736 in LNCS, pages 179--208, 1993.

....Duration Properties Now we consider the problem checking time Petri nets for linear duration properties, which are a linear inequality of integrated durations of system states. The satisfaction problems of timed automata and hybrid automata for linear duration properties have been considered in [6,7,9,12]. Linear duration properties can be represented formally by Duration Cal9 begin currentpath1 : hi; append node to currentpath1; repeat node : the last node of currentpath1; if node has no new successive node then delete the last node of currentpath1 else begin node : a new successive ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208.

....algorithm 2 13 problem has previously been solved for real time automata in [7] by using linear programming technique. This technique has been generalised for verifying a subset of timed automata [13] and for verifying a subset of hybrid automata [14,15] For timed automata, it has been shown in [8] that the problem can be solved but ones have to use the mixed integer and linear programming techniques, which are very complicated. In [9] it has been shown that for a timed automaton, the problem can be solved by using an integer time verification technique. In [10] an algorithm has been ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208.

....is defined below. To our experience, linear duration properties form an important class of Duration Calculus formulas in specifying requirements of real time systems, and the problem of checking a real time system for a linear duration property has attracted a great deal of attention (see, e.g. [11,15,12,6]) A predicate D of the form (K1) is evaluated to true for a finite sequence of transitions oe iff whenever the length joej (the number of elements) of oe satisfies the premise t 1 joej t 2 , the durations of the states of the process satisfy the inequality P m i=1 c i R q i M . A ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179--208. Springer Verlag, 1994.

....(reachability, TCTL model checking [ACD90, HNSY92] are decidable. However, many interesting extensions of this model have been shown to lose this decidability property: for instance, as soon as clocks may be frozen in some states, to count cumulated durations, reachability becomes undecidable [KPSY93] Hybrid automata [MMP91, ACHH93] are a much more general model, which has been proposed to model systems involving both discrete and continuous variables. A hybrid automaton is a finite automaton associated with a finite set of continuous variables. Each transition of the automaton can be ....

....guards are simple linear conditions, discrete actions are only reset actions, and in each state, the variable derivatives are equal to 1. If clocks may be frozen, the derivatives belong to f0; 1g. In this paper, we consider a class of linear hybrid automata (which has been identified elsewhere [KPSY93, ACHH93, AHH93] where guards are (general) linear conditions, actions are assignments of linear expressions, and derivatives are (symbolic) constants subject to linear This work has been partly supported ESPRIT BRA action REACT and by a grant from Schneider Electric. y Authors address: ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Workshop on Theory of Hybrid Systems, Lyngby, Denmark, October 1993. LNCS 736, Springer Verlag.

....subsyste Inste we propose practical nume te base onmixe te line programming. Keywords Hybrid syste controllability,obse ability, pie line syste pie a#ne syste mixe teline programming I. Introducti In recent yearsb oth control and computer science haveb een attractedb y hybridsystem [1] 2] [23], 25] 26] b ecause they provide a unified framework fordescribgARB( cesses evolving accordingto continuous dynamics, discrete dynamics, and logic rules. The interest is mainly motivatedb y the large variety of practical situations, for instance real time systems, where physical processes ....

.... that restrictions on the switchinghave tob e imposed in order to prove that a PWL composition ofstab# components remains stabWR Very little research focused onob#LL ab#LL y and controllaboll y properties of hyb#) systems, apart from contrib#WgAM limited to the field of timed automata [1] 20] [23] and the pioneeringwork of Sontag[30] for PWL systems. Needless to say, these concepts are fundamental for understanding if and how well a stateobegD er and a controller for a hyb(R system can b e designed. For instance,obanc abanc y properties were directly exploited for designing convergent ....

[Article contains additional citation context not shown here]

Y. Kesten,A . Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In R.L. Grossman,A Nerode,A .P. Ravn, and H. Rischel, editors, Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179--208. Springer Verlag, 1993.

....to infeasibility in T steps (X (0) # I T (0) Subsets of X (0) leading to none of the two previous cases are again labeled as non classiable in T steps. IV. COMPLEXITY The undecidability of reachability analysis in the context of formal verication of hybrid automata was proved in [16] [17]. However, the problem stated above is decidable, as we assume a nite time horizon T and work in discrete time.The reason for focusing on nite time reachability is that the time horizon T has a clear meaning, namely those states which are reachable in more than T steps are in practice ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel, editors, Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179--208. Springer Verlag, 1993.

....1 R s 1 R s 2 Gamma 2( R s 3 R s 4 ) 1 : Now, the problem we are concerned in this paper can be formulated as follows. Given a hybrid automaton A, given a linear duration invariant D, decide efficiently whether A satisfy D. The problem has attracted a great deal of attention. In [6] the authors have solved the problem for a subclass of integration graph using mixed integer linear programming techniques which inherit very high complexity. In [4] the authors have solved the problem for a simple class of real time automata using linear programming techniques, which is well ....

....of linear hybrid automata the problem is still undecidable in general. HREs define a subclass of linear hybrid automata for which the problem can be solved efficiently. It should be noticed that the subclass defined by HREs is not comparable with the class of linear hybrid systems defined in [6]. Thus, theoretically the paper gives a new result for the decidability of the model checking problem. Currently, a model checking tool based on the algorithms presented in this paper and in our previous ones is being developed. Hopefully, the tool will display more clearly the advantages of our ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208.

....themselves to a restricted class of systems and a restricted class of real time requirements. For the class of requirements written as linear duration invariants, i.e. linear constraints on the durations of the system states in the observation time interval, the problem has been considered in [1, 8, 3, 4]. In [1] the authors showed that for finitary timed automata, i.e. timed automata satisfying some restriction conditions, the problem can be solved using the mixed integer linear programming techniques. In [8, 3, 4] the authors show that with some restrictions on the models of real time ....

....a restricted class of systems and a restricted class of real time requirements. For the class of requirements written as linear duration invariants, i.e. linear constraints on the durations of the system states in the observation time interval, the problem has been considered in [1, 8, 3, 4] In [1], the authors showed that for finitary timed automata, i.e. timed automata satisfying some restriction conditions, the problem can be solved using the mixed integer linear programming techniques. In [8, 3, 4] the authors show that with some restrictions on the models of real time systems, the ....

[Article contains additional citation context not shown here]

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208. Report No. 118, July 1997 UNU/IIST, P.O. Box 3058, Macau References 22

....numbers (T may be 1) For real time automata, an algorithm [2] has been presented for checking the correctness with respect to a linear duration invariant, which reduces the correctness problem to a finite set of very simple linear programming problems. On the other hand, it has been shown in [5] that the satisfaction problem of a linear duration invariant for a timed automaton can be solved by mixed integer linear programming. Since integer programming is more complex than linear programming, it would be interesting to extend the techniques in [2] to the class of timed automata. In this ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208.

....in this paper can be formulated as follows. Given a hybrid Report No. 109, June 1997 UNU IIST, P.O. Box 3058, Macau Hybrid Regular Expressions 3 automaton A, given a linear duration invariant D, decide efficiently whether A satisfy D. The problem has attracted a great deal of attention. In [6] the authors have solved the problem for a subclass of integration graph using mixed integer linear programming techniques which inherit very high complexity. In [4] the authors have solved the problem for a simple class of real time automata using linear programming techniques, which is well ....

....of linear hybrid automata the problem is still undecidable in general. HREs define a subclass of linear hybrid automata for which the problem can be solved efficiently. It should be noticed that the subclass defined by HREs is not comparable with the class of linear hybrid systems defined in [6]. Thus, theoretically the paper gives a new result for the decidability of the model checking problem. Currently, a model checking tool based on the algorithms presented in this paper and in our previous ones is being developed. Hopefully, the tool will display more clearly the advantages of our ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid System, LNCS 736, pp.179-208. Report No. 109, June 1997 UNU/IIST, P.O. Box 3058, Macau Proofs of Lemmas 18

.... problems are PSPACE complete [AD94] Under restrictions (1) and (2) that result was later generalized to automata with variables that run at any constant positive slopes [ACH 95] and to the reachability problem for automata with nonstrict rectangular flow constraints [PV94] In [BES93, KPSY93, BER94, MV94, BR95, ACH97] it was shown that, under various strong side conditions, reachability is decidable for timed automata with one stopwatch, but the general problem of one stopwatch automata was left open. As far as undecidability results are concerned, in [Cer92] it was shown that ....

....for timed automata with one memory cell (a variable of constant slope 0) and assignments between variables. It was also known that reachability is undecidable for timed automata with six memory cells and no assignments [AHV93] for timed automata with two three slope variables and restriction (1) KPSY93] for timed automata with two nonclock constant slope variables [ACH 95] and for timed automata with additive clock constraints [AD94] 2 Rectangular Automata A hybrid automaton of dimension n is an infinite state machine whose state has a discrete part, which ranges over the vertices of a ....

[Article contains additional citation context not shown here]

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel, editors, Hybrid Systems, Lecture Notes in Computer Science 736, pages 179--208. SpringerVerlag, 1993.

.... because the problems of language emptiness, model checking, and controller synthesis are decidable for hybrid automata that are finitary and effective [1, 13, 19] There have been several results of the type the emptiness problem is undecidable for hybrid automata with clocks and a stopwatch [2, 12, 15]. While these results leave little hope for finding A preliminary version of this paper appeared in the Proceedings of the 22nd International Colloquium on Automata, Languages, and Programming (ICALP) Lecture Notes in Computer Science 944, Springer Verlag, 1995, pp. 324 335. y Supported in ....

Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine. Integration graphs: a class of decidable hybrid systems. Hybrid Systems, Springer LNCS 736, pp. 179--208, 1993.

....HyTech [17, 18, 19] Kronos [12, 13, 24] and UPPAAL [7] All the current analysis methods are based on symbolic state space exploration. Thanks to various search strategies and approximations, a wide range of properties can be decided or semi decided for some restricted classes of hybrid systems [22, 1, 4, 20, 5]. This paper deals with exact reachability analysis of hybrid systems, i.e. computing an exact and finite representation of their set of reachable states. We restrict our study to strongly linear hybrid systems, which are systems whose discrete variable changes are linear, and whose continuous ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Proceedings of Workshop on Theory of Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179--208, Lyngby, Denmark, 1992. Springer-Verlag.

....Timed Automata [2] TA) are one of the most widely used formalisms to model real time systems. Linear Duration Invariants (LDI) are a fragment of Duration Calculus (DC) 7] used to express linear constraints on the accumulated time for the presence of system states. They are first presented in [17] where it is shown that the reachability problem of the Integration Graphs, a class of Hybrid Automata, can be reduced to the verification of TA for LDI. Our goal is to develop a technique to verify algorithmically real time systems modeled as TA for this kind of realtime properties. To our ....

....goal is to develop a technique to verify algorithmically real time systems modeled as TA for this kind of realtime properties. To our knowledge, the existing theoretical methods which work for the whole class of TA seem to be useless even for a small example because of their high complexity. In [17], the authors present an algorithm for solving the problem, based on two techniques: digitization and mixed The paper was written during the fellowship of the first author with The United Nations University, International Institute for Software Technology from September 1997 to March 1998. He ....

[Article contains additional citation context not shown here]

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Proceedings of Workshopon Theory of Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179--208. Springer-Verlag, June 1992.

....graphs (resp. timed graphs) we deduce the following fact. Theorem 9.1 The verification problem of CDF (resp. pure time CDF) formulas w.r.t. RF (resp. simple RF) formulas is reducible to the emptiness problem of 1LHA s (resp. restricted 1 LHA s) The emptiness problem of 1 LHA is undecidable [12], however, it is decidable for restricted 1 LHA s (using [2] Hence, we obtain the following result. Theorem 9.2 The verification problem of pure time CDF formulas w.r.t. simple RF formulas is decidable. Consider now the fragments of CoD defined in [11] to describe control designs and their ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems. LNCS 736, 1993.

....interpreted automata, the control states of these automata will be called locations, to distinguish them from the global state of the system, made of a location and a valuation of the variables. In this section, we consider a class of linear hybrid automata (which has been identified elsewhere [KPSY93, ACHH93, AHH93] where guards are (general) linear conditions, actions are assignments of linear expressions, and in each location of which variable derivatives are (symbolic) constants subject to linear inequalities. This class is general enough to handle many practical problems, and the linear ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Workshop on Theory of Hybrid Systems, Lyngby, Denmark, October 1993. LNCS 736, Springer Verlag.

....0 8; 1; 0; 0 8; 0; 0; 0 II x II x II x II x 8; 1; 0; 0 8; 0; 0; 0 8; 1; 0; 0 8; 0; 0; 0 I x I x I x I x 7; 1; 0; 0 7; 1; 0; 0 7; 1; 0; 0 7; 1; 0; 0 II x (R12) II x (R12) II x (R1=1) II x (R1=1) Fig. 4 1 the formulation is taken from [KPSY] Figure 4 describes 4 possible segments of the game when line #7 of the program is R 1 : max(R 1 Gamma 1; 0) The double boxed states are the states in Q. We can modify the model, allowing an initial segment of the game in which player II can initialise the counters while player I playes ....

Y. Kesten, A. Pnueli, J. Sifakis and S. Yovine, Integration Graphs: A Class of Decidable Hybrid Systems, Lecture Notes in Computer Science 736 -- Hybrid Systems (R.L. Grossman, A. Nerode, A.P. Ravn and H. Rischel, eds.), Springer-Verlag, 1993, pp. 179--208.

.... timed versions of CTL [25, 3] The above method is a generalization of a similar method for timed systems for which the iterative computation of the fixed point is guaranteed to terminate [12] This is not generally true for hybrid systems (even under the restriction to constant slope evolutions) [3, 15]. In our view, however, the actual restriction in applying the semi decision procedure arises due to the class of systems covered. The requirement of time linearity, unfortunately rules out many interesting examples. Consider for example the state variables v A and v B in the two car system ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Grossman et al. [9], pages 179--208.

No context found.

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Hybrid Systems, number 736 in LNCS, pages 179--208. Springer, 1993.

....variables and in [45] for 2 dimensional extended integrator graphs. On the other hand and not surprisingly, many undecidability results were given. In [80] it was shown that relaxing some restrictions the reachability problem for some classes of rectangular automata become undecidable. In [4, 5, 6, 11, 90, 138] it was shown that the reachability question for many different extensions of TA with some non clock variables is undecidable under some restrictions. Some other undecidability results were given for low (three or less) dimensional spaces. In [19] it was shown that the reachability problem for ....

....(2) as well as for TA with 1 memory cell and allowing assignments between variables. Other undecidability results (always for the reachability problem) were given for TA with 6 memory cells without assignment between variables [11] for TA with two three slope variables under restriction (1) [90], for TA with two non clock constant slope variables [4] for TA with additive clock constraints [6] and for TA with two skewed clocks [5] Some other undecidability results were given for low (three or less) dimensional spaces. In [19] it was shown that the reachability problem for 3 dim PCDs is ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Hybrid Systems, number 736 in LNCS, pages 179-208. Springer, 1993.

....by combining the techniques used by the tool Caesar [4] and the Atp compiler [12] The main problem here is how to deal with the t ( at t ) operator. This operator declares a time variable t used to store the time of occurrence of an action. The variable t can be considered as an integrator [6, 2], i.e. a clock that can be stopped. The problem is that unrestricted use of integrators leads to undecidability of verification. Finally, we are currently implementing optimizations to improve on the tool Kronos in order to be able to cope with larger systems. Acknowledgements We are grateful ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Workshop on Theory of Hybrid Systems, pages 179--208. LNCS 736, Springer-Verlag, 1993.

....K 0 . The application of synthesis techniques is limited for two reasons. First, the practical complexity of the synthesis algorithm is high even in the case of timed automata without scheduling policy constraints. Second, scheduling with preemption requires the use of automata with integrators [5] which implies that iterative computation of control invariants may not terminate. The proposed methodology allows to decompose the global controller synthesis procedure into the application of simpler steps. At each step a control invariant corresponding to a particular class of constraints is ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: A class of decidable hybrid systems. Information and Computation, 736, 1992.

....use of the defined synchronization modes consider the following example. Example 2. 2 Amultimedia document is composed of the following basic activities and their corresponding duration constraints, noted as [minimal duration, maximal duration] music [30, 40] video [15, 20] audio [20, 30] text [5, 10], applet [20, 30] picture [20, 1] In the beginning, music, video, audio, and applet are launchedinparallel. The basic activities are submitted to the following synchronization constraints: 1) video and audio terminate as soon as any one of them ends# their termination is immediately followed by ....

....CPU Figure 14. PND of the robotic arm. We believe that the presented results are a basis for automatic scheduler generation of reactive applications that can be modeled as timed automata. They are not in principle applicable to scheduling with preemption, which requires models with integrators [10]. Compared to classical scheduling techniques (e.g. 12, 4] our framework is applicable without any assumptions about the structure of the application such as periodic ity or priorities of the tasks. Our algorithm is optimal in the sense that if it does not find a scheduler, then suchascheduler ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: A class of decidable hybrid systems. LNCS 736, Springer-Verlag. To appear in Information and Computation.

....K 0 . The application of synthesis techniques is limited for two reasons. First, the practical complexity of the synthesis algorithm is high even in the case of timed automata without scheduling policy constraints. Second, scheduling with preemption requires the use of automata with integrators [5] which implies that iterative computation of control invariants may not terminate. The proposed methodology allows to decompose the global controller synthesis procedure into the application of simpler steps. At each step a control invariant corresponding to a particular class of constraints is ....

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: A class of decidable hybrid systems. Information and Computation, 1992. LNCS 736, Springer-Verlag.

No context found.

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In A. Ravn and H. Rischel, editors, Workshop on Hybrid Systems, volume 736 of Lect. Notes in Comp. Sci., pages 179--208. Springer-Verlag, 1993.

....of subclasses of hybrid systems for which there exist decidability results and effective verification methods for various classes of properties. The main decidability results concern very restricted classes of hybrid systems like timed automata [AD90, ACD90, Alu91, NSY91] and integration graphs [KPSY93]. The second direction concerns the elaboration of a general verification methodology for classes of systems for which tractable semi decision methods are applicable. One interesting class is linear hybrid systems [ACHH93, NOSY93] i.e. systems where conditions on discrete transitions and ....

....preserved on these systems. The paper is organized as follows: Section 2 presents the model of Linear Hybrid Systems (LHS) where continuous variables evolve according to linear functions with slopes varying within an interval. We define two sub classes of LHS: Constant Slope Hybrid Systems (CSHS) [KPSY93], where the slopes of the evolution functions are constant and K Timed Graphs (K TG) that are CSHS where for all variables the slope is equal to a constant K. Supported by the ESPRIT project N ffi 6021 REACT P VERIMAG is a joint laboratory of CNRS, INPG, UJF and VERILOG S.A. Proc. ....

[Article contains additional citation context not shown here]

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Workshop on Theory of Hybrid Systems, Lyngby, Denmark, June 1993. LNCS 736, Springer-Verlag.

No context found.

Y. Kesten, A. Pnueli, J Sifakis, and S. Yovine. Integration Graphs: A Class of Decidable Hybrid Systems. In Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 179-208. Springer Verlag, 1994.

No context found.

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Hybrid Systems, Lecture Notes in Computer Science 736, pp. 179--208. Springer-Verlag, 1993.

No context found.

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Proceedings of the 1st Workshop on Theory of Hybrid Systems, volume 736 of LNCS, pages 179-208. Springer-Verlag, 1993.

No context found.

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Hybrid Systems, LNCS 736, p. 179--208, 1993.

No context found.

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine, "Integration graphs: A class of decidable hybrid systems," in Lecture Notes in Computer Science, vol. 736, pp. 179--208, 1993.

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