T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and F. G'ecseg, editors, ICALP 95: Automata, Languages, and Programming, pages 324--335. Springer-Verlag, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....generates a global non terminating solution. Roughly speaking, a global non terminating solution is a system trajectory which has an infinite number of switches between the discrete states. Prior work has addressed the existence of global solutions within the framework of algorithmic verification [1, 2, 3]. In algorithmic verification, one first identifies a cycle of arcs in the automaton s graph and then one recursively computes the set of all states that can satisfy the guard predicates on each arc of the cycle. If this recursive algorithm terminates in a non empty set, then we know there exists ....

T.A.Henzinger, "Hybrid Automata with Finite Bisimulation," ICALP 95: Automata, Languages, and Programming, Springer-Verlag, pp.324-335, 1995.

....variables q Q. A subset of Q is called a zone. Each zone Z Q can be uniquely decomposed into a collection l#L l , where R . Let #Z denote a set of formulas that define Z. We define the operator P re : 2 # # # by P re(Z, #) q # #q Z . q q # . Following [4], A is e#ective if there is a class of formulas which permits the symbolic analysis of A; namely (1) the emptiness problem for each predicate of cF is decidable, 2) cF is closed under boolean operations and P re (and Post) operations, 3) #Q , #Q . Suppose that the tangential and ....

T.A. Henzinger. Hybrid automata with finite bisimulations. In "Proc. 22nd ICALP: Automata, Languages and Programming, LNCS 944, pp. 324-335, Springer-Verlag, 1995.

....O#ce under grants DAAH 04 95 1 0588 and DAAH 04 96 1 0341. P. Antsaklis et al. Eds. Hybrid Systems V, LNCS 1567, pp. 186 203, 1999. c Springer Verlag Berlin Heidelberg 1999 multirate automata [1] x [a, b] for rectangular automata [19] and A x b for linear hybrid automata [11]. In this paper, we extend the bisimulation methodology to hybrid systems with more general dynamics. We first present the standard bisimulation algorithm which, upon termination, provides the desired finite bismilarity quotient. In [15] we used purely geometric methods to show that the ....

....the systems T and T # are called bisimilar. A bisimulation is called finite if it has a finite number of equivalence classes. Bisimulations are very important because checking reachability on the bisimilar transition system is equivalent to checking reachability of the original transition system [11]. Therefore, if T is infinite and T # is a finite bisimulation, then verification algorithms for infinite systems are guaranteed to terminate. If is a bisimulation, it can be easily shown that if q then B1 p QF i# q QF ,andp QO i# q QO B2 if p p # then there exists q # such ....

T.A. Henzinger, Hybrid automata with finite bisimulations, ICALP 95: Automata, Languages, and Programming (Z. Fulop and F. Gecseg, eds.), Springer-Verlag, 1995, pp. 324--335.

....case the systems T and T # are called bisimilar. We will also say that a partition is a bisimulation when its induced equivalence relation is a bisimulation. A bisimulation is called finite if it has a finite number of equivalence classes. Bisimilar transition systems generate the same language [5]. Recently, the above bisimulation methodology has been applied to hybrid systems which combine discrete and continuous dynamics. The main reason for doing this is that if T is a transition system with an infinite state space and T # is a finite bisimulation, then the reachability problem for ....

T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and F. Gecseg, editors, ICALP 95: Automata, Languages, and Programming, pages 324--335. Springer-Verlag, 1995.

....systems for large instances. Thus, a solution for the general problem also helps ameliorate state explosion. Algorithms are known for model checking many types of infinite state systems: Petri Nets [Esparza 94] asynchronous parameterized protocols [GS 92] timed automata [AD 91] hybrid systems [Henzinger 95] parameterized token ring protocols [EN 95] and parameterized synchronous protocols [EN 96] For other types of systems, semi algorithmic procedures have been proposed [PD 95, ID 96, BG 96, BGWW 97] In an interesting recent paper [ACJT 96] cf. Finkel 90] it is pointed out that programs in ....

....representations for infinite sets of states in general fixpoint computations. Many of the known algorithms, however, are based on a forward search, starting with the set of initial states [GS 92, Esparza 94, BG 96, EN 96] Algorithms based on quotients w.r.t. a bisimulation equivalence [AD 91, Henzinger 95] are also forward searches as the incremental computation of the quotient structure proceeds in a forward direction. In this chapter, we propose a new type of covering graph construction as a general method of forward search for Model Checking. The covering graph construction for Petri Nets is ....

[Article contains additional citation context not shown here]

Henzinger, T. A. Hybrid automata with finite bisimulations, in ICALP 1995. 149

....by using the finite quotient, also known as the region graph , on which a supervisory control problem a la Ramadge Wonham is solved. Our work in [35] solves the same problem in a direct manner. In verification of systems with constant slopes, the indirect approach is represented by papers like [42] and [17] which prove that for certain classes of systems such reductions are possible. The verification procedure in [12] and in [25] the latter proves decidability for a class of systems not having a finite quotient) and the synthesis algorithm of [38] are examples of the direct approach. More ....

T.A. Henzinger, "Hybrid automata with finite bisimulations," in Proc. ICALP'95, F. Vaandrager and J. van Schuppen, Eds. 1995, Lecture Notes in Computer Science 944, pp. 324--335, SpringerVerlag.

....systems for large instances. Thus, a solution for the general problem also helps ameliorate state explosion. Algorithms are known for model checking many types of infinite state systems : Petri Nets [Es 94] asynchronous parameterized protocols [GS 92] timed automata [AD 91] hybrid systems [H 95] parameterized token rings [EN 95] and parameterized synchronous protocols [EN 96] For other types of systems, semi algorithmic procedures have been proposed [PD 95, ID 96, BG 96, BGWW 97] In an interesting recent paper [ACJT 96] cf. Fi 90] it is pointed out that programs in these ....

....as representations for infinite sets of states in general fixpoint computations. Many of the known algorithms, however, are based on a forward search, starting with the set of initial states [GS 92, Es 94, BG 96, EN 96] Algorithms based on quotients w.r.t. a bisimulation equivalence [AD 91, H 95] are also forward searches as the incremental computation of the quotient structure proceeds in a forward direction. In this paper, we propose a new type of covering graph construction as a general method of forward search for Model Checking. The covering graph construction for Petri Nets is ....

[Article contains additional citation context not shown here]

Henzinger, T. A. Hybrid automata with finite bisimulations, in ICALP 1995.

....is a map oe : R 7 R, which is bijective, increasing, and continuous with continuous inverse 5 . Time changes change signals in the following way : Y = def oe(X) defined by Y t = X oe(t) 4 For different purposes, the importance of invariance via time change has been recognized and utilized in [6]. 5 In fact, the statement continuous with continuous inverse is a consequence of oe being bijective and increasing. 5 Lemma 1 (invariance) The following properties establish invariance under time change of all operations we have defined so far : on S : C(X;Y ) on oe(S) C (oe(X) oe(Y ....

T. Henzinger, Hybrid Automata with Finite Bisimulations, preprint, Cornell University, 1995.

.... of hybrid systems [1] Formalisms for input output hybrid automata have been also proposed in [26, 41, 23] A related approach to the work presented in this paper is based on the modeling formalism of hybrid automata and uses bisimulations to study the decidability of verification algorithms [14, 21, 2]. Bisimulations are quotient systems that preserve the reachability properties of the original hybrid system and therefore, problems related to the reachability of the original system can be solved by studying the quotient system. The idea of using finite bisimulations for the analysis and ....

T. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and G. Gecgeg, editors, ICALP'95: Automata, Languages, and Programming. Springer-Verlag, 1995.

.... 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 decidability for classes of reactive and hybrid ....

.... 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 classes of hybrid automata and or properties to be verified. In the following, we systematically pursue such decidability results. The restrictions we impose have an intuitive, physical sense, and they still allow to verify quite large and natural ....

T.A. Henzinger. Hybrid automata with finite bisimulations. In Proc. 22th International Colloquium on Automata, Languages, and Programming, LNCS 944, 1995.

....about termination of symbolic backward analysis in [LPY99,LPY00] is not compositional. Henzinger, Kopke, Puri and Varaiya [HKPV95] considered initialized rectangular automata, a subclass of linear hybrid systems, for which symbolic backward analysis is guaranteed to terminate. Henzinger [Hen95] considered hybrid automata with finite bisimulations for which symbolic backward analysis is guaranteed to terminate. But none of these works addressed the issue of compositional reasoning about sufficient termination conditions. Lam and Brayton [LB93] considered alternating RQ timed automata ....

T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and F. Gecseg, editors, ICALP 95: Automata, Languages, and Programming, LNCS 944, pages 324--335. Springer-Verlag, 1995.

No context found.

T.A. Henzinger. Hybrid automata with finite bisimulations. In Proceedings of ICALP: Automata, Languages, and Programming, Lecture Notes in Computer Science 944, pp. 324--335. Springer-Verlag, 1995.

No context found.

T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and F. G'ecseg, editors, ICALP 95: Automata, Languages, and Programming, Lecture Notes in Computer Science 944, pages 324--335. Springer-Verlag, 1995.

No context found.

T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and F. G'ecseg, editors, ICALP 95: Automata, Languages, and Programming, 1995.

No context found.

T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and F. G'ecseg, editors, ICALP 95: Automata, Languages, and Programming, Lecture Notes in Computer Science 944, pages 324--335. Springer-Verlag, 1995.

....automata to initialized multirate automata may not preserve branching properties, such as those expressible in CTL. In general, initialized rectangular automata do not admit finite bisimulation quotients. Theorem 4. 9 (Lack of Finite Bisimulation Quotients for Initialized Rectangular Automata [32]) There exist an initialized rectangular automaton and a finite set of rectangular sets such that every bisimulation of the transition system has infinitely many equivalence classes. In order to simplify the proof of the above theorem, we consider a slight extension of Definition 3.3 and allow ....

T. A. Henzinger, "Hybrid automata with finite bisimulations," in ICALP 95: Automata, Languages, and Programming, Z. Flp and F. Gcseg, Eds. New York: Springer-Verlag, 1995, vol. 944, Lecture Notes in Computer Science, pp. 324--335.

....all nonzero, finite endpoints of flow intervals. We note that the singular games are a maximal class of hybrid games for which finite game bisimilarity quotients exist. In particular, there exists a 2d rectangular game R such that the equality relation on states is the only game bisimulation for R [8]. 3.3 Game Similarity for 2D Rectangular Games Given a 2d rectangular game T , we define, following [10] the double region equivalence on the states of T as the intersection of two region equivalences. For 2 tuples a and b of integers, define the equivalence relation ja;b on R 2 11 as the ....

....results in the right column follow immediately from the corresponding results in the center column. Table 1. Summary of results Hybrid automata (single player) Hybrid games (multi player) Timed, singular finite bisimilarity [1, 2] finite game bisimilarity 2d rectangular infinite bisimilarity [8], infinite game bisimilarity, finite similarity [10] finite game similarity Rectangular infinite similarity [12] infinite game similarity, finite trace equivalence [14] finite game trace equivalence Triangular infinite trace equivalence [14] infinite game trace equivalence ....

Henzinger, T.A.: Hybrid automata with finite bisimulations. In: ICALP 95: Automata, Languages, and Programming. Lecture Notes in Computer Science, Vol.

....to time) of the variable in the corresponding region of the state space. In this paper, we improve on the rate translation technique by suggesting linear phase portrait approximations that are strictly more accurate. These approximations are motivated by a time invariant view of hybrid automata [Hen95] They differ from the rate translation by approximating directly over the vector field of flow tangents, thus taking into account the relative rates of variables. This leads to more accurate approximations that still allow algorithmic analysis using HyTech. The rate translation, which ....

....and convergence. Our work differs in two respects. First, we consider products of nondeterministic dynamical systems with discrete transition structures. Second, our goal is to analyze and derive simple properties of such systems automatically. The theory of hybrid automata is presented in [Hen95, HKPV95] In [HRP94, HH95c] abstract interpretation techniques are used to provide linear approximations of linear hybrid systems, whereas here we approximate nonlinear hybrid systems. 2 Hybrid Automata We define hybrid automata, which are used to model systems consisting of mixed discrete and ....

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T.A. Henzinger. Hybrid automata with finite bisimulations. ICALP 95: Automata, Languages, and Programming, LNCS 944, pp. 324--335. Springer-Verlag, 1995.

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T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fulop and F. G'ecseg, editors, ICALP 95: Automata, Languages, and Programming, pages 324--335. Springer-Verlag, 1995.

No context found.

T.A. Henzinger, Hybrid automata with finite bisimulations, ICALP 95: Automata, Languages, and Programming (Z. Fulop and F. G'ecseg, eds.), Springer-Verlag, 1995, pp. 324--335.

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T. Henzinger. Hybrid automata with finite bisimulations. In Proceedings of ICALP'95, volume 944 of LNCS, pages 324--335. Springer, 1995.

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T. A. Henzinger. Hybrid automata with finite bisimulations. In Proceedings of the 22nd International Colloquium on Automata, Languages, and Programming, ICALP 1995.

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Henzinger T. A., Hybrid automata with finite bisimulations, Proceedings of the 22nd International Colloquium on Automata, Language, and Programming (ICALP), Lecture Notes in Computer Science 944, Springer-Verlag (1995), pp. 324--335.

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T.A. Henzinger. Hybrid automata with finite bisimulations. In ICALP 95: Automata, Languages, and Programming, Lecture Notes in Computer Science 944, pages 324--335. Springer-Verlag, 1995.

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Henzinger T. A., Hybrid automata with finite bisimulations, Proceedings of the 22nd International Colloquium on Automata, Language, and Programming (ICALP), Lecture Notes in Computer Science 944, Springer-Verlag (1995), pp. 324--335. 23

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