T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR'99, LNCS 1664, pages 320 -- 335, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....be undecidable [2] Timed games have been considered in several papers. Reachability problems in timed games were solved in [6, 5] and the EXPTIME hardness of reachability timed games was proved in [14] Rectangular hybrid games with winning conditions expressed by LTL formulas were studied in [13]. An automata theoretic approach to solve LTL and CTL timed games is discussed in [11] In all these papers, while the game graph is a dense time model, the winning condition either does not take into account time or considers time only from a qualitative point of view (i.e. no bounds on the time ....

T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR'99, LNCS 1664, pages 320 -- 335, 1999.

....control synthesis problems for timed automata, based on the translation of this problem to the reachability and the non emptiness problem of timed tree automata. These games have been already considered in the literature but they have been solved using a di erent approach, see for example [AM99, HHM99] The rest of the paper is organized as follows. In Section 2 we introduce timed tree automata and give the basic de nitions. In Section 3 we show some crucial results relating timed tree languages to untimed ones. Section 4 is devoted to the reachability problem and its complexity. Closure ....

....by a subset of A locations with the meaning that the system wins if a location from P is reached. For timed B uchi and Muller games the winning condition is the same as for the corresponding acceptance condition. In the literature these games have been considered by other authors, see for example [HHM99] where Ltl games on rectangular hybrid automata have been solved. Here we present a di erent approach to decide them and to sythesize a winning strategy. Notice that a symmetric de nition of games is possible and all the results described in this section also hold in the general case. 19 ....

T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR'99, LNCS 1664, pages 320 - 335, 1999.

.... which a controller synthesis procedure always terminates are the initialized rectangular hybrid automata, systems where the dynamics in each state is of the form c # x i # d for every variable x i and for which controller synthesis was proved to be solvable for discrete [36] and continuous [37] time by Henzinger et al. In the rest of the constant slope world, exact verification and synthesis problems are undecidable, algorithms such as Algorithm 1 are not guaranteed to terminate, yet operators such as # and # can be computed exactly at every step using linear algebra (polyhedra are ....

T.A. Henzinger, B. Horowitz, and R. Majumdar, "Rectangular hybrid games," in Proc. CONCUR'99, F. Vaandrager and J. van Schuppen, Eds. 1999, Lecture Notes in Computer Science 1664, pp. 320--335, Springer-Verlag.

....( s if u . This definition was used in [5] and in this respect differs from the controller synthesis problem stated in [3, Def. 2.1.34] where all events except one at each state are prevented from occurring. Also a control problem under the hybrid games formalism has been considered in [6]. The supervisory control problem is defined as follows: A compact rectangular hybrid automaton A with fixed activity rectangle and two sets of locations T F , of A are given. Compute a supervisor such that in the controlled hybrid automaton ) A a) the locations in F are inaccessible, b) ....

T A Henzinger, B Horowitz and R Majumdar, Rectangular Hybrid Games, Proc. CONCUR'99, LNCC, vol. 1664, pp.320-335, 1999.

.... for which a controller synthesis procedure always terminates are the initialized rectangular hybrid automata, systems where the dynamics in each state is of the form c x i d for every variable x i and for which controller synthesis was proved to be solvable for discrete [36] and continuous [37] time by Henzinger et al. In the rest of the constant slope world, exact veri cation and synthesis problems are undecidable, algorithms such as Algorithm 1 are not guaranteed to terminate, yet operators such as and can be computed exactly at every step using linear algebra (polyhedra are closed ....

T.A. Henzinger, B. Horowitz, and R. Majumdar, \Rectangular hybrid games," in Proc. CONCUR'99, F. Vaandrager and J. van Schuppen, Eds. 1999, Lecture Notes in Computer Science 1664, pp. 320-335, Springer-Verlag.

.... for which a controller synthesis procedure always terminates are the initialized rectangular hybrid automata, systems where the dynamics in each state is of the form c x i d for every variable x i and for which controller synthesis was proved to be solvable for discrete [HK99] and continuous [HHM99] time by Henzinger et al. In the rest of the constant slope world, exact verification and synthesis problems are undecidable, algorithms such as Algorithm 1 are not guaranteed to terminate, yet operators such as and ffi can be computed exactly at every step using linear algebra (polyhedra are ....

T.A. Henzinger, B. Horowitz and R. Majumdar, Rectangular Hybrid Games, Proc. CONCUR'99, 320-335, LNCS 1664, Springer 1999.

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T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In CONCUR: Concurrency Theory, LNCS 1664, pp. 320--335. Springer, 1999.

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T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Concurrency Theory, Lect. Notes in Comp. Sci. 1664, pages 320--335. Springer, 1999.

....This process, repeated for in nitely many rounds, gives rise to a run of the game. Our de nition of moves preserves the element of surprise: a player cannot anticipate when the opponent s action will occur in the current round. This contrasts with many previous de nitions of timed games (e.g. [AH97,HHM99,dAHM01b,MPS95,AMPS98]) where players can only either play immediately an action a, or wait for a delay . Such formulations may be simpler and more elegant for timed transition systems (i.e. one player games) but in the case of two player formulations, the element of surprise is lost, because after each delay both ....

T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Concurrency Theory, Lect. Notes in Comp. Sci. 1664, pages 320-335. Springer, 1999.

....with finite i bisimilarity (or alternating bisimilarity [4] quotients. They permit symbolic model checking for the full game calculus (with negation) Examples of infinite state games from all four classes can be drawn from real time and hybrid systems: networks of timed games, rectangular games [10], 2D rectangular games, and timed games [15] fall into the classes 1 to 4, in that order. The termination criteria for solving games are insufficient if we wish to synthesize the corresponding winning strategies, which is important in control applications [18] This is because for different ....

.... for the special case of timed games [15] which fall into the more restrictive class 4 (finite i bisimilarity) In particular, as an instance of our results, we obtain symbolic algorithms also for the control and controller synthesis of rectangular hybrid systems, a problem that was left open in [10] (where a reductionist solution is given) These symbolic algorithms can be executed directly by symbolic model checkers for hybrid systems, such as HyTech [9] 2 Symbolic Game Structures A (two player) game structure G = S; A; Gamma 1 ; Gamma 2 ; ffi; P; p Deltaq) consists of a (possibly ....

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T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In CONCUR 99, LNCS 1664, pp. 320--335. Springer-Verlag, 1999.

.... time instant (e.g. turn o the furnace after y seconds ) This can be formalized in several ways, and consequently, a variety of similar but di erent mathematical formulations of the safety control problem for timed and hybrid systems can be found in the literature (e.g. HW92, HK99, AMPS98, HHM99, Won97, ABD 00, TLS00] We unify and classify these formulations into three classes, compare their relative strengths, and ll in some important gaps that had been left open previously. In doing so, we focus on safety control purely for reasons of clarity; the treatment of more general ....

....discrete time control problem can be solved algorithmically for all rectangular automata [HK99] see [HW92] for the timed case) 2. The known switch conditions dense time control problem, while undecidable for general rectangular automata, is solvable for all initialized rectangular automata [HHM99] 3. The unknown switch conditions dense time control problem, while undecidable for initialized rectangular automata [HKPV98] is solvable for all timed automata [MPS95, AMP95] While none of these papers explicitly mention switch conditions, we obtain equivalent formulations in terms of switch ....

[Article contains additional citation context not shown here]

T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In J.C.M. Baeten and S. Mauw, editors, CONCUR 99: Concurrency Theory, Lecture Notes in Computer Science 1664, pages 320-335. Springer-Verlag, 1999.

....with nite i bisimilarity (or alternating bisimilarity [4] quotients. They permit symbolic model checking for the full game calculus (with negation) Examples of in nite state games from all four classes can be drawn from real time and hybrid systems: networks of timed games, rectangular games [10], 2D rectangular games, and timed games [15] fall into the classes 1 to 4, in that order. The termination criteria for solving games are insucient if we wish to synthesize the corresponding winning strategies, which is important in control applications [18] This is because for di erent states in ....

.... for the special case of timed games [15] which fall into the more restrictive class 4 ( nite i bisimilarity) In particular, as an instance of our results, we obtain symbolic algorithms also for the control and controller synthesis of rectangular hybrid systems, a problem that was left open in [10] (where a reductionist solution is given) These symbolic algorithms can be executed directly by symbolic model checkers for hybrid systems, such as HyTech [9] 2 Symbolic Game Structures A (two player) game structure 1 G = S; A; 1 ; 2 ; P; p q) consists of a (possibly in nite) set S of ....

[Article contains additional citation context not shown here]

T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In CONCUR 99, LNCS 1664, pp. 320-335. Springer-Verlag, 1999.

..... This result is sharp: for simple extensions to the model of rectangular automata, even backward reachability (A3 ) may not terminate [22] 5. 3 Example: assembly line scheduler We describe an assembly line scheduler that must assign elements from an incoming stream to one of two assembly lines [21]. The stream has an inter arrival time of four minutes. The lines process the parts at different speeds: on the first line, jobs travel between one and two meters per minute, while on the second, jobs travel between two and three meters per minute. The first line is three meters long and the ....

T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In CONCUR 99: Concurrency Theory, LNCS 1664, pages 320--335, 1999.

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T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR'99, LNCS 1664, pages 320 -- 335, 1999.

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T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR'99, LNCS 1664, pages 320 -- 335, 1999.

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T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR '99, LNCS 1664, pages 320 - 335, 1999.

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T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR'99, LNCS 1664, pages 320 - 335, 1999.

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T. A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In S. Mauw J. Baeten, editor, Proc. CONCUR '99: Concurrency Theory, volume 1664 of LNCS, pages 320-335. Springer, 1999. 19

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T A Henzinger, B Horowitz and R Majumdar, Rectangular Hybrid Games, Proc. CONCUR'99, LNCS, vol. 1664, pp.32033.

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Thomas A. Henzinger, Benjamin Horowitz, and Rupak Majumdar. Rectangular hybrid games. In Proc. 10th International Conference on Concurrency Theory (CONCUR'99), volume 1664 of Lecture Notes in Computer Science, pages 320--335. Springer, 1999.

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T.A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR '99, LNCS 1664, pages 320 - 335, 1999.

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T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR'99, LNCS 1664, pages 320 - 335, 1999.

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