O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Proc. of the 12th Annual Symposium on Theoretical Aspects of Computer Science, STACS'95, LNCS 900, pages 229 - 242. Springer, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a vocabulary. It is very much tailored towards timed scenarios, and for the moment, it exists essentially on paper. Timed automata [HNSY92] BST98b] have been used for modelling real time aspects of systems, for de ning semantics of modelling languages and for studying controller synthesis [MPS95,AMP95] and scheduling frameworks [BGS00] HHK01] A number of validation and analysis tools, such as Hytech [HHWT97] the tra c light presented in section 4 is an instance of this type of use Kronos IF [Yov97,BGGM00,BGM02] or Uppaal Time [LPY97,FPY02] exist for the framework of timed automata ....

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS'95, LNCS 900, 1995.

....these tools allow symbolic parameters in the 12 model, and researchers began to study the problem of synthesizing values for these parameters in order to satisfy some kind of control objective, such as minimizing the size of the backwards reachable set. Our algorithm was motivated by the work of [65, 66] for reachable set computation and controller synthesis for timed automata, and by that of [67] for controller synthesis for linear hybrid automata. Our hybrid system analysis tool [7] is built upon our implicit reachable set representation and level set implementation for continuous systems. ....

O. Maler, A. Pnueli, and J. Sifakis, "On the synthesis of discrete controllers for timed systems," in STACS 95: Theoretical Aspects of Computer Science (E. W. Mayr and C. Puech, eds.), no. 900 in LNCS, pp. 229-242, Munich: Springer Verlag, 1995.

....and define the synthesis problems in Section 2. The first tool we present is called SynthKro. It is a module of the tool suite Kronos [12, 8] SynthKro is based on the notion of controllable states, which are computed using a backward fixpoint iteration of special symbolic predecessor operators [29, 16, 19, 5]. The tool SynthKro, its algorithms and experimental results are presented in Section 3. The second tool we present is called FlySynth. It is based on an on the fly synthesis algorithm [25] which works on finite graphs with edges marked controllable or uncontrollable. The algorithm is on the fly ....

....perform controller synthesis for various objectives including safety, reachability and various combinations of the two. Our main contribution with respect to the above works is the tool FlySynth which performs synthesis on the fly. Controller synthesis in a dense time context has been studied in [29, 16, 19, 5]. To our knowledge, we provide the first concrete implementation of the ideas introduced in the above works. There are also some di#erences between our model and the ones used in the works above. First, we use a notion of urgency # BIP, INRIA Rhone Alpes, 38330 Montbonnot, France. E mail: ....

[Article contains additional citation context not shown here]

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS '95, 1995.

....are used to ad hoc design methodologies that almost always lead to solutions that must be validated by simulation, rapid prototyping and testing. In some cases, it is possible to solve the composition problem by synthesizing a controller or supervisor that restricts the behavior of the components [16] so that the overall system behaves correctly by construction or is amenable to formal analysis. Both veri cation at the global system level and synthesis techniques have well known limitations due to their inherent complexity or undecidability, and cannot be applied to complex systems. As an ....

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In E. Mayr and C. Puech, editors, STACS'95, volume 900 of LNCS, pages 229-242. Springer-Verlag, 1995.

....creation of programs obeying temporal logic specifications has been done by Pnueli. He has given algorithms for both the creation of finite state machines meeting temporal specifications and the creation of infinite state machines, based on the timed automata model, meeting temporal specifications [29, 34]. A much earlier work by Buchi and Landweber investigates the conditions for a relation between input and output # sequences to be satisfiable by a finite state automaton [3] 10.6 Abstract State Machines The description of computational processes as abstract state machines (ASMs) is similar to ....

Maler, Pnueli, and Sifakis. On the synthesis of discrete controllers for timed systems. In STACS: Annual Symposium on Theoretical Aspects of Computer Science (1995).

....function is minimized, for each initial condition in a specified set Y2 C IR n. Casting the problem into the domain of hybrid control is not appealing per se, on the contrary Algorithmic approaches for solving the controller synthesis problem for specific classes of hybrid systems have appeared [8, 12] but no general, efficient algorithm is yet available. Hence, to be able to solve the (nonlinear) hybrid optimal control problem, we must exploit some additional property. We have a feasible and quite appealing approach if we can translate the problem to an equivalent discrete problem, which ....

O. Maler, A Pnueli, J. Sifakis. On the synthesis of discrete controllers for timed systems. In Proc. $TACS '95, E.W. Mayr and C. Puech, eds. LNCS 900, SpringerVerlag, p. 229-242, 1995.

....are played on a state space and proceed in an in nite sequence of rounds. In each round, the players choose actions to play, and the chosen actions determine the successor state. For the synthesis and modular analysis of real time systems, we need to use games where time elapses between actions [MPS95]. In such timed games, each player chooses both which action to play, and when to play it. Timed games di er from their untimed counterparts in two essential ways. First, players can take each other by surprise, because actions are played with delays that cannot be anticipated by Supported in ....

....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 ....

[Article contains additional citation context not shown here]

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Theor. Aspects of Comp. Sci., Lect. Notes in Comp. Sci. 900, pages 229-242. Springer, 1995.

....the field of hardwaresoftware codesign of embedded systems [10] Previously, a large effort was directed towards hardware synthesis and comparatively little attention paid to software synthesis. Partial software synthesis was mainly carried out for communication protocols [18] plant controllers [17], and real time schedulers [1] because they generally exhibited regular behaviors. Only recently has there been some work on automatically generating software code for embedded systems [2,16,20,22] Except for MetaH from Honeywell, no other automatic software synthesis method is available for ....

Maler, O., A. Pnueli and J. Sifakis, On the synthesis of discrete controllers for timed systems, in: 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS'95), Lecture Notes in Computer Science 900, 1995, pp. 229 -- 242.

....research in the field of hardware software codesign of embedded systems [11] Previously, a large effort was directed towards synthesis of hard real time systems, especially in the application of formal methods. Synthesis was mainly carried out for communication protocols [19] plant controllers [4, 18, 5], and real time schedulers [25, 1] because they generally exhibited regular behaviors. Only recently has there been some work on automatically generating code for embedded systems [17, 16, 23, 26, 6] In the following, we will briefly survey the existing works on the synthesis of non real time ....

.... synthesis) was mainly performed in the discrete time domain, with a large portion of classical work done by Ramadge and Wonham [21, 22] Around 1994, when timed automata was proposed as a dense time model for real time systems [3] controller synthesis was extended to dense real time systems [4, 18, 25] as well as to hybrid systems [24] Recently, the same technique was further extended to multimedia scheduler synthesis [1] Given a dense real time system modeled by timed t3(2, 8) t2(1, 4) t( 2,3) l(q, 2) 2.fi 2 Pl P3 t3(5, 10) 23 t2(0, 5) P2 Figure 1. A Time Free Choice Petri Net ....

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS'95), volume 900, pages 229 242. Lecture Notes in Computer Science, Springer Verlag, March 1995.

....allows the use of constructive methods that ensure, a priori, required properties on the system behavior. In this approach, the validation phase is reduced to properties not guaranteed by the programming process. There exist di erent theories for control of Discrete Event Systems since the 80 s [59, 9, 30, 42]. Usually, the starting point of these theories is: given a model for the system and the control objectives, a controller must be derived by various means such that the resulting behavior of the closed loop system meets the control objectives. 3.1.1 Behaviors as transition systems The basic ....

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In E. W. Mayr and C. Puech, editors, Proceedings STACS'95, volume 900 of Lecture Notes in Computer Science, pages 229-242. Springer-Verlag, 1995.

....no exhaustive study, but we give references to approaches also other than the one we will adopt. The basic models are discrete event systems, and can be formulated in terms of formal languages [59] Petri nets [2, 32, 33] dynamical equations systems [47] or nite state machines (possibly hybrid [41, 7]) The latter cases take us close to the models that are at the basis of synchronous techniques. The transitions between states are labelled, typically with events: in reactive systems, the transitions can be taken upon the occurrence of these events. The states can be characterized by valuations ....

.... temporal properties of robot applications in relation with Orccad [34] For these formalisms, an approach to controller synthesis has been described as nding a winning strategy in a game between controller and environment, where the outcome depends on the player s actions as well as their timing [41]. The use of Kronos for controller synthesis is based on this work, with a x point operation [3] Another technique is an on the y method [68] where a forward search returns the rst solution. Two algorithms are proposed: one for invariance, the other one for reachability; they are adapted to ....

O. Maler, A.Pnueli, and J.Sifakis. On the synthesis of discrete controllers for timed systems. In Proceedings of STACS'95, volume 900 of Lecture Notes in Computer Science (LNCS). Springer Verlag, 1995.

....[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 states in CPre i (oe) player i may have to ....

....can be overcome. We show how winning strategies can be synthesized symbolically over all class 2 game structures (finite i trace equivalence) for all regular winning conditions. Previously, symbolic infinite state controller synthesis has been solved only 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 ....

[Article contains additional citation context not shown here]

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS 95, LNCS 900, pp. 229--242. Springer-Verlag, 1995.

....lim (t) Ei U E, E lim j=l where Gi is the set of initial conditions of the reachability problem and El (G) c. Simple modifications of this algorithm suffice to solve finite time reacha bility problems. The procedure described above, developed in [1,3] was motivated by the work of [4, 5] for reachability computation and controller synthesis on timed automata, and that of [6] for controller synthesis on linear hybrid automata. In that development the reachability problem s objective was to determine E the largest controllable invariant subset of the state space by computing the ....

O. Maler, A. Pnueli, and J. Sifakis, "On the synthesis of discrete controllers for timed systems," in STACS 95: Theoretical Aspects of Computer Science (E. W. Mayr and C. Puech, eds.), no. 900 in LNCS, pp. 229-242, Munich: Springer Verlag, 1995.

....topic of research in the field of hardware software code sign. Previously, a large effort was directed towards hardware synthesis and comparatively little attention paid to software synthesis. Partial software synthesis was mainly carried out for communication protocols [24] plant controllers, [8,9,23] and real time schedulers [2,26] because they generally exhibited regular behaviors. Only recently has there been some work on automatically generating software code for embedded systems [10,21,22,25,27] As far as the authors know, no automatic software synthesis method is available for ....

O. Maler, A. Pnueli, J. Sifakis. On the synthesis of discrete controllers for timed systems, in: E. Mayr, C. Puech (Eds.), Proceedings of the 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS'95), vol. 900, Lecture Notes in Computer Science, Springer, Berlin, March 1995, pp. 229 242.

....M. Le Borgne and P. Le Guernic methods that ensure, a priori, required properties on the system behavior. In this approach, the validation phase is reduced to properties not guaranteed by the programming process. There exist different theories for control of Discrete Event Systems since the 80 s [24, 1, 10, 17]. Usually, the starting point of these theories is: given a model for the system and the control objectives, a controller must be derived by various means such that the resulting behavior of the closed loop system meets the control objectives. In our case, the specification of the physical model ....

Maler, O., A. Pnueli and J. Sifakis: 1995, `On the Synthesis of Discrete Controllers for timed Systems'. Proceedings STACS'95, , Vol. 900 of Lecture Notes in Computer Science, pp. 229--242.

....is specifically adapted to hybrid systems in [97] where the system model is essentially a hybrid automaton over state space and , with reset maps indexed by events , and for , a supervisor can override and disable a reset at states . Earlier work on controller synthesis for timed automata in [98] is along the same general lines. In work on controller synthesis in this special issue, 41] considers a class of control problems in which one starts with a complete hybrid automaton , and the synthesis task is to find the largest subsystem , in the sense that the state space and flows are the ....

O. Maler, A. Pnueli, and J. Sifakis, "On the synthesis of discrete controllers for timed systems," in Proceedings of STACS'95,E.W. Mayr and C. Puech, Eds: Springer-Verlag, 1995, pp. 229--242. LNCS 900.

....the value 0, which serves as a speci c guard for activating a transition. To distinguish them, we have chosen to call the rst type of clock stopwatch and the second one egg timer : The former will allow to model Ctgs and EndClbs, while the latter will be necessary to model BeginClbs. In [Maler et al. 1995, Asarin et al. 1995] such tools are claimed to t real time games , where transitions are divided in two groups (such as constraints in CTCN) depending on which of the two players control it, and some states are designated as winning for one of the players. The strategy for each player is to ....

....of the players. The strategy for each player is to select controlled transitions that will lead her to one of her winning states. This extension of the classical discrete game approach has the following features: 1) there are no turns and the adversary need not wait for the player s next move [Maler et al. 1995], and (2) each player not only choose between alternative transitions, but also between waiting or not before taking it, from which one can view the two player game as now a three player one where Time can interfere in favor of both of the two players [Asarin et al. 1995] This is especially ....

[Article contains additional citation context not shown here]

Maler, O., Pnueli, A., and Sifakis, J. (1995). On the synthesis of discrete controllers for timed systems. In Proceedings of the 12th Symposium on Theoretical Aspects of Computer Science, Munchen (Germany).

....are available elsewhere [14] as well as comparative studies [13] Model: labeled transition systems. The basic models are discrete event systems, and can be formulated in terms of formal languages [14] Petri nets [2, 8] dynamical equations systems [10] or finite state machines (possibly hybrid [9]) The latter cases take us close to the models that are at the basis of synchronous techniques. The transitions between states are labelled, typically with events: in reactive systems, the transitions can be taken upon the occurrence of these events. The states can be characterized by valuations ....

....with recent techniques in optimal discrete control synthesis [11] with which an automatic controller can be synthesized, always switching to the best solution. Also, it would be interesting to consider temporal or even hybrid extensions of transition systems and controller synthesis there [9]. Acknowledgement is due to constructive discussion with B. Espiau, D. Simon, A. Girault, H. Marchand (a lot) F. Maraninchi, amongst others. ....

O. Maler, A.Pnueli, J.Sifakis. On the Synthesis of Discrete Controllers for Timed Systems. In Proceedings of STACS'95, 1995, LNCS 900, Springer.

....so that all possible outcomes of the game satisfy Our main result shows that the Ltl control problem can be decided for rectangular games. Previously, beyond the finite state case, control problems have been solved only for the special case of timed games (which corresponds to timed automata) [6, 16, 20], and for rectangular games under the assumption that the controller can move only at integer points in time (sampling control) 13] Semialgorithms for control have also been proposed for more general linear [27] and nonlinear [18, 26] hybrid games, but in these cases termination is not ....

....variables. Even more specific is the case of a timed game, which is a rectangular game with deterministic jumps all of whose variables are clocks. An essentially identical class of timed games has been defined and solved in [6] and closely related notions of timed games are studied in [3, 15, 16, 20]. 3.2 Game Bisimilarity for Singular Games Given an n dimensional singular game S, we define the region equivalence on the states of S following [1, 2] For a real number u, let frac(u) denote the fractional part of u. For a vector u 2 R n , let frac(u) denote the vector whose kth coordinate ....

Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: STACS 95: Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, Vol. 900. Springer-Verlag (1995) 229--242

....are verified for these models using either model checking, which exhaustively check all system trajectories, or deductive theorem proving techniques [26] which prove the specification by induction on all system trajectories. In this framework, controller design has also been developed [27], 28] Automated computational tools have been developed for both model checking [29] 30] and theorem proving [31] Control theoretic approaches to modeling, analysis, and controller design for hybrid systems have extended the theory of dynamical systems to include discrete modes of operation. ....

O. Maler, A. Pnueli, and J. Sifakis, "On the synthesis of discrete controllers for timed systems," in STACS 95: Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 900, E. W. Mayr and C. Puech, Eds. Munich, Germany: Springer Verlag, 1995, pp. 229--242.

....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 conditions, which allow us to see that the three formulations 1 3 are of strictly increasing generality. Intuitively, if all switch conditions are known, then they are ....

....switch, or let an amount of time pass which is constrained only by the location invariant of the hybrid automaton. Since all timing constraints are already part of the model (in the form of location invariants and edge guards) this is also called time abstract control [HHM99] By contrast, in [MPS95, AMP95] the controller may strengthen the location invariants of the hybrid automaton model to achieve the control objective: at each plant state, the controller decides whether to cause a mode switch, or let an amount of time pass which is constrained by some new, derived predicate on the plant ....

[Article contains additional citation context not shown here]

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In E.W. Mayr and C. Puech, editors, STACS 95: Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 900, pages 229-242. Springer-Verlag, 1995.

....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 CPre i ( player i may have to choose ....

....can be overcome. We show how winning strategies can be synthesized symbolically over all class 2 game structures ( nite i trace equivalence) for all regular winning conditions. Previously, symbolic in nite state controller synthesis has been solved only 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 ....

[Article contains additional citation context not shown here]

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS 95, LNCS 900, pp. 229-242. Springer-Verlag, 1995.

.... is the finite sequence of states x[0] x[1] x[n] The set of trajectories of G is denoted by T (G) and the set of finite sequences of states of G is denoted by T (G) We give two examples of sequences of states accepted by G with respect to (Xm ; Theta) other examples are given by Maler et al. 1995)) S(G; Xm ; a) f[0: n] 2 T (G) x[n] 2 Xm g and (0.1) S(G; Xm ; Sigma) f 2 T (G) Inf( Xm 6= g; 0.2) where Inf( the infinity set of , denotes the set of all states appearing in infinitely many times (i.e. Inf( fx 2 X j (9 i) x[i] x)g) According to (0.1) ....

....There are many ways to translate a synthesis procedure into a program. On the one hand, one can implement mathematical operators or formulas explicitly into the code. The 7 June 1, 1999 15:21 WorldScientific ws b8 5x6 0 ensemble algorithms resulting from this approach are based on a fixpoint [ Maler et al. 1995); Wonham and Ramadge (1987) algebraic [ Wonham (1994) or linear integer mathematical programming [ Li and Wonham (1994) calculation. On the other hand, one can adopt various search space techniques and heuristics in the area of artificial intelligence [ Barbeau et al. 1998) Ben ....

Maler, O., Pnueli, A., and Sifakis, J. (1995) "On the synthesis of discrete controllers for timed systems," In Proc. of 12th Annual Symp. on Theoretical Aspects of Computer Science, Munich, Germany, March, 1995, E. W. Mayr and C. Puech, Eds. (Lecture Notes in Computer Science, vol. 900), Berlin: Springer-Verlag, 229--242.

No context found.

O. Maler, A. Pnueli and J. Sifakis. On the Synthesis of Discrete Controllers for Timed Systems, Proc. STACS'95, 229-242, LNCS 900, Springer, 1995.

No context found.

O. Maler, A. Pnueli and J. Sifakis. On the Synthesis of Discrete Controllers for Timed Systems, Proc. STACS'95, 229-242, LNCS 900, Springer, 1995.

....of G, that is, the maximal F G for which there exists an update strategy s : F . n, # such that all trajectories starting in F stay in F . To compute F and s we use a variant of the fixed point computation described in 00] This approach was first presented for timed automata [MPS95] where it is guaranteed to converge, and then adapted for hybrid automata [W97,TLS99,ABD 00] Definition 4 (Delayed Predecessors) Let H be a subset of X and let f be a vector field. The set # (f,d) H) d x H (1) consists of all points from which the system can reach H after ....

O. Maler, A. Pnueli and J. Sifakis. On the Synthesis of Discrete Controllers for Timed Systems, in E.W. Mayr and C. Puech (Eds), Proc. STACS'95, 229-242, LNCS 900, Springer, 1995.

....in a control invariant subset of K, set of states from which the constraint K can be maintained in spite of disturbances of the environment and of internal actions of the tasks. The existence of a scheduler maintaining K depends on the existence of non empty control invariants contained in K [MPS95,AGP 99] Control invariants can be characterized as xpoints of monotonic functions (predicate transformers) representing the transition relation of the timed system to be scheduled. There exists a scheduler maintaining K i there exist non empty xpoints implying K. Computing such xpoints is ....

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In E.W. Mayr and C. Puech, editors, STACS'95, volume 900 of LNCS, pages 229-242. Springer-Verlag, 1995.

....21 # F 2 in the right. The final results show for each state the safe region where the system can spiral and then make a transition to the safe region of the other state. Wong Toi and Ho#mann [34] were the first to consider the application of supervisory control methodology to this class. In [35] (see also [20] 28] we have defined an algorithm similar to Algorithm 1 and have shown that the exact computation of P # can be performed over the set of zones (a restricted class of polyhedra underlying the verification of timed automata) Another class of systems for which a controller ....

....cannot be detected by any realistic controller) The work of [34] is an example of the rigorous application of the indirect approach to timed automata 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 ....

O. Maler, A. Pnueli, and J. Sifakis, "On the synthesis of discrete controllers for timed systems," in Proc. STACS'95, E.W. Mayr and C. Puech, Eds. 1995, Lecture Notes in Computer Science 900, pp. 229--242, Springer-Verlag.

....can be extended into a timed one by preserving progress properties. In this paper we study a methodology for constructing a scheduled system from scheduling requirements and a timed speci cation of the processes to be scheduled. The methodology is based on the controller synthesis paradigm [11, 9, 1]. A scheduler is considered as a controller of the processes to be scheduled which restricts their behavior by triggering their controllable actions. The restricted behavior must respect the timing constraints of the processes as well as constraints characterizing the scheduling requirements. We ....

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS'95, volume 900 of LNCS. Springer Verlag, 1995.

....to one or more optimal paths. 5 The problems are taken from ftp: mscmga.ms.ic.ac. uk pub jobshop1.txt The idea of applying synthesis to timed automata was first explored in [WH92] An algorithm for safety controller synthesis for timed automata, based on operation on zones was first reported in [MPS95] and later in [AMP95] where an example of a simple scheduler was given, and in [AMPS98] This algorithm is a generalization of the verification algorithm for timed automata [HNSY94,ACD93] used in Kronos [Y97,BDM 98] In these and other works on treating scheduling problems as synthesis ....

O. Maler, A. Pnueli and J. Sifakis. On the Synthesis of Discrete Controllers for Timed Systems, in E.W. Mayr and C. Puech (Eds), Proc. STACS'95, LNCS 900, 229-242, Springer, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Proc. of the 12th Annual Symposium on Theoretical Aspects of Computer Science, STACS'95, LNCS 900, pages 229 - 242. Springer, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS 95: Theoretical Aspects of Computer Science, LNCS 900, pages 229-242. Springer-Verlag, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Theoretical Aspects of Computer Science, volume 900 of Lect. Notes in Comp. Sci., pages 229-242. Springer, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS'95, LNCS 900, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Proc. 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS'95), volume 900 of Lecture Notes in Computer Science, pages 229--242. Springer, 1995. 20 P. Bouyer et al.

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O. Maler, A.Pnueli, and J.Sifakis. On the synthesis of discrete controllers for timed systems. In in Proc.of STACS'95, volume 900, pages 229--242. Springer Verlag, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Proceedings of STACS: Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 900, pp. 229--242. Springer-Verlag, 1995.

No context found.

O. Maler, A.Pnueli, and J.Sifakis. On the synthesis of discrete controllers for timed systems. In in Proc.of STACS'95, volume 900, pages 229--242. Springer Verlag, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS: Theoretical Aspects of Computer Science, LNCS 900, pp. 229--242. Springer, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In E.W. Mayr and C. Puech, editors, STACS 95: 12th Annual Symposium on Theoretical Aspects of Computer Science, Munich, Germany, March 2--4, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Theoretical Aspects of Computer Science, volume 900 of Lect. Notes in Comp. Sci., pages 229--242. Springer, 1995.

No context found.

Oded Maler, Amir Pnueli, and Joseph Sifakis. On the synthesis of discrete controllers for timed systems (an extended abstract). In 12th Annual Symposium on Theoretical Aspects of Computer Science, volume 900 of lncs, pages 229--242, Munich, Germany, 2--4 March 1995. Springer.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In E. W. Mayr and C. Puech, editors, Proceedings STACS'95, volume 900 of Lecture Notes in Computer Science, pages 229--242. Springer-Verlag, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Theor. Aspects of Comp. Sci., Lect. Notes in Comp. Sci. 900, pages 229--242. Springer, 1995.

No context found.

Oded Maler, Amir Pnueli, and Joseph Sifakis. On the synthesis of discrete controllers for timed systems. In Proc. 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS'95), volume 900, pages 229--242. Springer, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In STACS: Theoretical Aspects of Computer Science, LNCS 900, pages 229--242. Springer, 1995.

No context found.

Oded Maler, Amir Pneuli, and Joseph Sifakis. On the synthesis of discrete controllers for timed systems. In Ernst W. Mayr and Claude Puech, editors, STACS 95: Theoretical Aspects of Computer Science, pages 229--242. Springer Verlag, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Theoretical Aspects of Computer Science, number 900 in LNCS, pages 229--242. Springer Verlag, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Proc. of the 12th Annual Symposium on Theoretical Aspects of Computer Science, STACS'95, LNCS 900, pages 229 - 242. Springer, 1995.

No context found.

O. Maler, A. Pnueli, and J. Sifakis, \On the synthesis of discrete controllers for timed systems," in STACS 95: Theoretical Aspects of Computer Science (E. W. Mayr and C. Puech, eds.), no. 900 in LNCS, pp. 229-242, Munich: Springer Verlag, 1995.

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