S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....when the set of constraints is consistent) but not always, as shows the second example of Figure 3. Moreover, our aim is to keep constraints as loose as possible, and thus to characterize the largest set of timed behaviours of (sequential) subsystems and to enable compositional analysis. In [BS00] is described a framework for more exible composition of duration constraints than conjunction which could be used to further extend the real time pro le presented here. 3.3 Derived duration expressions Our approach is based on duration constraints between the occurrences of an event ev1 and a ....

.... based on a dynamic priority, initialized arbitrarily to init(priority) forall j (priority(j) j) 5) and updated each time TLCP (i) changes to green by update(i,priority) forall j (priority(j) if j=i then 0 else priority(j) 1) 6) using the min synchronization of the framework of [BS00] instead of conjunction with constraint (2) would allow to simplify a lot the expression of constraint (4) taking into account that the green and the red phase alternate, and simpli ed by the assumption that tra c cannot go away in the red phase in order to allow a non deterministic ....

S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163, 2000.

....other formalism, model, or tool that is powerful enough to cover the complete spectrum spanned by this classification. Some approaches however come close, among them [29,4,10,7,26] We achieve the full expressiveness by using a model that integrates timed automata [1] using the deadline style of [6]) stochastic automata [13,11] and (simple) probabilistic automata [31] These three ingredient models have been selected from a wide range of possible alternative models. They were chosen because they complement each other very well and yield precisely the desired expressiveness. Due to their ....

....otherwise specified when(true) is a default constraint (that can be omitted) When clauses thus indicate when a certain action may (i.e. is allowed to) happen. Similar to location invariants in safety timed automata [18] and deadlines in timed automata with deadlines [6], we need a separate mechanism to force certain actions to happen at some time instant. To that end, we use deadlines. For instance, the process on the right specifies that set pri e is enabled from 120 time units after catching the exception (as before) and that it should happen before ....

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S. Bornot and J. Sifakis. An algebraic framework for urgency. Inf. and Comp., 163:172--202, 2001.

....run leading from waiting to running must be taken by t = T E and resets another clock x measuring the time passed in state running. Finally, with transition done, the process returns to sleeping after having spent E time units in running. We use a exible parallel composition k of timed systems [6]. Maximal progress semantics ensures that synchronization transitions are taken whenever this is possible; a synchronizing transition may interleave only when no synchronization is possible. We refer to the parallel composition of timed systems as a timed system of processes. 3.2 Coordination ....

....For these reasons, partial priority orders between the actions of processes are particularly interesting, since they allow to express local properties as priority relations that only apply between certain transitions, without side e ect on other transitions. We adopt the approach developed in [6, 5, 12], providing a general framework for dynamic priorities on the actions of a timed system of processes TS. The key to a modular description of di erent behavioral aspects by dynamic priorities is the composability principle studied in [1] A priority order is a strict partial order on the set of ....

S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163:172-202, 2000.

....if the light is on and no earlier than 1 time unit after the switch event. When the condition is reached, execution will be advanced only when both of these are true. Placing a maximal delay in conjunction with a regular guard is somewhat similar to the notion of delayed deadline as appears in [8]. The combination of real time constraints and regular ones can be taken one step further, as seen in Fig. 3(d) This is an existential LSC, which describes a simple test stating our expectation that the light should be on no more than D time units after the switch was turned on. Or in other ....

S. Bornot and J. Sifakis, "An Algebraic Framework for Urgency", Information and Computation 163 (2000), 172--202.

....that certain commands will always be executed as soon as they become enabled that is, time is not allowed to advance if one or more of these urgent commands are enabled. As we shall see in Sect. 2.5, the program invariant and the urgency predicate are used to ensure progress of a tgc program. See [45] for a more thorough treatment of urgency in timed systems. Example 3. An example of a tgc program is P = fbg; fx; yg; ft 1 ; t 2 g; I ; U) t 1 : b (1 x 3) b : false t 2 : b (7 x 9) b; y : false; 0 : The program invariant is given by the expression I = b ) x 9) b ....

S.Bornot and J.Sifakis. An algebraic framework for urgency. Information and Computation, 163(1):172202, 2000.

....of Kleene s star operator, in the sense that the automaton recognize the same timed language as denoted by the expression. However, the issue of axiomatisation was not considered there. In [DAB96] a set of equational axioms was proposed for timed automata, but no completeness result was reported. [BS98] presents an algebraic framework for real time systems which is similar to timed automata where invariants are replaced by deadlines (to express urgency ) together with some equational laws. Apart from these, we are not aware of any other published work on axiomatising timed automata. On the ....

S. Bornot and J. Sifakis. An Algebraic Framework for Urgency. Information and Computation, 163:172-202, 2000.

....alternating free calculus model checker Evaluator. At the same level are also available the Tctl model checker Kronos [11] and the test generator Tgv [7] 2 Modeling Real Time Systems 2. 1 Modeling Real Time Processes Consider the two periodic processes P 1 and P 2 modeled as timed systems [4], as shown in gure 2. We suppose them to share two non preemptable resources r 1 and r 2 . In 2 bgn 1 1 bgn 2 1 end u 1 arrive u 1 (t1 6 4) x1 : 0 (x1 = 3 t1 6 7) 5 6 x1 6 6 t1 6 10) t1 = 10) t1 : 0 (t2 6 9) x2 : 0 bgn 2 2 (t2 = 12) t2 : 0 arrive u 2 ....

....guaranteed to be structurally live. Prometheus implements these results. 2.2 Modeling with Priorities Priorities are widely used in modeling formalisms to restrict system behavior, especially for con ict resolution and scheduling, or to reduce non determinism. We adopt the approach discussed in [4, 3], providing a general framework for dynamic priorities on the actions of a timed system of processes TS. A priority order is a strict partial order on the set of actions of TS. Priority 3 functions associate priority orders with subsets of states of the system. More formally, a priority ....

S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163:172-202, 2000.

....and time steps. Transitions are timeless state changes that represent the e ect of actions of the untimed system; their execution may depend on and modify time variables. Time steps represent time progress and increase uniformly only time variables. They are speci ed by time progress conditions [BS00] time can progress from a state by t if the time progress condition remains true in all intermediate states reached by the system. During time steps state components of the untimed model remain unchanged. There exists a variety of timed formalisms extensions of Petri nets [Sif77] process ....

....on timed behavior. For example, if C1 and C2 is the code of two tasks and CkC2 represents the system after application of synchronization constraints, then we need a timed extension k T of k to compose the timed models C1 T and C2 T of C1 and C2. C1 T k T C2 T is the timed model of C1kC2. In [BS00] it has been shown that untimed composition operators k admit various timed extensions k T depending on the way urgency constraints (deadlines) of timed tasks are composed. Extending untimed composition operators to timed ones is an important problem for the construction of the global timed ....

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S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163:172-202, 2000.

....the controller is to forbid or to force certain control lable actions to ensure the state of the system remains in a desired set. In [2] we have proposed a method ology for model based schedulability of real time systems that combines (1) recent results on compositional modeling of timed systems [11] and (2) the controller synthesis algorithm for timed automata [4] developed in [5] Our approach has been experimented on several case studies that illustrated its interest but also ex posed its weaknesses, notably its high computational cost. A compositional methodology to try to overcome this ....

S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163:172202, 2000. Academic Press.

....particular case where interactions are atomic, component behaviors are transition systems, and the constraints are modeled as priority orders on interactions. Transition systems with dynamic priorities have already been studied and used to model timed systems. The interested reader can refer to [6, 1]. Definition 4 (Transition system) A transition system B is a triple (Q, I(A) where Q is a set of states, I(A) is a set of interactions on the action vocabulary A, and Q I(A) is a transition relation. As usual, we write q 1 q 2 instead of (q 1 , #, q 2 ) ##. Definition 5 ....

S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163:172--202, 2000.

....constraints to untimed models. Correct means, for instance, to avoid artifacts of the mathematical model (e.g. zeno behaviors) that do not correspond to real phenomena. Also, in order to have a modular modeling approach, it is desirable that time constraints are added in a compositional manner [30]. ....

S. Bornot and J. Sifakis, "An algebraic framework for urgency," Inform. Comput., vol. 163, pp. 172--202, 2000.

....of the controller is to forbid or to force certain controllable actions to ensure the state of the system remains in a desired set. In [2] we have proposed a methodology for model based schedulability of real time systems that combines (1) recent results on compositional modeling of timed systems [11] and (2) the controller synthesis algorithm for timed automata [4] developed in [5] Our approach has been experimented on several case studies that illustrated its interest but also exposed its weaknesses, notably its high computational cost. A compositional methodology to try to overcome this ....

S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163:172{ 202, 2000. Academic Press.

....the one of a delayable action where d = g# is the falling edge of a right closed guard g (cannot be disabled without enforcing the action) The differences between these actions are illustrated in fig. 1. g eager = ffl delayable = ffi lazy = Fig. 1. Types for guards It has been shown in [7] that any timed system can be described by a bisimilar system with only eager and lazy timed actions. In practice, we use the notation g ffl , g ffi and g to denote a guard g of an action that is respectively eager (d = g) delayable (d = g#) and lazy (d = false) The containment of ....

....2 7 x 8 (immediate priority) g 0 1 = g 1 :3 1 g 2 = 0 x 1 7 x 8 (priority within a delay of 1) g 0 1 = g 1 :3g 2 = 7 x 8 (priority within an unbounded delay) Fig. 3 illustrates the above example. The following definition of priority order has been introduced and studied in [7]. Definition 15 (Priority order) Consider the relation OE A Theta (R [f1g) Theta A. We write a 1 OE k a 2 for (a 1 ; k; a 2 ) 2OE and suppose that 8k 2 R [ f1g: OE k is a partial order a 1 OE k a 2 implies 8k 0 k: a 1 OE k 0 a 2 a 1 OE k a 2 a 2 OE l a 3 implies a 1 OE k l ....

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S. Bornot and J. Sifakis. An Algebraic Framework for Urgency. In Calculational System Design, NATO Science Series, Computer and Systems Science 173, Marktoberdorf, July 1998.

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S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163, 2000.

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S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163, 2000.

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S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163(1):172202, 2000.

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S. Bornot and J. Sifakis. An algebraic framework for urgency. Information and Computation, 163, 2000.

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