Li Xuan Dong and Dang Van Hung, Checking Linear Duration Invariants by Linear Programming, Joxan Jaffar and Roland H. C. yap (Eds.), Concurrency and Parallelism, Programming, Networking, and Security LNCS 1179, Springer-Verlag, Dec 1996, pp. 321--332.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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 ....

....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 problem can be solved even using only the linear programming techniques. All of these results are interesting, but they are not dealing with the parallelism directly, and hence, could not be applied directly to ....

[Article contains additional citation context not shown here]

Li Xuan Dong and Dang Van Hung, Checking Linear Duration Invariants by Linear Programming, Joxan Jaffar and Roland H. C. yap (Eds.), Concurrency and Parallelism, Programming, Networking, and Security LNCS 1179, Springer-Verlag, Dec 1996, pp. 321--332.

....the behaviour of the systems for a time interval, while by the instant properties we mean point properties of the behaviour of the systems for a moment of time. It is no doubt that checking real time systems for a time duration property is much more difficult than for a time instant property. In [4, 5, 9], we have restricted ourselves to a small class of duration properties written as very simple Duration Calculus formulae called Linear Duration Invariants, and considered the problem of checking whether a real time system whose behaviours could be represented by a timed regular expression, ....

....transition system S with a finite index k which is consistent with D then the history safety verification problem for S and D is decidable, and can be solved in linear time in k. 2. 2 Real Time Automata and Linear Duration Invariants Now, we show that the model checking techniques presented in [3, 4, 5] can also fit in this framework. A real time automaton A ( 3] is a special timed automaton which has only one clock and is reset by any transition. A can be considered as a finite transition system RA b = Q; Sigma; Q) where for each q 2 Q, q is of the form q = s; a; b] s is a location ....

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Li Xuan Dong and Dang Van Hung. Checking Linear Duration Invariants by Linear Programming. Research Report 70, UNU/IIST, P.O.Box 3058, Macau, May 1996.

....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 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 ....

Li Xuan Dong and Dang Van Hung. Checking Linear Duration Invariants by Linear Programming. Research Report 70, UNU/IIST, P.O.Box 3058, Macau, May 1996.

....(real time automaton networks of single process) in [3] by using linear programming technique. In that paper, an algorithm was given for reducing the problem to a finite set of very simple linear programming 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 ....

Li Xuan Dong and Dang Van Hung. Checking Linear Duration invariants by Linear Programming. Research Report 70, UNU/IIST, P.O.Box 3058, Macau, May 1996.

....are closely related to DC simple formulas, has been employed earlier under various other conditions as part of model checking algorithms by Dang and Pham[DP97] and Li, Dang and Zheng[LDZ97] The contents of Lemma 1, Lemma 2, and Proposition 2 give a slightly stronger form of Lemma 3. 6 from [LD96]. Iteration can be locally eliminated from a formula , if, for every DC interpretation I and every interval [ 1 ; 2 ] 2 I, there exists a free formula ) Due to the distributivity of conjunction and chop ( over disjunction, simple formulas that have no occurrences of are ....

....decidability of the satisfiability of simple DC and the related work. One of the notions in the literatures that are closed to our notion of simple DC is the notion of Timed Regular Expressions introduced by Asarin et al. in [EPO97] a subset of which has been introduced by us earlier in [LD96]. Each simple DC formula syntactically corresponds exactly to a timed regular expression, and their semantics coincide. Therefore, a simple DC formula can be viewed as a timed regular expression. In [EPO97] it has been proved that from a timed regular expression E one can build a timed ....

[Article contains additional citation context not shown here]

Li Xuan Dong and Dang Van Hung. Checking Linear Duration invariants by Linear Programming. Joxan Jaffar and Roland H. C. Yap (Eds.), Concurrency and Palalellism, Programming, Networking, and Security LNCS 1179, Springer-Verlag, Dec 1996, pp. 321-332.

.... of Lemmas and Theorems 28 From [14] we know that maximum occurs at integer computations (integer timed sequences) we also know that all time transitions are bounded by a deadline, hence there is a finite number of possible values for the time sequences for under Delta. Using a pigeon hole argument there must be a ....

....same situation, there are no deadlines crossing and the delays are satisfied if more iterations are added. Hence, the objective function is a strictly increasing function (remember that f Pi; j 1 ; Delta 00 ) 0 ) that eventually violates the invariant. 2 Report No. 135, 22 April 1998 UNU IIST, P.O. Box 3058, Macau Proofs of Lemmas and Theorems 27 In the case (b) if i (i 3 Gamma i 2 ) i 4 Gamma 1 and last T in oe 0 i Gamma1] i 1 we are analysing a constraint that goes from an iteration instance to another one. Thanks to independence we can argue that the constraint is ....

[Article contains additional citation context not shown here]

Li Xuan Dong and Dang Van Hung. Checking linear duration invariants by linear programming. In Joxan Jaffar and Roland H. C. Yap, editors, Concurrency and Paralellism, Programming, Networking, and Securiry, number 1179 in Lecture Notes on Computer Science, pages 321--332, December 1996.

....P) to currentpath; end; end; end; end; until currentpath = hi; return true. Figure 4: Improved 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 ....

Li Xuandong, Dang Van Hung. Checking Linear Duration Invariants by Linear programming. In Concurrence and Parallelism, Programming, Networking, and Security, LNCS 1179, pp.321-332.

....are closely related to DC simple formulas, has been employed earlier under various other conditions as part of model checking algorithms by Dang and Pham[DP97] and Li, Dang and Zheng[LDZ97] The contents of Lemma 9, Lemma 10, and Proposition 12 give a slightly stronger form of Lemma 3. 6 from [LD96]. Iteration can be locally eliminated from a formula , if, for every DC interpretation I and every interval [ 1 ; 2 ] 2 I, there exists a free formula 0 such that I; 1 ; 2 ] j= 2( 0 ) Due to the distributivity of conjunction and chop ( over disjunction, simple formulas ....

....of the satisfiability of simple DC formulas and the related work. One of the notions in the literatures that are closed to our notion of simple DC is the notion of Timed Regular Expressions introduced by Asarin et al. in [EPO97] a subset of which has been introduced by us earlier in [LD96]. Each simple DC formula syntactically corresponds exactly to a timed regular expression, and their semantics coincide. Therefore, a simple DC formula can be viewed as a timed regular expression. In [EPO97] it has been proved that from a timed regular expression E one can build a timed ....

[Article contains additional citation context not shown here]

Li Xuan Dong and Dang Van Hung. Checking Linear Duration invariants by Linear Programming. Joxan Jaffar and Roland H. C. Yap (Eds.), Concurrency and Palalellism, Programming, Networking, and Security LNCS 1179, Springer-Verlag, Dec 1996, pp. 321-332.

....are closely related to DC simple formulas, has been employed earlier under various other conditions as part of model checking algorithms by Dang and Pham[DP97] and Li, Dang and Zheng[LDZ97] The contents of Lemma 1, Lemma 2, and Proposition 2 give a slightly stronger form of Lemma 3. 6 from [LD96]. Iteration can be locally eliminated from a formula , if, for every DC interpretation I and every interval [ 1 ; 2 ] 2 I, there exists a free formula 0 such that I; 1 ; 2 ] j= 2( 0 ) Due to the distributivity of conjunction and chop ( over disjunction, simple ....

.... Box 3058, Macau Decidability Results for Simple DC and Discussion 15 One of the notions in the literatures that are closed to our notion of simple DC is the notion of Timed Regular Expressions introduced by Asarin et al. in [EPO97] a subset of which has been introduced by us earlier in [LD96]. Each simple DC formula syntactically corresponds exactly to a timed regular expression, and their semantics coincide. Therefore, a simple DC formula can be viewed as a timed regular expression. In [EPO97] it has been proved that from a timed regular expression E one can build a timed ....

[Article contains additional citation context not shown here]

Li Xuan Dong and Dang Van Hung. Checking Linear Duration invariants by Linear Programming. Joxan Jaffar and Roland H. C. Yap (Eds.), Concurrency and Palalellism, Programming, Networking, and Security LNCS 1179, Springer-Verlag, Dec 1996, pp. 321-332.

....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 established. Because of the advantages of the approach of [4] in comparison to the others, in [9] we have generalised it to a subclass of timed automata [5] In this paper, by developing the techniques in [4,9] further, we show that by linear programming techniques the problem can be solved totally for a wellformed subclass of linear hybrid automata. The paper is organised as follows. In the ....

....for a simple class of real time automata using linear programming techniques, which is well established. Because of the advantages of the approach of [4] in comparison to the others, in [9] we have generalised it to a subclass of timed automata [5] In this paper, by developing the techniques in [4,9] further, we show that by linear programming techniques the problem can be solved totally for a wellformed subclass of linear hybrid automata. The paper is organised as follows. In the next section, we introduce the notion of hybrid regular expressions to express the behaviour of hybrid automata. ....

Li Xuandong, Dang Van Hung. Checking Linear Duration Invariants by Linear Programming. In Concurrence and Parallelism, Programming, Networking, and Security, LNCS 1179, pp.321-332.

....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 ....

....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 problem can be solved even using only the linear programming techniques. All of these results are interesting, but they are not dealing with the parallelism directly, and hence, could not be applied directly to ....

[Article contains additional citation context not shown here]

Li Xuan Dong and Dang Van Hung, Checking Linear Duration Invariants by Linear Programming, Joxan Jaffar and Roland H. C. yap (Eds.), Concurrency and Parallelism, Programming, Networking, and Security LNCS 1179, Springer-Verlag, Dec 1996, pp. 321--332.

....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 expressions for real time languages. Some previous linear programming based approaches [8] work for algebraic notations which are less expressive than Timed Automata. In comparison to these approaches, our method is more general: Timed Automata are our starting point and we provide an accurate answer to the problem for a larger (and representative) class of them. Victor Braberman is ....

....Obtaining regular languages through the digitisation of the TA as well as the transformation of the DC formula into a finite state automaton are the main sources of the high complexity. In order to get more practical algorithms there are several proposals based on linear programming techniques (LP)[7, 8]. The common idea is to represent a real time system as a language described by some sort of timed regular expression. They follow the style of classical regular expressions [11] adding some sort of timing constraints (e.g. the minimum and the maximum length of the timed words described by an ....

[Article contains additional citation context not shown here]

Li Xuan Dong and Dang Van Hung. Checking linear duration invariants by linear programming. In Joxan Jaffar and Roland H. C. Yap, editors, Concurrency and Paralellism, Programming, Networking, and Securiry, number 1179 in Lecture Notes on Computer Science, pages 321--332, December 1996.

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Li Xuan Dong and Dang Van Hung. Checking linear duration invariants by linear programming. In Concurrency and Paralellism, Programming, Networking, and Securiry, volume 1179 of LNCS, pages 321--332, December 1996.

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