X.D. Li, H. Dang Van and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. In R. Shyamasundar and K. Ueda, editors, Advances in Computing Science - ASIAN'97, volume 1345 of Lecture Notes in Computer Science, pages 166--180. Springer Verlag, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....given number. Using our technique, we can reduce the problem into several systems of integer linear constraints, which have been well studied, and therefore we can give a polynomial time algothims to solve the problem. There have been several work on model checking for Duration Calculus, such as [8, 15, 12]. But these technique could not be used in this context. A technique for deductive reasoning about the dependability using Probability Duration Calculus has been developed in [5] and [13] which can be considered to be complementary to our work. 2 Model Checking for Probabilistic Real Time ....

....see below. To our experience, linear duration properties form an important class of Duration Calculus formulas in specifying requirements of real time systems, and the problem of checking a realReport time system for a linear duration property has attracted a great deal of attention (see, e.g. [10, 15, 12, 6]) A predicate D of the form (K1) is evaluated to true for a finite sequence of transitions oe iff whenever the length joej (the number of elements) of oe satisfies the premise t 1 joej t 2 , the durations of the state of the process satisfy the inequality q i M . A predicate D of the form ....

X.D. Li, H. Dang Van and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. In R. Shyamasundar and K. Ueda, editors, Advances in Computing Science - ASIAN'97, volume 1345 of Lecture Notes in Computer Science, pages 166--180. Springer Verlag, 1997.

....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, Dang Van Hung, and Zheng Tao, Checking Hybrid Automata for Linear Duration Invariants, UNU/IIST Research Report 109, June 1997.

....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 ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997.

....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, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997.

....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 programming techniques, which are very complicated. In [1] an algorithm has been developed for checking durationbounded reachability which asks whether there is a run ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997.

....The class of simple DC formulas has an interesting property that it is decidable, which means that we can decide if a design is implementable. Furthermore, for some class of DC formulas nonleak leak [0,1] 30, Figure 1: Simple Design of Gas Burner such as linear duration invariants (see [ZZY94, LDZ97, DP97]) the implication from a simple formula to a formula in the class can be checked by a simple algorithm. The paper is organised as follows. In the next section, we give the syntax and semantics of our Duration Calculus with Iteration. In the third section we will give a proof system for the ....

....same expressive power as DC 3 as DC . Elimination of iteration from timed regular expressions, that 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 ....

[Article contains additional citation context not shown here]

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. R.K.Shamasundar, K.Ueda (eds.), Advances in Computing Science, LNCS 1345, Springer-Verlag, 1997, pp.166-180.

.... ; l = 0; ff : ff) Elimination of iteration from timed regular expressions that are closely related to duration calculus, 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 15, Lemma 16, and Proposition 17 give a slightly stronger form of Lemma 3.6 from [LD96] Definition 14 (Dang, Wang) DW94] Consider a language for duration calculus. A formula built from de and formulas of the kinds dSe and dSe l a l b using , is called ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997. Also published in R.K.Shamasundar, K.Ueda (eds.), Advances in Computing Science, LNCS 1345, Springer-Verlag, 1997, pp.166-180.

....examples of hybrid systems use linear inequalities for the specification of transitions or to define the set of initial states. Linear inequalities occur also in approximation techniques of nonlinear hybrid systems [HH95, PBV95] and are also used to verify invariants hybrid regular expressions [XHT97]. Given the linear inequality a T x b (3) with x 2 R n , a 2 R n and b 2 R, the set of solutions K is a half space of R n . The vector a is a normal on the hyper plane which separates K from K c , i.e. a is orthogonal to the hyper plane, and points to the complement of K. An 1 The ....

Li Xuandong, Dang Van Hung, and Zheng Tao. Checking hybrid automata for linear duration invariants. In ASIAN' 97, LNCS 1345, pages 166--180. Springer-Verlag, 1997.

....invariant of a system is much more difficult than checking for a safety written in other real time logics because the satisfaction of a linear duration invariant by a behaviour at time t depends also on its prefixes. There have been several work on model checking for Duration Calculus, such as [8,15,12]. But these technique could not be used in this context. A technique for deductive reasoning about the dependability using Probability Duration Calculus has been developed in [5] and [13] which can be considered to be complementary to our work. For the simplicity, in this paper we consider the ....

....is defined below. To our experience, linear duration properties form an important class of Duration Calculus formulas in specifying requirements of real time systems, and the problem of checking a real time system for a linear duration property has attracted a great deal of attention (see, e.g. [11,15,12,6]) A predicate D of the form (K1) is evaluated to true for a finite sequence of transitions oe iff whenever the length joej (the number of elements) of oe satisfies the premise t 1 joej t 2 , the durations of the states of the process satisfy the inequality P m i=1 c i R q i M . A ....

X.D. Li, H. Dang Van and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. In R. Shyamasundar and K. Ueda, editors, Advances in Computing Science - ASIAN'97, volume 1345 of Lecture Notes in Computer Science, pages 166--180. Springer Verlag, 1997.

....examples of hybrid systems use linear inequalities for the specification of transitions or to define the set of initial states. Linear inequalities occur also in approximation techniques of nonlinear hybrid systems [HH95, PBV95] and are also used to verify invariants hybrid regular expressions [XHT97]. Given the linear inequality a T x b (3) 1 The hybrid automata used in [SMF97] uses on some places strict equalities like . 8 4. TRANSITIONS AND LINEAR INEQUALITIES with x 2 R n , a 2 R n and b 2 R, the set of solutions K is a half space of R n . The vector a is a normal on the ....

Li Xuandong, Dang Van Hung, and Zheng Tao. Checking hybrid automata for linear duration invariants. In ASIAN' 97, LNCS 1345, pages 166--180. Springer-Verlag, 1997.

.... elimination of iteration from simple DC formulas Elimination of iteration from timed regular expressions that are closely related to duration calculus, 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 15, Lemma 16, and Proposition 17 give a slightly stronger form of Lemma 3.6 from [LD96] Definition 14 (Dang, Wang) DW94] Consider a language for duration calculus. A formula built from de and formulas of the kinds dSe and dSe l a l b using , and is ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997. Also published in R.K.Shamasundar, K.Ueda (eds.), Advances in Computing Science, LNCS 1345, Springer-Verlag, 1997, pp.166-180.

....states at a given time intervel with a probability not less then a given number. Using our technique, we can reduce the problem into a finite number of systems of integer linear constraints, which have been well studied. There have been several work on model checking for Duration Calculus, such as [8, 15, 12]. But these technique could not be used in this context. A technique for deductive reasoning about the dependability using Probability Duration Calculus has been developed in [5] and [13] which can be considered as a complementary to our work. Report No. 155, February 1999 UNU IIST, P.O. Box 3058, ....

.... reference interval) To our experience, linear duration properties form an important class of Duration Calculus formulas in specifying requirements of real time systems, and the problem of checking a realtime system for a linear duration property has attracted a geat deal of attention (see, e.g. [10, 15, 12, 6]) A predicate D of the form K1 is evaluated to true for a finite sequence of transitions oe iff whenever the length joej (the number of elements) of oe satisfies the premise t 1 joej t 2 , the durations of the state of the process satisfy the inequality P m i=1 c i R q i M . A predicate D ....

X.D. Li, H. Dang Van and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. In R. Shyamasundar and K. Ueda, editors, Advances in Computing Science - ASIAN'97, volume 1345 of Lecture Notes in Computer Science, pages 166--180. Springer Verlag, 1997.

....finite set of very simple linear programming problems. This technique has been generalised for verifying a subset of timed automata in [6] and for verifying a parallel composition of real time automata in [12] This technique has also been generalised for verifying a subset of hybrid automata in [7]. 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 programming techniques, which are very complicated. In [1] an algorithm has been developed for checking duration bounded reachability which asks whether there is a run ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997. Published in R.K.Shamasundar, K.Ueda (Eds.), Advances in Computing Science, Lecture Notes in Computer Science 1345, Springer-Verlag, pp.166-180.

....= 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 problem can be solved by using an integer time verification ....

Li Xuandong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. In Advances in Computing Science - ASIAN'97, LNCS 1345, pp.166-1180.

....high complexity. In order to make the problem easier, many authors have limited the problem to the cases for a restricted class of systems and a restricted class of real time requirements. For the class of requirements written as linear duration invariants, the problem has been considered in [2, 3, 4, 8, 7, 1]. In [2] real time systems are taken to be real time automata, while real time requirements are taken to be linear duration invariants, and the satisfaction problem is then translated into a family of linear programming problems. The authors have given an algorithm for reducing an infinite ....

....are taken to be linear duration invariants, and the satisfaction problem is then translated into a family of linear programming problems. The authors have given an algorithm for reducing an infinite family of linear programming problems to an equivalent one with only finite members. In [4], the authors considered the problem of checking hybrid systems modelled by hybrid automata for the requirements of above mentioned class. They have extended the traditional regular expressions with time constraints to form the so called hybrid regular expressions which is used as a language to ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997. Published in R.K.Shamasundar, K.Ueda (Eds.), Advances in Computing Science, Lecture Notes in Computer Science 1345, Springer-Verlag 1997, pp. 166-180.

....nonleak leak [0,1] 30, Fig. 1. Simple Design of Gas Burner The class of simple DC formulas has an interesting property that it is decidable, which means that we can decide if a design is implementable. Furthermore, for some class of DC formulas such as linear duration invariants (see [ZZY94,LDZ97,DP97]) the implication from a simple DC formula to a formula in the class can be checked by a simple algorithm. The paper is organised as follows. In the next section, we give the syntax and semantics of our Duration Calculus with Iteration. In the third section we will give a proof system for the ....

.... of iteration from simple DC formulas Elimination of iteration from timed regular expressions, that 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 ] ....

[Article contains additional citation context not shown here]

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. R.K.Shamasundar, K.Ueda (eds.), Advances in Computing Science, LNCS 1345, Springer-Verlag, 1997, pp.166-180.

....means that we can decide if a design is implementable. Furthermore, for some class of DC formulas Report No. 163, April 1999 UNU IIST, P.O. Box 3058, Macau Duration Calculus with Iteration 2 nonleak leak [0,1] 30, Figure 1: Simple Design of Gas Burner such as linear duration invariants (see [ZZY94, LDZ97, DP97]) the implication from a simple DC formula to a formula in the class can be checked by a simple algorithm. The paper is organised as follows. In the next section, we give the syntax and semantics of our Duration Calculus with Iteration. In the third section we will give a proof system for the ....

.... of iteration from simple DC formulas Elimination of iteration from timed regular expressions, that 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 ] ....

[Article contains additional citation context not shown here]

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. R.K.Shamasundar, K.Ueda (eds.), Advances in Computing Science, LNCS 1345, Springer-Verlag, 1997, pp.166-180.

....; where p = bb=m (R)c 1 : ut Lemma 8. Let R be a nonzero simple HRE. Then L(C( Phi p j=0 R j ) L(C(R ) where p = b (C(X) m (R)c 1 : ut These lemmas are either obvious or can be proved easily from Definitions 1,2 and 3. For the details of their proofs, readers are referred to [10]. From these lemmas, we can prove the following theorems. Theorem 1. Let R and R 0 be HREs. If L(R 0 ) L(R) then C(R) j= D iff C(R 0 ) j= D : Proof. The claim follows immediately from Lemma 3. ut Theorem 2. Let R 1 and R 2 be HREs. Then C( R 1 Phi R 2 ) j= D iff C( R 1 ) R ....

Li Xuandong, Dang Van Hung, and Zheng Tao. Checking Hybrid automata for Linear Duration Invariants. Research report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997. This article was processed using the L A T E X macro package with LLNCS style

....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, Dang Van Hung, and Zheng Tao, Checking Hybrid Automata for Linear Duration Invariants, UNU/IIST Research Report 109, June 1997.

.... the timed automata are real time automata [1] or in more general, are represented by a so called timed regular expressions [2] The technique has been generalised for verifying linear duration invariants of the parallel composition of real time automata in [6] and of a class of hybrid automata in [3]. In [4] we proposed a verification algorithm for checking a parallel composition of real time automata w.r.t. a linear duration property by using the state exploration technique. In that paper, we introduced the compatibility relation between configurations to avoid exhaustive stateexploration. ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997. Published in R.K.Shamasundar, K.Ueda (Eds.), Advances in Computing Science, Lecture Notes in Computer Science 1345, Springer-Verlag, pp.166-180.

....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 programming techniques, which are very complicated. In [1] an algorithm has been developed for checking durationbounded reachability which asks whether there is a run ....

Li Xuan Dong, Dang Van Hung, and Zheng Tao. Checking Hybrid Automata for Linear Duration Invariants. Research Report 109, UNU/IIST, P.O.Box 3058, Macau, June 1997. Acepted to present at ASIAN'97, Asian Computing Science Conference, Kathmandu, Nepal, December 9--12, 1997, to apear in LNCS.

No context found.

X. Li, D. Van Hung, and Z. Tao. Checking hybrid automata for linear duration invariants. In Advances in Computing Science, volume 1345. Lect. Notes in Comp. Sci., 1997.

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