Emerson, E. A., A. K. Mok, A. P. Sistla and J. Srinivasan, Quantitative temporal reasoning, in: Proceedings of the 2nd International Workshop on Computer Aided Verification (1991), pp. 136--145.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....139.2 T2 141 140.7 140.5 140.4 140.2 140.1 139.9 139.8 139.6 139.5 139.3 139.2 139 138.9 y1 0 0 0 0 0 0 0 1 30 2 30 3 30 4 30 5 30 6 30 8 30 y2 0 0 0 0 0 0 0 0 0 1 30 2 30 3 30 4 30 5 30 Table 1. Counterexample Using not only invariant conditions but RTCTL (Real Time Computational Tree Logic [7]) expression one can check the trajectory on which the system proceed. For example, starting from the lowest possible temperatures (t 1 = 138 and t 2 = 138) the formula AF (AG (T1 =10 T1 =60 T2 =10 T2 =30) is true if the system gets back to stable state for sure and remains there forever. ....

E.A. Emerson, A.K. Mok, A.P. Sistla, and J. Srinivasan. Quantitative Temporal Reasoning. Journal of Real Time Systems, 4:331--352, 1992.

....on variables are su#cient. An undecidability result holds for these logics if dense time domain is assumed ( 16] 14] and [17] There are algorithms for simple cases (where decidability holds) which visit the graph of regions, where regions encapsulate infinite evaluations ( 8] 16] and [35]) A di#erent way to obtain decidability is to relax punctuality, i.e. it is not permitted to consider singleton intervals (see [15] and [67] Also for the mentioned logics, symbolic model checking methods ( 16] and [8] are proposed. In order to make checking easier, di#erent abstractions are ....

Emerson, E. A., Mok, A. K., Sistla, A. P., Srinivasan, J.: Quantitative Temporal Reasoning. Lecture Notes in Computer Science 531, Springer, Berlin, 1995, 136--145.

....approach considers time as a variable growing continuously and uniformly in the domain of positive real numbers. Temporal logics, which consider explicitly time, constitute a new research area of increasing interest. For temporal logics based on either discrete time or fictitious clock models see [AH94, EMSS90, JM86, Koy90, Ost90, PH88]. The dense time model has been considered in [ACD93, AFH96, AH91, AH93, LN98, LN, PH88] A well known timed temporal logic that uses a dense time model is TCTL (see [ACD93] Model checking is decidable in TCTL, but the satisfiability problem is undecidable. A branching real time temporal logic ....

....continuously over the domain of positive reals) but usually requires more efforts to obtain tools that can be effectively used. Temporal logics which consider explicitly the time constitute a new research area of increasing interest. Temporal logics based on discrete time models are treated in [AH94, EMSS90, JM86, Ost90, PH88]. Dense time models are considered in [ACD93, AFH96, AH91, AH93, LN98, LN, PH88] 68 In this chapter we introduce a new branching time temporal logic (STCTL) whose semantics is based upon timed w trees [LN, LN98] Branching time logics are more suitable than linear ones for reasoning about ....

[Article contains additional citation context not shown here]

E.A. Emerson, A.K. Mok, A.P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. In Proceedings of the 2nd International Conference on Computer Aided Verification, LNCS 531, pages 136-145. Springer-Verlag, 1990.

....139.2 T2 141 140.7 140.5 140.4 140.2 140.1 139.9 139.8 139.6 139.5 139.3 139.2 139 138.9 y1 0 0 0 0 0 0 0 1 30 2 30 3 30 4 30 5 30 6 30 8 30 y2 0 0 0 0 0 0 0 0 0 1 30 2 30 3 30 4 30 5 30 Table 1. Counterexample Using not only invariant conditions but RTCTL (Real Time Computational Tree Logic [7]) expression one can check the trajectory on which the system proceed. For example, starting from the lowest possible temperatures (t 1 = 138 and t 2 = 138) the formula AF (AG (T1 =10 T1 =60 T2 =10 T2 =30) is true if the system gets back to stable state for sure and remains there forever. ....

E.A. Emerson, A.K. Mok, A.P. Sistla, and J. Srinivasan. Quantitative Temporal Reasoning. Journal of Real Time Systems, 4:331-352, 1992.

....properties are fundamental for the correctness of realtime systems, a number of real time extensions of temporal and modal logics have been proposed over the past few years. There are three main approaches for extending both linear time and branching time temporal logics. ffl Bounded operators [31, 3, 8, 6, 63, 76] The idea is of replacing the classical temporal operators by time bounded operators. The operator 3 [2;4] is interpreted as eventually within 2 and 4 units of time. For instance, the bounded response property is expressed by the formula A2(p oe A3 [0;3] q) in a branching time framework. ffl ....

....and timing constraints for relating the times of different states. Since we are dealing with synchronous languages, we assume next time to be equal to next state. The logic permits to express properties such as bounded invariance, bounded response, and so on. Actually, the discrete logic RTCTL [31, 29] is trivially subsumed by RTL . We propose a proof system for local model checking RTL . It checks whether a set of timed states of a discrete timed graph satisfies an RTL formula. Judgments of the proof system are of the form s; A, where s is a state of the timed graph, is a clock ....

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E.A. Emerson, A.K. Mok, A.P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. In First Annual Workshop on Computer-Aided Verification, 1989.

....this enables checking of some time related properties. In [8] we show that the reduction preserved all properties expressed in the temporal logic RTCTL , a logic obtained from CTL [11] by the addition of time bounded operators, in the same way as the temporal logic RTCTL was obtained from CTL in [13]. Consequently, queries expressible in this logic can be answered from the condensed state space. Time : 0 0 Idle: a [0] b [0] Mutex: e [0] 1 Time : 0 1 Idle: b [0] Running: a [1] 2 Time : 0 1 Idle: a [0] Running: b [1] 3 Time : 1 3 Idle: a [2] b [0] Mutex: e [3] 4 Time : 1 3 ....

E.A. Emerson, A.K. Mok, A.P Sistla, and J. Srinivasan, Quantitative Temporal Reasoning, Proceedings of CAV'90, Lecture Notes in Computer Science, vol. 531, Springer-Verlag, 1990, pp. 136{ 145.

....families of timed models, for which polynomialtime model checking is possible. Usually, these are based on classical, discrete, Kripke structures (KS) Here there is no inherent concept of time (contrary to clocks in Timed Automata) and the elapsing of time is encoded by events. For example, in [EMSS92] each transition of a KS is viewed as taking exactly one time unit, and in [LST00] a tick proposition labels states where the clock is incremented. This framework is less expressive than Timed Automata, but it is conceptually simpler, it allows ecient model checking algorithms, and is 2 F. ....

....while TCTL ; is the fragment of TCTL where the = c constraints are forbidden. Other classical temporal logics can be extended in the same way, and we call TCTL , TLTL ; etc. the resulting formalisms. Model checking TCTL over Kripke structures can be done in time 1 O(jSj 3 j j) [EMSS92]. This is in sharp contrast with model checking over Timed Automata (PSPACE complete [ACD93] and with model checking CTL extended by freeze variables (PSPACE complete over KSs [LST00] Thus it appears that polynomial time model checking of timed properties is possible if one picks the right ....

[Article contains additional citation context not shown here]

E. A. Emerson, A. K. Mok, A. P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. Real-Time Systems, 4(4):331-352, 1992.

.... HNSY92] However, only few proof algorithms have been proposed which are suited for efficient implementations, comparable to state of the art model checkers like SMV [McMi93a] Defining quantitative temporal operators by keeping the standard CTL unit delay structures has been done previously [EMSS92a]. However, the critical part for real time model checking is the support of timed transition graph structures. In usual model checkers, the temporal structures are symbolically treated by storing the Boolean transition relation efficiently using BDDs [Brya86] If time has to be considered in the ....

E.A. Emerson, A.K. Mok, A.P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. Journal of Real Time Systems, pages 331--352, 1992.

....[HP85] Qualitative temporal logics, PLTL [Pn77] and CTL [CE81] for example, express properties of the temporal ordering of events without, in general, a regard for any quantitative measure on the elapsed time between the occurrences of the events. Real time temporal logics ( JM86] AH89] ACD90] [EMSS92]) and more generally quantitative logics ( BEH95] BEH95a] BBEL96] ET97] c.f. CCMMH94] cater for the expression of quantitative bounds on the occurrence of events. Such logics allow operators of the form AF P meaning that inevitably event P will occur within five time steps. The use of ....

....s j= Q n x n : Q 0 x 0 f(x 0 ; x n ; a) iff for all a 2 N M; s j= Q n x n jSj : Q 0 x 0 jSjf(x 0 ; x n ; a) This formula can be interpreted as a short hand for a set of formulae where the quantifiers are replaced by and . For any (a n ; a 0 ) 2 jSj it was shown [EMSS92] that for any a jSj, M; s j= f(a 0 ; a n ; a) iff M; s j= f(a 0 ; a n ; jSj) So for all a 2 N M; s j= Q n x n jSj : Q 0 x 0 jSjf(x 0 ; x n ; a) iff M; s j= 8x n 1 jSjQ n x n jSj : Q 0 x 0 jSjf(x 0 ; x n ; x n 1 ) M; s j= 9x n 1 Q n x n : Q 0 x 0 ....

[Article contains additional citation context not shown here]

Emerson, E. A., Mok, A. K., Sistla, A. P., and Srinivasan, J., Quantitative Temporal Reasoning. In CAV 90: Computer-aided Verification. E. M. Clarke and R.P. Kurshan Eds. Lecture Notes in Computer Science, vol. 531. Springer-Verlag, New York, pp. 136-145, 1990; journal version appears in Journal of Real Time Systems, vol. 4, pp. 331-352, 1992.

....systems [16] Qualitative temporal logics, PLTL [18] and CTL [10] for example, express properties of the temporal ordering of events without, in general, a regard for any quantitative measure on the elapsed time between the occurrences of the events. Real time temporal logics ( 17] 5] 2] 13] [14]) and more generally quantitative logics ( 7] 8] 6] 15] c.f. 9] cater for the expression of quantitative bounds on the occurrence of events. Such logics allow operators of the form AF 5 P meaning that inevitably event P will occur within five time steps. The use of constants, 5 in this ....

....2 N, M; s j= Qnxn : Q 0 x 0 f(x 0 ; xn ; a) iff for all a 2 N M; s j= Qnxn jSj : Q 0 x 0 jSjf(x 0 ; xn ; a) This formula can be interpreted as a short hand for a set of formulae where the quantifiers are replaced by and . For all (a 0 ; an ) 2 jSj n 1 it was shown [14] that for all a jSj, M; s j= f(a 0 ; an ; a) iff M; s j= f(a 0 ; an ; jSj) So, for all a 2 N M; s j= Qnxn jSj : Q 0 x 0 jSjf(x 0 ; xn ; a) iff M; s j= 8xn 1 jSjQn xn jSj : Q 0 x 0 jSjf(x 0 ; xn ; xn 1 ) M; s j= 9xn 1Qnxn : Q 0 x 0 f(x 0 ; xn ; ....

[Article contains additional citation context not shown here]

E. A. Emerson, A. K. Mok, A. P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. In E. M. Clarke and R. Kurshan, editors, CAV90: Computeraided Verification, pages 136--145. Springer-Verlag,

No context found.

Emerson, E. A., A. K. Mok, A. P. Sistla and J. Srinivasan, Quantitative temporal reasoning, in: Proceedings of the 2nd International Workshop on Computer Aided Verification (1991), pp. 136--145.

No context found.

Emerson, Mok, Sistla, and Srinivasan. Quantitative temporal reasoning. In Journal of Real Time System, pages 331352, 1992.

No context found.

E.A.Emerson, A.K.Mok, A.P.Sistla, J.Srinivasan, "Quantitative Temporal Reasoning," Proc. of the Workshop on Computer Aided Verification Methods for Finite State Systems, Grenoble, France, 1989.

No context found.

E. Allen Emerson, A. K. Mok, A. Prasad Sistla, and Jai Srinivasan. Quantitative temporal reasoning. In Edmund M. Clarke and Robert P. Kurshan, editors, Proceedings of Computer-Aided Verification (CAV '90), volume 531 of LNCS, pages 136--145, Berlin, Germany, June 1991. Springer.

No context found.

E A Emerson, A K Mok, A P Sistla, and J Srinivasan. Quantitative temporal reasoning. Real-Time Systems, 4(4):331--352, December 1992.

No context found.

E. A. Emerson, A. K.-L. Mok, A. P. Sistla, and J. Srinivasan. Quantitative Temporal Reasoning. Real-Time Systems, 4, pages 331--352, Kluwer Academic, 1992.

No context found.

E A Emerson, A K Mok, A P Sistla, and J Srinivasan. Quantitative temporal reasoning. Real-Time Systems, 4(4):331--352, December 1992.

No context found.

E. Emerson, A. Mok, A. Sistla, and J. Srinivasan. Quantitative Temporal Reasoning. Journal of Real-Time Systems, 4(4):331--352, 1992.

No context found.

E. Emerson, A. Mok, A. Sistla, and J. Srinivasan. Quantitative Temporal Reasoning. Journal of Real-Time Systems, 4(4):331--352, 1992.

No context found.

E. A. Emerson, A. K. Mok, A. P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. Real-Time Systems, 4(4):331352, 1992.

No context found.

E. A. Emerson, A. K. Mok, A. P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. Real-Time Systems, 4(4):331--352, 1992.

No context found.

E. Allen Emerson, A. K. Mok, A. Prasad Sistla, and Jai Srinivasan. Quantitative temporal reasoning. In Edmund M. Clarke and Robert P. Kurshan, editors, Proceedings of Computer-Aided Verification (CAV '90), volume 531 of LNCS, pages 136--145, Berlin, Germany, June 1991. Springer.

No context found.

E. Emerson, A. Mok, A. Sistla, and J. Srinivasan. Quantitative Temporal Reasoning. Journal of Real-Time Systems, 4(4):331--352, 1992.

No context found.

E.A. Emerson, A.K. Mok, A.P. Sistla, and J. Srinivasan. Quantitative temporal reasoning. In Proc. 2nd Workshop on Computer Aided Verification, volume 531 of Lecture Notes in Computer Science, pages 136--145. Springer-Verlag, 1990.

No context found.

E.A. Emerson, A. Mok, A.P. Sistla, and J. Srinivasan. Quantitative Temporal Reasoning. In 1st Workshop on Computer Aided Verification. 1989.

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