A. Pnueli and E. Harel. Applications of temporal logic to the specification of realtime systems. In M. Joseph, editor, Formal Techniques in Real-Time and FaultTolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. SpringerVerlag, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 ....

....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 with a decidable satisfiability problem is STCT [LN98, LN] It differs from TCTL ....

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A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In Formal Techniques in Real-time and Fault-tolerant Systems, LNCS 331, pages 84-98. Springer-Verlag, 1988.

....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 ....

....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 Explicit clock [76, 38] In this approach no new temporal operators are introduced but one state variable T representing the current time is used. With this understanding, the requirement of bounded response is expressed as A2( p x = T oe A3[q T x 3] ffl Freeze quantification [7, 40, 2, 41] A quantifier x: is ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In Formal Techniques in Real-time and Fault-tolerant Systems, volume 331 of Lecture Notes in Computer Science, pages 84--98. SpringerVerlag, Berlin, 1988.

....requires two changes: the underlying temporal structure has to be extended to timed transition graphs, where transitions with arbitrary delay can be modeled, and the logic has to be augmented by quantitative temporal operators. Recently these real time logics have found considerable attention [PnHa88, AlHe89, Koym90, Ostr90, AlCD91, 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] ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real time systems. In M. Joseph, editor, Formal Techniques in Real Time and Fault Tolerant Systems: Proceedings of a Symposium, volume 331 of Lecture Notes in Computer Science, pages 84--98, New York, 1988. Springer-Verlag.

....time size graph autom trans states timers LOGIN 0.01s 0.01s 6 4 2 CSMA CD 0.11s 0.33s 380 185 4 BITALT 0.06s 0.28s 461 187 4 CONTROLLER 0.61s 0.36s 453 124 3 Table 1: Performance results. 5 Verification Many logics have been proposed for specifying real time properties, for instance [JM87, PH88, AH89, Koy89, Ost90, ACD90, Alu91, HNSY92]. We consider the real time temporal logic TCTL, an extension of CTL where temporal operators have subscripts that limit their scope in time [ACD90] CTL [EC81, CES86] is a branching time temporal logic which proposes two binary temporal operators 9U and 8U , corresponding to reachability ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In Formal Techniques in Real-time and Fault-tolerant Systems, pages 84--98, Lecture Notes in Computer Science 331, Springer-Verlag, 1988.

....why researchers have been looking for languages that are interpreted over state structures in which a time is associated with every state. The obvious solution is to employ a first order temporal logic, with a state variable T that represents, in every state, the current value of the time (e.g. [PH88], Os89] the real time response property stated above can then be written as 28x: p x = T ) 3(q T x 5) where the rigid variable x is used to record the time of any request p. We have argued that this upgrade from a propositional logic to its full first order version may be both ....

A. Pnueli, E. Harel, "Applications of temporal logic to the specification of real-time systems, " Formal Techniques in Real-time and Fault-tolerant Systems, Springer LNCS 331, 1988. 25

....it is decidable for the deterministic ones. As an application of the introduced theory, we give a new branching time temporal logic (STCTL) whose semantics is based upon timed trees. Temporal logics which consider explicitly the time constitute a new research area of increasing interest. See [13, 15, 19] for temporal logics based on either discrete time or fictitious clock models. A timed temporal logic that uses a dense time model is TCTL (see [1] TCTL presents an undecidable satisfiability problem even if the structures are restricted to dense trees obtained from timed graphs (finite ....

....by means of which the semantics is defined and for the lack of the equality in the timing constraints. A decidable linear time logic with dense time model is MITL in [3] For specifying real time systems, the Global Clock Temporal Logic (GCTL) with a dense time domain, is also introduced in [19]. For more about real time logics, see also [4, 14] Here the main result is the decidability of the satisfiability problem which follows from the decidability of the emptiness problem for finite automata on timed trees. Introducing the equalities in the timing constraints causes the lost of the ....

A. Pnueli, E. Harel, "Applications of Temporal Logic to the Specification of Real Time Systems", Formal Techniques in Real-time and Fault-tolerant Systems, Lecture Notes in Computer Science, Vol. 331 (Springer-Verlag, 1988) 84 - 98.

....and then we want to check that some hard real time constraints are satisfied. Besides the usual classification in linear and branching time logics, real time logics are classified 1 according to the nature of the time model they use. Temporal logics based on discrete time models are presented in [EMSS90, JM86, Koy90, PH88]. An alternative approach is to model time as a dense domain. Temporal logics with this time model are Mitl [AFH96] Tctl [ACD93] Stctl [LN97] and Gctl [PH88] For more about real time logics, see [AH93, Hen98] In this paper we are interested in branching time temporal logics which use a dense ....

....1 according to the nature of the time model they use. Temporal logics based on discrete time models are presented in [EMSS90, JM86, Koy90, PH88] An alternative approach is to model time as a dense domain. Temporal logics with this time model are Mitl [AFH96] Tctl [ACD93] Stctl [LN97] and Gctl [PH88]. For more about real time logics, see [AH93, Hen98] In this paper we are interested in branching time temporal logics which use a dense time domain and in particular we will consider the satisfiability problem in Tctl. Given a formula we want to determine if there exists a structure M ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In Formal Techniques in Real-time and Fault-tolerant Systems, LNCS 331, pages 84 -- 98. Springer-Verlag, 1988.

.... presented above is similar in spirit although not in the chosen formalism to work by Leveson [40, 34] and Parnas [64] The Duration Calculus builds on Moszkowski s interval temporal logic [53, 54, 75] Time may also be handled explicitly as in TLA [38, 39] or within a conventional temporal logic [36, 65, 30]. In a proof assistant, model checking [20, 7] might be very useful. The refinement approach outlined above is inspired by the hierarchical state machines of Harel [23] Designs can also be subjected to reliability analysis [79] 3 Architecture and Programs The formalisms of duration calculus, ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems (extended abstract). In M. Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 331 of LNCS, pages 84--98. Springer, 1988.

.... associating lower and upper bounds on enabled transitions [Lam77, BH81] or by introducing explicit clocks [AD90, AL92] The first approach has led to the extensions to LTL with bounded operators [KVdR83, Koy89, AH90] and the second has advocated the use of LTL in dealing with the explicit clocks [PdR82, PH88, AL92]. The relationship between the two approaches, that more or less one can be translated into another, is investigated in [HMP94] An advantage of TTS frameworks is that they are quite close to implementations using digital hardware and thus reflect semantics of programming languages. Another ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. Springer-Verlag, 1988.

.... introduced into transition systems either by associating lower and upper bounds on enabled transitions [Lam77] or by introducing explicit clocks [AD90, AL92] The first approach has led to extensions of LTL with bounded operators [Koy89, AH90] and the second has used LTL with the explicit clocks [PH88, AL92]. The relationship between the two approaches, that more or less one can be translated into another, is investigated in [HMP94] An advantage of the LTL frameworks is that transition systems are quite close to an implementation using digital hardware and thus reflect semantics of programming ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. Springer-Verlag, 1988.

....on their behavior are always met. Examples are flight control systems and many process control systems. Methods for reasoning about such hard deadlines can be obtained by adding time to existing methods. One can add time as an explicit (virtual) variable, and use standard verification techniques [PH88, SL87, OW87]. Logics that deal explicitly with time quantities have been designed [BH81, JM86, KVdR83, EMSS89] For some systems, one is interested in the overall average performance, such as throughput, average response times, etc. Methods for analyzing such properties usually employ Markov analysis. Often ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor, Proc. Symp. on Formal Techniques in Real-Time and FaultTolerant Systems, pages 84--98. Springer Verlag, 1988. LNCS 331.

.... specification of timing properties has been advocated by Koymans, Vytopil, and de Roever [KVdR83, KdR85, Koy90] although an early proposal by Bernstein and Harter can be viewed as a precursor [BH81] More applications of the boundedoperator method for expressing timing constraints can be found in [SPE84, Har88, PH88, HW89, Lew90]. Bounded operators have been analyzed for their expressiveness and complexity in [EMSS89, ACD90, AH90, AFH91] To be concrete, let us define a propositional linear time logic that employs time bounded temporal operators. The formulas of this bounded operator logic are built from atomic ....

....specified by the formula 8x: 2( p T = x) 3(q T x 3) Here, the global variable x is bound to the time of every state in which p is observed. We refer to the use of a clock variable as the explicit clock notation. Examples of this method for expressing timing constraints can be found in [PdR82, Ron84, Har88, PH88, Ost90, LA]; it has been studied for its expressiveness and complexity in [AH90, HLP90] Let us once again define a propositional linear time logic with an interval based strictly monotonic real time semantics. As before, let V be a set of (global) time variables, and let Pi(V [fTg) be a set of timing ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of realtime systems. In M. Joseph, editor, Formal Techniques in Real-time and Fault-tolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. Springer-Verlag, 1988.

.... of validating systemlevel error recovery must take into account both precedence constraints (the order in which commands occur) and timing constraints (the time between commands) These two types of constraints are fundamentally different in that precedence does not require a notion of duration [16]. Consequently, the tools that currently exist to model precedence constraints tend to ignore timing requirements and to be inadequate for modeling the timing constraints on spacecraft [6, 12, 15] On the other hand, many techniques that are currently available to model timing constraints tend to ....

.... aspects of a system specification to establish timing properties (periodic events and deadlines) 8] Various extensions to temporal logic and temporal logic model checking have been developed to formally describe timing requirements and to verify automatically that the system satisfies them [16, 3]. These methods provide a good basis for specifying timing requirements but are either more ambitious (in that they model states) or less expressive (in that they only model a subset of timing constraints) than is needed for the spacecraft. The work described here discusses many of the same timing ....

Pnueli, Amir, and Eyal Harel. "Applications of Temporal Logic to the Specifications of Real Time Systems."Formal Techniques in Real-Time and Fault-Tolerant Systems. Ed. M. Joseph. Berlin: Springer-Verlag, 1988, pp. 84-98.

....the basis of specification languages such as TRIO [12] Albert [8, 11] They use real numbers for time, which has advantages for specification and compositionality. Several syntaxes are possible to deal with real time: freeze quantification [4, 13] explicit clocks in a firstorder temporal logic [19] and time bounded operators [15, 16] studied here. The propositional fragment of these logics (MetricTL R ) is undecidable, but becomes decidable with mild restrictions (MetricIntervalTL[3] allowing automatic reasoning, animation, and verification of programs using automata based techniques. ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor, Formal Techniques in Real-time and Fault-tolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. Springer-Verlag, 1988.

....a dynamic state variable T the clock variable and first order quantification for global variables over the time domain. The clock variable T assumes, in each state, the value of the corresponding time. Examples of using this method for expressing timing constraints can be found in e.g. [17, 18]. 3 The Language of LSCs In this section we go briefly through the elements and constructs of LSCs that we use in our work. For more details of the original language and the extensions we made, the reader is referred to [10] and [12] respectively. We illustrate the LSC elements we use by the ....

A. Pnueli and E. Harel, "Applications of temporal logic to the specification of real-time systems", In Formal Techniques in Real-Time and Fault-tolerant Systems, (M. Joseph, ed.), Lecture Notes in Computer Science, Vol. 331, pp. 84--98. Springer-Verlag, 1988.

.... an sequence of state changes, more refined models are necessary to study continuous processes [21] Despite (or, often, because of) these limitations, discrete trace models have been used successfully for the analysis of a wide variety of real time systems and phenomena that arise in practice [1, 3, 15, 17, 20, 23, 25, 27]. Discrete trace models differ significantly in the kinds of systems and phenomena they can capture adequately [5] These differences are caused by different models of time. We distinguish between analog clock models, which record the precise real numbered time of every snapshot (using a ....

.... [1, 3, 4] In comparison, containment of integraltime properties can be tested for transition system based, automata based, and temporal logic based languages [3, 4, 5, 12] This is why many researchers have sacrificed the density of time and given their languages digital clock interpretations [11, 14, 17, 24, 25, 27]. We follow the same path, but rather than being content with solving the simpler integral time verification problem, we would like to employ integer time techniques to solve the original dense time verification problem (or some approximation thereof) Our aim is to interpret real time systems ....

Pnueli, A., and Harel, E. Applications of temporal logic to the specification of real-time systems. In Formal Techniques in Real-time and Fault-tolerant Systems, M. Joseph, Ed., Lecture Notes in Computer Science 331. Springer-Verlag, 1988, pp. 84--98. 17

....at situation hs i ; t i i is always t i , the current value of the clock variable T . Consequently, we allow formulas in TL Gamma to refer explicitly to the clock variable T . In this respect, TL Gamma can be viewed as an extension of the Explicit Clock Temporal Logic considered, for example, in [PH88], HLP90] and [Ost90] 11 Referring to the clock T , we can specify the bounded response property by the formula p T = t 0 = 3 (q T t 0 d) An assertion that may refer to the clock variable T or contain age expressions of the form Gamma( where is an assertion, is called a timed ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real time systems. In M. Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 331 of Lect. Notes in Comp. Sci., pages 84--98. Springer-Verlag, 1988.

....variable now) as the current time. We refer to this approach as the explicit clock approach, because the only new element is the ability to refer explicitly to the clock. Scattered examples of this method of expressing timing properties have been presented in [PdR82] in [Ron84] and in [Har88, PH88] A more systematic exposition of this approach and its applications can be found in [Ost90] where the explicit clock language is called Real time Temporal Logic, and in [LA92] Explicit clock temporal logics have been analyzed for their complexity and expressiveness in [AH90] and in [HLP90] To ....

....of transition systems ( Kel76, Pnu77] We generalize this model by imposing timing constraints on the transitions and show that the timing constraints can be interpreted operationally. Similar state transition formalisms with minimal and maximal delays on the transitions have been defined in [PH88] in [Ost90] and in [LA90, MMT91] 2.1 Transition systems A transition system is a set of states together with a set of transitions (actions) that transform states. In this paper, we will be concerned with a concrete notion of state that provides values for a certain set of variables. Hence we ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of realtime systems. In M. Joseph, editor, Formal Techniques in Real-time and Fault-tolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. Springer-Verlag, 1988.

....To specify properties of hybrid systems, we use the language of temporal logic, as presented in [MP91b] with the extension that state formulas (assertions) may refer to the variable T representing the real time clock. This logic has been considered under the name Explicit Clock Temporal Logic in [PH88], HLP90] and [Ost90] However, since it is always possible to introduce a continuous variable z with the activity z = 1, leading to the fact that always z = T , one may argue that, under the hybrid context, this is no extension at all. There have been several proposals for more radical ....

A. Pnueli and E. Harel. Applications of temporal logic to the specification of real time systems. In M. Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 331 of Lect. Notes in Comp. Sci., pages 84--98. Springer-Verlag, 1988.

....variable t) as the current time at each state. We refer to this approach as the explicit clock approach, because the only new element is the ability to refer explicitly to the clock. Scattered examples of this method to express timing properties are presented in [PdR82] Ro84] and in [Ha88] [PH88], where it is referred to as GCTL. A more systematic exposition of this logic and its applications can be found in [Os90] where it is called RTTL. To compare the two approaches, consider the requirement of a timed response of q to p within at most 3 time units. In the bounded operator approach, ....

A. Pnueli, E. Harel, "Applications of temporal logic to the specification of real-time systems, " Formal Techniques in Real-time and Fault-tolerant Systems, Springer LNCS 331, 1988.

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A. Pnueli and E. Harel. Applications of temporal logic to the specification of realtime systems. In M. Joseph, editor, Formal Techniques in Real-Time and FaultTolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. SpringerVerlag, 1988.

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A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. Springer-Verlag, 1988.

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A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, Lecture Notes in Computer Science 331, pages 84--98. Springer-Verlag, 1988.

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A. Pnueli and E. Harel. Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor, Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, LNCS 331, pages 84--98. Springer-Verlag, 1988.

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A. Pnueli and E. Harel. Applications of temporal logic to the specification of real time systems. In M. Joseph, editor, Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 331 of Lecture Notes in Computer Science, pages 84--98. Springer-Verlag, 1988.

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