Z. Chaochen, C. A. R. Hoare, and A. Ravn. A calculus of duration. Inform. Proc. Lett., 40(5):269--279, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....run, i.e. Runs is false. Some of Existing Approaches. Two approaches to veri cation are widely used: one dealing with model checking mainly for temporal logics and another one based on theorem proving in predicate logics. The rst approach uses temporal or duration logics [Pnu77] Eme90] CHR91] MP92] Han94] Eme96] Var96] Hen98] Rab98b] as requirement speci cation language, and usually timed automata [AD94] LSVW96] ACHH93] ACH 95] or regular process algebras [Mil90] as algorithms speci cation languages. Model checking is supported by many implemented algorithms. ....

Z. Chaochen, C. A. R. Hoare, and A. Ravn. A calculus of duration. Inform. Proc. Lett., 40(5):269-279, 1991.

....and ffi 2 from the splitting point up to the end of the run. It holds ffi 1 Psi true Omega ffi 2 ) ffi 1 ffi 2 , but the opposite is not true, since the chopping point can be also inside of a phase. This is visualised in Figure 4. Phase chopping satisfies the basic law known from the DC [1] dOEe , dOEe dOEe: The two different chopping operators should be used for different design phases. The transition chopping, ffi 1 ffi 2 , is mostly used for software design to describe properties of a 16 d 1 d 2 d 1 d 2 Phase Transition Time Time Value Value Figure 4: Two examples ....

Chaochen, Z., Hoare, C., and Ravn, A. A calculus of duration. In Information Processing Letters (December 1991), vol. 40, pp. 269--276.

.... with all their advantages concerning particular questions cannot cover the full scale veri cation as they are based on formalisms with bounded expressive power and that are not quite convenient from user s viewpoint, e.g. on temporal or duration logics to specify requirements (see e.g. Pnu77] CHR91] MP92] Han94] Var96] Rab98a] and, say, on timed automata to specify algorithms [AD94] LSVW96] ACH 95] So we are approaching the veri cation problem from the same side as, e.g. PVS [PVS] but paying more attention on foundations and algorithmic eciency. Sure, this approach may ....

Z. Chaochen, C. A. R. Hoare, and A. Ravn. A calculus of duration. Inform. Proc. Lett., 40(5):269-279, 1991.

....of a property. To gain a logic that combines the advantages of interval logic and the possibility to denote margins of an interval we introduce the Point Interval Logic (PIL) PIL is an interval logic based on the Duration Calculus (DC) extend its applicability. The DC was introduced in [1] and extended in [13] as a notation to specify hybrid and real time systems. Thus PIL inherits the capabilities of the DC for example to use differential equations to specify hybrid systems. Apart from that, PIL is designed with a special emphasis on the appearance of the formulas. The DC is ....

....system quantity is: gate : TIME #0 # ; 90 # # The type of gate is TIME #0 # ; 90 # #, but since TIME is the fixed domain for all system quantities, we say for short the type of gate is #0 # ; 90 # #. We adopt this convention for arbitrary system quantities. In the original DC [1] only system quantities Lattemann with a binary type were used. We adopt the extension of [13] and use arbitrary types for system quantities. Especially reals are used to specify continuous quantities. By the use of continuous system quantities hybrid systems can be specified. Rigid Variables ....

Z. Chaochen, C.A.R. Hoare, and A.P. Ravn. A calculus of duration. In Information Processing Letters, volume 40, pages 269--276, Dezember 1991.

....for any of our decidability results, but which is natural in a state based view of the world: we do not admit models in which there are instantaneous states, i.e. states with no duration. The 80 only other logic we are aware of that explicitly makes this restriction is the Duration Calculus [21]. Without this restriction, we could have the anomalous situation of two events (marking, respectively, the transitions into and out of an instantaneous state) occurring at the same real time, yet being ordered one after the other. As stated before, such a semantics can be quite unituitive. Note, ....

Chaochen Z, Hoare C A R, Ravn A P, A Calculus of Durations, Inf. Proc. Let. 40 (5), 1991, pp 269-276.

....[Pn77] and [ScMe82] In the case of branching non metric temporal logic see for example [ClEmSi86] where the Computation Tree Logic (CTL) has been introduced. More complex extensions are the interval logic [ScMeVo83] Me88] and in the case of linear metric temporal logic the Duration Calculus [ChHoRa91], HaCh92] and MTL R [LaHo95] In this paper, we formally introduce the typical patterns we have detected, define the tailored temporal operators we used, and discuss several of their properties (Section 3) In Section 2, we describe the underlying general purpose temporal logic. In Section ....

Z. Chaochen, C. A. R. Hoare, A. P. Ravn. A Calculus of Durations. In Inform. Process. Lett. 40, p. 269-276, 1991.

....development of systems in this case is achieved by a set of correctness preserving refinement steps. Examples of these form are TAM [25] and the Refinement Calculus [24] Below we list the most popular logic based formalisms: ITL (Interval Temporal Logic) 4] 21] 3] Duration Calculus [5]. Hoare Logic [8] WP Calculus (Weakest Precondition Calculus) 7] Modal Logic [18] Temporal Logic [17] RTTL (Real Time Temporal Logic) 22] TPCTL (Timed Probabilistic Computation Tree Logic) 11] ffl Algebraic Approach. In this approach, an explicit definition of ....

Chaochen, Z., Hoare, C. A. R. and Ravn, A. P., "A Calculus of Durations ", Information Processing Letters, Vol. 40, pp. 269--276 (05 1991).

....reals as time domain and functions fB : IR 0 f0; 1g, for each state B, to represent whether the system is at time t in state B (f B (t) 1) or not (f B (t) 0) one can calculate the duration of a state B in an interval [a; b] as the integral R b a fB (x)dx. The duration calculus [9, 11] (DC for short) provides a requirement specification language that allows to express properties about such durations and a calculus to reason about them. Many examples have been analysed using DC [34, 33] such as the classical gas burner system. While DC only allows the expression of safety ....

....calculus. We show that any formula of the duration calculus can be translated into an MTL R formula and that MTL R is more expressive than the duration calculus. To do so we briefly introduce the duration calculus. For a more detailed presentation of the duration calculus we refer to [9, 11]. It has been introduced in [9] as a notation to specify real time requirements, and a calculus to verify theorems about such requirements, and can be considered as an extension of interval temporal logic [28] The duration calculus has also been used to give semantics to communicating processes ....

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Zhou Chaochen, C.A.R. Hoare, and A.P. Ravn, A calculus of durations, Inf. Proc. Letters 40(5) (1991) 269-276.

....communication protocols taking into account how long it takes for the sender to change the signal from high to low and vice versa. The DC model of communication protocols given in that paper is proved to be more general and intuitive than the others in the literature [9, 1] Duration Calculus (DC) [2] is a logic to reason about boolean functions based on interval temporal logics. This makes it one of the most suitable logics for specifying the communication protocols because the signal sent and received are usually modelled by boolean functions of time. In a previous paper we found that using ....

....received by the receiver are functions from the set (R) of nonnegative real numbers (representing time) to f0; 1g (1 represents that the signal is high, and 0 represents that the signal is low) we can consider them as boolean functions of time, which are called states in DC. Duration Calculus [2], introduced by Zhou et al., is a logic for reasoning about the behaviour of the states. This makes it really suited for modelling the communication protocols. For the convenience of readers who Receiver clock sent signal Sender Receiver Digitizing received signal decode encode Bus Figure 1: ....

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Z. Chaochen, C. A. R. Hoare, A. P. Ravn, "A calculus of durations", Information Processing Letters, 40, 1992, 269-276.

.... clocks (to measure time) or integrators (to measure durations) 13, 14, 3] and timed hybrid logics that are temporal logics allowing time or duration constraints, as for instance the timed temporal logics TPTL [6] and MITL [5] the duration temporal logic DTL [7] or the calculus of durations CoD [10]. The verification problem of hybrid systems is whether some given control design of a system satisfies (implements) some given requirements on its behaviours. There are three approaches to tackle this problem depending on the formalisms used to describe the control design and the requirements. ....

Z. Chaochen, C.A.R. Hoare, and A.P. Ravn. A Calculus of Durations. IPL, 40, 1991.

.... a notion of accumulated properties that is in rough analogy to derivation of macroscopic properties from microscopic ones in physics, thus being dedicated to non algorithmic description of system requirements (primary examples of such logics are the duration calculi [Zho93] starting with [ZHR91] As the more abstract temporal logics feature a more well suited vocabulary for describing what the circuit ought to do without getting too involved in how to achieve this, we will head for a synthesis method based on a temporal logic at the highest of above levels, namely Duration Calculus ....

.... As the more abstract temporal logics feature a more well suited vocabulary for describing what the circuit ought to do without getting too involved in how to achieve this, we will head for a synthesis method based on a temporal logic at the highest of above levels, namely Duration Calculus [ZHR91] Unfortunately, Duration Calculus is undecidable [ZHS93] Thus, although it has a kind of vocabulary we might like to have in our source language, we have no clue on how to built an automatic hardware synthesis procedure for Duration Calculus. In the following, we briefly sketch Duration ....

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Zhou Chaochen, C. A. R. Hoare, and Anders P. Ravn. A calculus of durations. IPL, 40(5):269--276, 1991.

....system to use formal mathematical reasoning in determining whether a design conforms to the system requirements. Intelligent autonomous system development is decomposed into four phases: system modeling, requirements specification, behavior verification [Ravn et al. 1993, Chaochen et al. 1993, Chaochen et al. 1991] and system implementation. A methodology for an alyzing a complex system, composed of individual sub systems integrated together, would enable a design engineer to refine the control structure for improved performance. The effects on the entire system of modifying an individual sub system ....

....to robotics will result in a more efficient, systematic, and reliable robotic system design process. In the following sections we present a formal specification and verification of a visual grasping task using the techniques of duration calculus [Chaochen et al. 1993, Ravn et al. 1993, Chaochen et al. 1991] We apply DC to a complex system, a robot performing visual grasping, where DC is used to describe state durations, progress from state to state, and stability of the robotic system states. The task of visual grasping (or robotic catching) is of interest in both manufacturing, and in ....

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Chaochen, Z., Hoare, C., and Ravn, A. (1991). A calculus of durations. Information Processing Lett., 40(5):269--276.

....of states which include quantitative timing information; each state is labeled by a time of occurrence. Temporal operators defined in PVS are used to assert properties of these sequences. PVS also provides tool support for the duration calculus (DC) a real time interval temporal logic [15] [16]. DC has been partly embedded in PVS. Several theories define the semantics of the calculus and DC proof rules are introduced as PVS theorems. A dedicated interface makes the encoding largely transparent to the user. Specifications are written in a syntax close to standard DC and verification is ....

Z. Chaochen, C. A. R. Hoare, and A. P. Ravn, "A calculus of durations," Information Processing Letters, vol. 40, no. 5, pp. 269--276, December 1991.

....is a need for formal methods which allow us to model and reason about time. Research in this area has produced a number of different approaches, notable among which are those based on timed traces, i.e. where systems are modelled by time varying functions. Examples include the duration calculus [Zhou Chaochen et al. 1991], the Temporal Agent Model (TAM) Scholefield and Zedan, 1993; Scholefield et al. 1994] the timed stream model [Broy, 1993; Broy, 1997] and Proceedings of the Twenty Second Australasian Computer Science Conference, Auckland, New Zealand, January 18 21 1999. Copyright SpringerVerlag, Singapore. ....

Zhou Chaochen, Hoare, C.A.R., and Ravn, A.P. (1991). A calculus of durations.

.... work, we intend to study the relationship between DTL and interval based temporal logics, e.g. 3] and [10] where we also find a completeness proof for an axiom system that involves operators based on ternary relations) as well as the realtime aspects that can be associated with durative actions [2]. ....

Z.Chaochen, C.A.R.Hoare and A.P.Ravn, "A Calculus of Durations", Information Processing Letters 40, pp. 269-276, North-Holland 1991.

....a growing number of computer controlled systems we face a major challenge: development of reliable, robust, and safe real time intelligent systems. Intelligent autonomous system development can be decomposed into three phases: system modeling, requirements specification, and behavior verification [7, 19, 6]. Robotic systems are usually complex, hierarchical, and physically distributed. They must deal with inconsistent, incomplete, and delayed information from various sources. To address these problems, this paper demonstrates suitable analytical tools which would allow a designer of a complicated ....

....no model has reached a level of universal acceptance. The adaptation of these theoretical techniques for real world applications is a subject for future investigation. In the following sections we present a formal verification of a visual grasping task using the techniques of duration calculus [7, 19, 6]. Duration calculus (DC) is an extended temporal or interval logic [1, 15] which can be used to specify and reason about real time and logical constraints in dynamical systems without the explicit mention of time instants. Duration calculus has already been used to design a gas burner [7, 19] a ....

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Z. Chaochen, C. Hoare, & A. Ravn. A calculus of durations. Info. Proc. Lett., 40(5):269--276, 1991.

....a major goal of both the SafeFM and MORSE projects. For safety critical systems, timing is often of great importance. This has proved to be a difficult area to formalize in a manner that is usable in practice. However research in this area is gathering momentum (e.g. using the Duration Calculus [139]) 51, 102] 4.2 Design The design process refines a specification down to a program using (possibly) provably correct transformations or some other kind of rigorous refinement method. In general this must involve input from the engineer since there are many programs that meet a particular ....

ZHOU ChaoChen, HOARE, C.A.R., and RAVN, A.P.: `A calculus of durations', Information Processing Letters, 1991, 40, (5), pp. 269--276

.... decided with no essential complexity penalty[26] over a dense time domain, of the real time interval logics of Narayana and Aaby [22] and of Razouk and Gorlick [27] can also be proved, by a simple adaptation of the proof of undecidability of MITL with singular intervals [5] The Duration Calculus [9] differs from the interval logics noted above in that it treats intervals as primitive. The calculus is well suited to describing and reasoning about cumulative behaviour, a feature extremely useful for hybrid systems. The operator R in that logic, for instance, allows one to bound the duration ....

Chaochen Z, Hoare C A R, Ravn A P, A Calculus of Durations, Inf Proc Let 40(5), 1991, pp 269-276.

....to use formal mathematical reasoning in determining whether a design conforms to the system requirements. Intelligent autonomous system development is decomposed into three phases: system modeling, requirements specification, and behavior verification [Ravn et al. 1993, Chaochen et al. 1993, Chaochen et al. 1991] A methodology for analyzing a complex system, composed of individual sub systems integrated together, would enable a design engineer to refine the control structure for improved performance. The effects on the entire system of modifying an individual sub system become explicit. The specific ....

....techniques to robotics will result in a more efficient, systematic, and reliable robotic system design process. In the following sections we present a formal specification and verification of a visual grasping task using the technique of duration calculus [Ravn et al. 1993, Chaochen et al. 1993, Chaochen et al. 1991] We apply DC to a complex system, a robot performing visual grasping, where DC is used to describe state durations, progress from state to state, and stability of the robotic system states. The task of visual grasping (or robotic catching) is of interest in both manufacturing, and in ....

[Article contains additional citation context not shown here]

Chaochen, Z., Hoare, C., and Ravn, A. (1991). A calculus of durations. Information Processing Lett., 40(5):269--276.

....left to digital computers. However, the main result of ProCoS was that we had some reason to believe that this particular code would have controlled suitable hardware, such that top level requirements for a gas burner [11] were satisfied. These requirements are specified in duration calculus [14], a real time interval logic. In order to illustrate the gap between requirements and code we give the formal requirements here, along with an informal explanation of the duration 2 calculus. The logical foundations of duration calculus are treated thoroughly in [3] while other selected ....

Chaochen Zhou, C. A. R. Hoare, and A. P. Ravn. A calculus of durations. Information Proc. Letters, 40(5), Dec. 1991.

....to DC formulas. The method is illustrated by the Gas Burner case study. Keywords Real time systems; Duration Calculus; Timed Transition Systems, Specification, Verification. 1 INTRODUCTION Duration calculus (DC) was introduced to specify and reason about properties of embedded real time systems (Zhou, Hoare Ravn 1991, Ravn, Rischel Hansen 1993) it has also been successfully used to reason about circuits and digital designs and hybrid systems (Ravn Rischel 1991, Zhou, Ravn Hansen 1993) Introductions to the applications are found in (Zhou 1993) while the logic and its foundation is given a thorough ....

....of Leak must be stopped within 4 seconds. The other formula Des 2 is a bounded invariance: it says that once a Leak is stopped, this persists for at least 26 seconds. The correctness of the design, i.e. implication of the validity of Req by that of Des def = Des 1 Des 2 , is shown in (Zhou et al. 1991) and for a more complex design in (Ravn et al. 1993) The formula Des may be interpreted as a real time automaton or a real time program, which is refined further in a detailed design. However, this is in general a big formula and a direct proof of refinement in DC may be tedious, because many ....

[Article contains additional citation context not shown here]

Zhou, C., Hoare, C. & Ravn, A. (1991), `A calculus of durations', Information Processing Letters 40(5), 269--276.

No context found.

Z. Chaochen, C. A. R. Hoare, and A. Ravn. A calculus of duration. Inform. Proc. Lett., 40(5):269--279, 1991.

No context found.

Z. Chaochen, C.A.R. Hoare, A.P. Ravn, "A calculus of durations", Information Proc. Letters, 40(5), Dec., 1991.

No context found.

Chaochen, Z., Hoare, C.A.R., and Ravn, A.P. (1991). A calculus of durations. In: Information Processing Letters, Vol. 40, pp. 269-276.

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Zhou Chaochen, C.A.R. Hoare, and Anders P. Ravn, "A Calculus of Durations ", ProCos Working Paper, Oxford University Computing Laboratory, (1991).

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