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## Truth of duration calculus formulae in timed frames (1996)

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Venue: | Fundamenta Informaticae |

Citations: | 7 - 5 self |

### Citations

3932 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...mbedding into TFL, we consider these logics to be closely related to TFL. The use of Hennessy-Milner logic as a basic specification language for reactive systems has been illustrated in, for example, =-=[24]-=-. The extension outlined above allows for specifying time constraints. Therefore, it may well be used as specification language in a ProCoS-like approach. The results from Section 6 concerning the emb... |

1769 | The C++ Programming Language
- Stroustrup
- 1991
(Show Context)
Citation Context ...subset of SDL [10]; and it is envisaged to use it for the semantics of other languages related to programming as well, e.g. a tractable subset of a widely used modern programming language such as C++ =-=[33]-=- or Java [2]. A useful topic for further work is the lifting of the results from Section 5 concerning the connection of duration calculus with timed frames to processes as studied in the setting of th... |

852 |
The Java Programming Language
- Arnold, Gosling
- 1996
(Show Context)
Citation Context ... [10]; and it is envisaged to use it for the semantics of other languages related to programming as well, e.g. a tractable subset of a widely used modern programming language such as C++ [33] or Java =-=[2]-=-. A useful topic for further work is the lifting of the results from Section 5 concerning the connection of duration calculus with timed frames to processes as studied in the setting of the discrete t... |

596 | R.: Algebraic laws for nondeterminism and concurrency
- Hennessy, Milner
- 1985
(Show Context)
Citation Context ... to look at the fragment. It may be convenient when devising a ProCoS-like approach with a logic closely related to timed frame logic, e.g. a timed version of Dicky logic [1] or Hennessy-Milner logic =-=[20]-=-, as specification language. Strictly speaking, we consider an extension of the original duration calculus, known as the mean value calculus [37], which allows to deal with point intervals and consequ... |

327 |
Automatic verification of finite state concurrent systems using temporal logic
- Clarke, Emerson, et al.
- 1986
(Show Context)
Citation Context ...This matter is treated as well in this paper. Various other well-known logics can be embedded into timed frame logic. Among these logics are CTL and Dicky logic, which underlie the model checkers EMC =-=[7]-=- and MEC [1], respectively. Besides, timed frame logic is expressive enough to distinguish any timed frame from another one. The structure of this paper is as follows. First of all, we give a survey o... |

267 |
A calculus of durations
- Chaochen, Hoare, et al.
- 1992
(Show Context)
Citation Context ...5] for which a process algebra semantics is given in [5]. In this paper, we study the connection between timed frames with signal inserted states and duration calculus, a temporal logic introduced in =-=[12]-=-. More precisely, we consider the extension of the original duration calculus proposed in [13], known as the mean value calculus. This study is motivated by the need to understand better the problem o... |

213 |
Modal and temporal logics
- Stirling
- 1992
(Show Context)
Citation Context ...deling timed processes [10]. There is a well-developed tradition of thinking about transition systems from modal logic (for an overview of modal formalisms for describing transition systems, see e.g. =-=[11]). Process-=- algebra studies transition systems at a more abstract level: transition systems modulo an appropriate "process equivalence", e.g. bisimilarity. Time determinism is not built into timed fram... |

171 | Real time process algebra
- Baeten, Bergstra
- 1991
(Show Context)
Citation Context ...and the discrete time extension of ACP presented in [5]. Two-phase transition systems are closely related to the real-time transition systems that underlie the real-time extension of ACP presented in =-=[3]-=-. In [4], it is shown that the model of the discrete time extension of ACP based on two-phase transition systems is isomorphic to a model based on the real-time transition systems that are discretized... |

145 |
Finite Transition Systems.
- Arnold
- 1994
(Show Context)
Citation Context ...ny time that it is sufficient to look at the fragment. It may be convenient when devising a ProCoS-like approach with a logic closely related to timed frame logic, e.g. a timed version of Dicky logic =-=[1]-=- or Hennessy-Milner logic [20], as specification language. Strictly speaking, we consider an extension of the original duration calculus, known as the mean value calculus [37], which allows to deal wi... |

125 | The algebra of timed processes, ATP: theory and application
- Nicollin, Sifakis
- 1994
(Show Context)
Citation Context ...ectively. Equipped with a root marker and optionally with termination markers, timed frames make up the transition systems that match with the twophase functioning scheme for modeling timed processes =-=[10]-=-. There is a well-developed tradition of thinking about transition systems from modal logic (for an overview of modal formalisms for describing transition systems, see e.g. [11]). Process algebra stud... |

100 |
Specification-oriented semantics for communicating processes
- Olderog, Hoare
- 1986
(Show Context)
Citation Context ...esulting system conforms to the requirements expressed for it. The programming language considered is an occam-like language with real-time features, called PL. A timed version of the readiness model =-=[27]-=- is the basis of the semantics of PL. To bridge the gap between the state-based duration calculus and the event-based PL, a specification language for reactive systems with time constraints is introdu... |

92 |
Duration calculus: Logical foundations,
- Hansen, Zhou
- 1997
(Show Context)
Citation Context ...ied out while the author was at UNU/IIST (United Nations University, International Institute for Software Technology). Note: This paper is a revised version of [23]. 1. Introduction Duration calculus =-=[18, 36]-=- is an interval temporal logic intended for expressing real-time requirements for systems and refining these requirements to specifications for one or more computer hardware and software components. F... |

88 |
A.: SDL - Formal Object-Oriented Language for Communicating Systems. Prentice Hall, Upper Saddle River
- Ellsberger, Hogrefe, et al.
- 1997
(Show Context)
Citation Context ...ncerns a simple telephone answering machine. We use timed frame algebra for the description of the control component of the telephone answering machine. The example is based on a specification in SDL =-=[14]-=- due to Mauw [22]. In order to control the telephone answering, the control component of the answering machine has to communicate with the recorder component of the answering machine, the telephone co... |

77 |
An extended duration calculus for hybrid real-time systems.
- Chaochen, Ravn, et al.
- 1993
(Show Context)
Citation Context ...roduced in [12]. Its discrete time semantics can be found in e.g. [8]. Several extensions have been proposed, notably the Mean Value Calculus (MVC) in [13] and the Extended Duration Calculus (EDC) in =-=[14]-=-. Here we consider MVC with discrete time semantics. In both DC and MVC, a system is modelled by a number of functions from a time domain to the Boolean domain f0; 1g. These functions are called the s... |

63 | The discrete time toolbus – a software coordination architecture,
- Bergstra, Klint
- 1998
(Show Context)
Citation Context ...presented in [5]. This extension has already been used as the basis of the semantics of some languages related to programming, e.g. the language T of the ToolBus software interconnection architecture =-=[9]-=- and a semantically clear subset of SDL [10]; and it is envisaged to use it for the semantics of other languages related to programming as well, e.g. a tractable subset of a widely used modern program... |

55 |
Design of Embedded Real-Time Computing Systems”,
- Ravn
- 1995
(Show Context)
Citation Context ...or which it is interesting to verify whether they are met by frames. These refinements will be formulated in a fragment of MVC anyhow, e.g. the fragment consisting of the implementables introduced in =-=[30]-=-. Identifying a fragment of MVC that can be embedded into TFL is not too difficult if one realizes that: (1) with the discrete time semantics the value of terms of the form P ∗ ℓ (i.e. � P)isalwaysin ... |

50 | Models for reactivity
- Manna, Pnueli
- 1993
(Show Context)
Citation Context ...than necessary and a simpler kind of transition systems is used in [15]. They are also closely related to the transition systems underlying Timed CCS [12] and the timed transition systems proposed in =-=[21]-=-. The discrete time case is considered suitable for formalisms aimed at programming. It permits to consider systems at a more abstract level than the continuous time case, a level where time is measur... |

31 |
Chopping a point”.
- Chaochen, Hansen
- 1996
(Show Context)
Citation Context ...sequence at the same time point. Ongoing work on duration calculus aims to deal with such cases, both in discrete and continuous time, in a more satisfactory way by introducing a micro time (see e.g. =-=[28, 35]-=-). In [7], results concerning the connection between timed frames and discrete time processes are given in the setting of the discrete time extension of ACP presented in [5]. This extension has alread... |

27 |
An interleaving model for real-time systems
- Chen
- 1991
(Show Context)
Citation Context ...me transition systems of [3] are more complicated than necessary and a simpler kind of transition systems is used in [15]. They are also closely related to the transition systems underlying Timed CCS =-=[12]-=- and the timed transition systems proposed in [21]. The discrete time case is considered suitable for formalisms aimed at programming. It permits to consider systems at a more abstract level than the ... |

23 | Hung: “Duration calculus of weakly monotonic time”.
- Pandya, Van
- 1998
(Show Context)
Citation Context ...sequence at the same time point. Ongoing work on duration calculus aims to deal with such cases, both in discrete and continuous time, in a more satisfactory way by introducing a micro time (see e.g. =-=[28, 35]-=-). In [7], results concerning the connection between timed frames and discrete time processes are given in the setting of the discrete time extension of ACP presented in [5]. This extension has alread... |

20 |
A Mean Value Calculus of Durations
- CHAOCHEN, XIAOSHAN
- 1994
(Show Context)
Citation Context ...on between timed frames with signal inserted states and duration calculus, a temporal logic introduced in [12]. More precisely, we consider the extension of the original duration calculus proposed in =-=[13]-=-, known as the mean value calculus. This study is motivated by the need to understand better the problem of verifying whether the implementation of a software system obeys certain real-time requiremen... |

20 |
Provably Correct Systems
- Jifeng
- 1995
(Show Context)
Citation Context ...rdware and software components. Formalisms aimed at programming should subsequently be used for the stepwise development of the software components of the system to be realized. In the ProCoS project =-=[19]-=-, a particular approach has been developed to safeguard that the resulting system conforms to the requirements expressed for it. The programming language considered is an occam-like language with real... |

18 |
Discrete time process algebra
- Baeten, Bergstra
- 1992
(Show Context)
Citation Context ...int. Before proceeding, we have a look at the origin of this peculiarity. Timed frames are meant for modeling the time-dependent behaviour of programs at a level of abstraction where time is measured with finite precision by using a discrete time scale. It means that the discrete time points just divide real time into time slices and, although actions and state changes take place in real time, only the time slices in which actions and state changes take place are considered to be of importance. Discrete time process algebras such as ATP [26] and the discrete time extension of ACP presented in [5] offer exactly 16 C.A. Middelburg /Truth of Duration Calculus Formulae in Timed Frames this abstraction. Naturally, it is in accordance with the intended meaning of a time step – the passage of time to the next time slice – for it derives this meaning from its use in these discrete time process algebras. However, the discrete time semantics of MVC does not offer a similar abstraction because it only allows for state changes at the discrete time points. For this reason, the sequence of actions taking place within a time slice must be treated as a single transition that yields only one state cha... |

15 | Process Algebra Semantics of 'SDL
- Bergstra, Middelburg
- 1995
(Show Context)
Citation Context ...tivated by ongoing work on devising a suitable logic for reasoning about timed processes described in 'SDL. This is an interesting subset of SDL [15] for which a process algebra semantics is given in =-=[5]-=-. In this paper, we study the connection between timed frames with signal inserted states and duration calculus, a temporal logic introduced in [12]. More precisely, we consider the extension of the o... |

14 |
Proposal for a programming language core for
- Franzle, Karger
- 1993
(Show Context)
Citation Context ...In this connection, it is interesting to see that it is not entirely clear how the definitions of the semantics of SL and PL presented in [32] relate to the earlier definitions, presented in [31] and =-=[16, 25]-=-, which they replace. A main purpose of this paper is to make it generally easier to establish semantic links between duration calculus and formalisms aimed at programming. Various mathematical models... |

12 |
Discrete time process algebra. Formal Aspects of Computing 8:188–208,
- Baeten, Bergstra
- 1996
(Show Context)
Citation Context ... is not built into timed frame algebra: states may have more than one outgoing time steps. In [3], the connection between timed frames and discrete time processes is studied in the setting of ACP drt =-=[2]-=-. A special kind of bisimilarity, called oe-bisimilarity, is introduced to see to time determinism. Further structure on timed frames is provided by adding an operation, called signal insertion, to as... |

12 |
Discrete time process algebra (extended abstract)”.
- Baeten, Bergstra
- 1992
(Show Context)
Citation Context ...discrete time extension of ACP presented in [5]. Two-phase transition systems are closely related to the real-time transition systems that underlie the real-time extension of ACP presented in [3]. In =-=[4]-=-, it is shown that the model of the discrete time extension of ACP based on two-phase transition systems is isomorphic to a model based on the real-time transition systems that are discretized. For di... |

12 |
Discrete time process algebra: Absolute time, relative time and parametric time”,
- Baeten, Bergstra
- 1997
(Show Context)
Citation Context ...lae in timed frames is studied. Timed frames [7] cover virtually all kinds of transition systems for the discrete time case. Timed frames are in essence the two-phase transition systems considered in =-=[6]-=- as the objects underlying discrete time process algebras. They underlie well known discrete time process algebras such as ATP [26] and the discrete time extension of ACP presented in [5]. Two-phase t... |

12 | A timed specification language for concurrent reactive systems”.
- Schenke
- 1994
(Show Context)
Citation Context ... nicely. In this connection, it is interesting to see that it is not entirely clear how the definitions of the semantics of SL and PL presented in [32] relate to the earlier definitions, presented in =-=[31]-=- and [16, 25], which they replace. A main purpose of this paper is to make it generally easier to establish semantic links between duration calculus and formalisms aimed at programming. Various mathem... |

11 | Algebra of timed frames”,
- Bergstra, Fokkink, et al.
- 1996
(Show Context)
Citation Context ...and timing may be absolute or relative. The nature of the time scale makes all the difference. In this paper, the interpretation of duration calculus formulae in timed frames is studied. Timed frames =-=[7]-=- cover virtually all kinds of transition systems for the discrete time case. Timed frames are in essence the two-phase transition systems considered in [6] as the objects underlying discrete time proc... |

11 | Discrete time process algebra and the semantics of SDL”,
- Bergstra, Middelburg, et al.
- 1998
(Show Context)
Citation Context ...y been used as the basis of the semantics of some languages related to programming, e.g. the language T of the ToolBus software interconnection architecture [9] and a semantically clear subset of SDL =-=[10]-=-; and it is envisaged to use it for the semantics of other languages related to programming as well, e.g. a tractable subset of a widely used modern programming language such as C++ [33] or Java [2]. ... |

10 | Frame algebra with synchronous communication”.
- Bergstra, Ponse
- 1995
(Show Context)
Citation Context ... s 0 (TFA2) s 0 \Phi (s oe \Gamma! s 0 ) = s oe \Gamma! s 0 Table 1: Axioms for timed frames. timed frames as objects consisting of a finite set of states and a finite set of transitions (axioms 1 In =-=[6]-=-, the pairing function is used to define a frame product function. Report No. 82, September 18, 1996 UNU/IIST, P.O. Box 3058, Macau Timed frames 5 (FA1)--(FA4)). In addition, timed frames are identifi... |

9 |
Model checking discrete duration calculus”,
- Hansen
- 1994
(Show Context)
Citation Context ...September 18, 1996 UNU/IIST, P.O. Box 3058, Macau Duration calculus 11 4 Duration calculus The original Duration Calculus (DC) was introduced in [12]. Its discrete time semantics can be found in e.g. =-=[8]-=-. Several extensions have been proposed, notably the Mean Value Calculus (MVC) in [13] and the Extended Duration Calculus (EDC) in [14]. Here we consider MVC with discrete time semantics. In both DC a... |

8 | and Zhou Chaochen: “Duration calculus: Logical foundations”, - Hansen - 1997 |

7 |
An e ective axiomatization for real time ACP
- Fokkink, Klusener
- 1995
(Show Context)
Citation Context ... n + 1, may also occur at any other time between n and n + 1. Note that the real-time transition systems of [3] are more complicated than necessary and a simpler kind of transition systems is used in =-=[15]-=-. They are also closely related to the transition systems underlying Timed CCS [12] and the timed transition systems proposed in [21]. The discrete time case is considered suitable for formalisms aime... |

6 |
Hung and Phan Hong Giang: “A sampling semantics of duration calculus”.
- Van
- 1996
(Show Context)
Citation Context ... continuous time if all of the specifications are satisfied in discrete time. The problem of refining real-time requirements to such specifications in the setting of duration calculus is addressed in =-=[13]-=-. In duration calculus, real-time requirements are formulated as properties about the duration of phases of system behaviour. These phases, which are called state variables, are interpreted as functio... |

6 |
A new proposal for TimedPL’s semantics”,
- Muller-Olm
- 1994
(Show Context)
Citation Context ...In this connection, it is interesting to see that it is not entirely clear how the definitions of the semantics of SL and PL presented in [32] relate to the earlier definitions, presented in [31] and =-=[16, 25]-=-, which they replace. A main purpose of this paper is to make it generally easier to establish semantic links between duration calculus and formalisms aimed at programming. Various mathematical models... |

5 | Development of Correct Real-Time Systems by Refinement”,
- Schenke
- 1997
(Show Context)
Citation Context ...e semantics of PL. SL and PL have been given a semantics using duration calculus formulae to describe the meaning of SL specifications and using timing diagrams to describe the meaning of PL programs =-=[32]-=-. Because timing diagrams are in essence the objects with respect to which the truth of duration calculus formulae is usually defined, thus semantic links between duration calculus, SL and PL have bee... |

4 | A logic for signal inserted timed frames
- Bergstra, Fokkink, et al.
- 1996
(Show Context)
Citation Context ...cerning natural numbers, states, propositions, transition labels and paths; 3. equality and some additional standard predicates concerning paths. TFL was first proposed as a logic for timed frames in =-=[4]-=-. That paper reports in detail about various issues, including the distinctive power of TFL and the embedding of other logics (CTL and Dicky logic) in TFL. In this section, we only present the syntax ... |

4 |
Example specifications in 'SDL. Computing Science
- Mauw
- 1996
(Show Context)
Citation Context ...le telephone answering machine. We use timed frame algebra for the description of the control component of the telephone answering machine. The example is based on a specification in 'SDL due to Mauw =-=[9]-=-. In order to control the telephone answering, the control component of the answering machine has to communicate with the recorder component of the answering machine, the telephone connected with the ... |

4 | Ravn, "A calculus of durations - Chaochen, Hoare, et al. - 1991 |

3 |
a system for constructing and analysing transition systems
- MEC
- 1990
(Show Context)
Citation Context ...is treated as well in this paper. Various other well-known logics can be embedded into timed frame logic. Among these logics are CTL and Dicky logic, which underlie the model checkers EMC [7] and MEC =-=[1]-=-, respectively. Besides, timed frame logic is expressive enough to distinguish any timed frame from another one. The structure of this paper is as follows. First of all, we give a survey of timed fram... |

3 |
Description Language (SDL). ITU-T Recommendation Z.100, International Telecommunication Union, Gen`eve
- Specification
- 1992
(Show Context)
Citation Context ...changes can be modelled. The study in [3] was partly motivated by ongoing work on devising a suitable logic for reasoning about timed processes described in 'SDL. This is an interesting subset of SDL =-=[15]-=- for which a process algebra semantics is given in [5]. In this paper, we study the connection between timed frames with signal inserted states and duration calculus, a temporal logic introduced in [1... |

2 |
Algebra of timed frames. Logic Group Preprint Series 148
- Bergstra, Fokkink, et al.
- 1995
(Show Context)
Citation Context ...: : : : : : : : : : : : : : : : : : : : : : : 20 7 Closing remarks 23 Report No. 82, September 18, 1996 UNU/IIST, P.O. Box 3058, Macau Introduction 1 1 Introduction Timed frame algebra, introduced in =-=[3]-=-, is a simple, general algebraic setting for the objects of the kind that generally underlies models for theories concerning discrete time process behaviour. Timed frames are built from states and lab... |

2 | DC/RJ - : A justification assistant for duration calculus
- Yong
- 1997
(Show Context)
Citation Context ...onceivable. Interesting ones may be obtained by retaining duration calculus as requirement language but choosing another specification language and/or programming language, e.g. RSL [29] is chosen in =-=[34]-=-. The mathematical model that is thes1. Introduction 2 basis of the semantics of the language(s) concerned will bring on certain basic concepts and special notations. To describe the meaning of the la... |

1 |
Example specifications in ϕSDL. Computing Science
- Mauw
- 1996
(Show Context)
Citation Context ...elephone answering machine. We use timed frame algebra for the description of the control component of the telephone answering machine. The example is based on a specification in SDL [14] due to Mauw =-=[22]-=-. In order to control the telephone answering, the control component of the answering machine has to communicate with the recorder component of the answering machine, the telephone connected with the ... |

1 | C.A.: "Algebra of timed frames - Bergstra, Fokkink, et al. - 1996 |

1 | C.A.: "A logic for signal inserted timed frames - Bergstra, Fokkink, et al. - 1996 |

1 | C.A and Usenko, Y.S.: "Discrete time process algebra and the semantics of SDL - Bergstra, Middelburg - 1998 |

1 | Hung and Phan Hong Giang: "A sampling semantics of duration calculus - Van - 1996 |

1 | An effective axiomatization for real time ACP", Information and Computation - Fokkink, Klusener - 1995 |

1 | Zhou Chaochen: "Duration calculus: Logical foundations - Hansen - 1997 |

1 | Example specifications in 'SDL", Computing Science - Mauw - 1996 |

1 | Hung: "Duration calculus of weakly monotonic time - Pandya, Van - 1998 |

1 | DC/RJ \Gamma : A justification assistant for duration calculus - Yong - 1997 |

1 | Chaochen and Li Xiaoshan: "A mean value calculus of durations - Zhou - 1994 |

1 |
A logic for signal inserted timed frames”, Logic Group
- Bergstra, Fokkink, et al.
- 1996
(Show Context)
Citation Context ...e also counterparts of the axioms (Ins7) and (Ins8) for time steps. Note that the equation s⊕ (φqs) = φqs (reminiscent of the axioms (FA5) and (FA6)) is derivable from the axioms (Ins2) and (Ins4). 3. Timed frame logic Timed Frame Logic (TFL) is a classical first-order logic with: 1. quantification over natural numbers, states, transition labels and paths; 2. standard constants and functions concerning natural numbers, states, propositions, transition labels and paths; 3. equality and some additional standard predicates concerning paths. TFL was first proposed as a logic for timed frames in [8]. That paper reports in detail about various issues, including the distinctive power of TFL and the embedding of other logics (CTL and Dicky logic) in TFL. In this section, we only present the syntax and semantics of TFL. 3.1. Syntax The signature for the terms of TFL is the signature of signal inserted timed frames restricted to natural numbers, states and propositions, and extended with the following: Sorts: L transition labels; Π paths; Constants & Functions: + : N2 → N addition; a : L for each a ∈ A; σ : L time step label; ıS : S→ Π embedding of states in paths; .−→: Π× L× S→ Π appending o... |

1 | An effective axiomatization for real time ACP”, - Fokkink, Klusener - 1995 |

1 | Example specifications in ϕSDL”, - Mauw - 1996 |

1 | Group: The RAISE Specification Language, - Language - 1992 |