Algebra of timed frames

Bergstra, Jan A.; Fokkink, Wan; Middelburg, Cornelis A.

doi:10.1080/00207169608804514

Cited by 3 publications

(7 citation statements)

References 8 publications

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“…[11]. The initial ideas about the use of a timed variant of the process algebra with propositional signals for hybrid systems were born while the second author was working on timed frames [17,43]. Similar ideas, born independently, were outlined in Ref.…”

Section: Discussion Of Main Choicesmentioning

confidence: 99%

Process algebra for hybrid systems

Bergstra

Middleburg

2005

Theoretical Computer Science

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We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg (Process Algebra with Timing, Springer, Berlin, 2002, Chapter 4), and the process algebra with propositional signals from Baeten and Bergstra (Theoret. Comput. Sci. 177 (1977) 381-405). The proposed process algebra makes it possible to deal with the behaviour of hybrid systems, i.e. systems in which the instantaneous state transitions caused by performing actions are alternated with continuous state evolutions. This process algebra has, in addition to equational axioms, rules to derive equations with the help of real analysis. (J.A. Bergstra), keesm@win.tue.nl (C.A. Middelburg) URL: http://www.win.tue.nl/∼keesm (C.A. Middelburg).0304-3975/$ -see front matter

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Section: Discussion Of Main Choicesmentioning

confidence: 99%

Process algebra for hybrid systems

Bergstra

Middleburg

2005

Theoretical Computer Science

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“…For that purpose, we h a v e a v ailable the axioms presented in Section 2 and RSP (see Section 2.4). In [10], timed frames, which are closely related to the kind of transition systems presented by the operational semantics of, for example, BPA drt -ID and PA drt -ID, are studied in a general algebraic setting and results concerning the connection between timed frames and discrete time processes with relative timing are given. In [14], a model for BPA drt -IDlin (BPA drt -ID with nite linear recursive specications) is presented that gives an interpretation of its constants and operators on timed frames; and it is shown that the bisimulation model induced by the original structured operational semantics is isomorphic to the timed frame model.…”

Section: Discussionmentioning

confidence: 99%

Discrete Time Process Algebra and the Semantics of SDL

Bergstra¹,

Middelburg²,

Usenko³

2001

Handbook of Process Algebra

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We p resent an extension of discrete time process algebra with relative timing where recursion, propositional signals and conditions, a counting process creation operator, and the state operator a re combined. Except the counting process creation operator, which subsumes the original process creation operator, these features have been developed earlier as largely separate extensions of time free process algebra. The change to the discrete time case and the combination of the features turn out to be far from trivial. We also propose a semantics for a simplied version of SDL, using this extension of discrete time process algebra to describe the meaning of the language constructs. This version covers all behavioural aspects of SDL, except for communication via delaying channels { which can easily be modelled. The semantics presented here facilitates the generation of nitely branching transition systems for SDL specications and thus it enables validation.

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“…The frames TAMC0 and TAMC1 defined here differ slightly from the ones defined in [7]. There states 46 and 47 were identified, because both were considered states of playing.…”

Section: Examplementioning

confidence: 99%

“…This section contains a survey of simple timed frame algebra and its extension with signal insertion. We refer to [7] for further details, which include results about the connection between timed frames and discrete time processes. The survey is preceded by a small example to illustrate the use of timed frames.…”

Section: Timed Framesmentioning

confidence: 99%

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Truth of Duration Calculus Formulae in Timed Frames

Middelburg

1998

Fundamenta Informaticae

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Duration calculus is a logical formalism designed for expressing and refining real-time requirements for systems. Timed frames are essentially transition systems meant for modeling the time-dependent behaviour of programs. We investigate the interpretation of duration calculus formulae in timed frames. We elaborate this topic from different angles and show that they agree with each other. The resulting interpretation is expected to make it generally easier to establish semantic links between duration calculus and formalisms aimed at programming. Such semantic links are prerequisites for a solid underpinning of approaches to system development that cover requirement capture through coding using both duration calculus and some formalism(s) aimed at programming.

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Algebra of timed frames

Cited by 3 publications

References 8 publications

Process algebra for hybrid systems

Process algebra for hybrid systems

Discrete Time Process Algebra and the Semantics of SDL

Truth of Duration Calculus Formulae in Timed Frames

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