Denotational semantics in the cpo and metric approach

Baier, Christel; Majster-Cederbaum, Mila

doi:10.1016/0304-3975(94)00046-8

Cited by 32 publications

(34 citation statements)

References 4 publications

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“…e.g. the sequence operator on prime event structures [1]). vVe do not see a way to formalize the 'maximal computations' of the elements in branching time models.…”

Section: Resultsmentioning

confidence: 99%

“…Our aim is to give a denotational semantics Me for Prag on some powerdomain construction of M such that Me(P) can be viewed as the set of maximal computations of P. By our results in [1] we need a suitablepowerdomain P,. (M) which is a complete metric space and which is endowed with semantkoperators as follows:…”

Section: A Denotationallinear Time Semantics On Pco(m)mentioning

confidence: 99%

“…• there is a binary non-distance-increasing operator + on P*(M) As shown in [1]: Under the assumptions of above there is a unique meaning function which satisfies:…”

Section: (M)mentioning

confidence: 99%

“…• Mecms(P I ; P 2 ) = Mecms(Pd~Me cms (p 2 ) • Mecms(P I + P 2 ) = Mecms(P I ) + Me crns (p 2 ) • lV1e cms (w(P I , ... , P k )) = w(Mecms(P I ), ..…”

Section: (M)mentioning

confidence: 99%

“…As shown in [1]: Under these assumptions there is aleast meaning function • MeCPO(P[; P 2 ) = MeCPO(Pt};-Me CP O(P 2 )…”

Section: P (D)mentioning

confidence: 99%

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Denotational linear time semantics and sequential composition

Baier

Majster-Cederbaum

1996

Information Processing Letters

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This paper focuses on the issue of modelling sequential composition in denotational linear time semantics for (nondeterministieJ languages which admit infinite computations. This operator deserves special attention as it causes problems to meet the requirements of a standard denotational semantics based on metric or cpo. We present a general framework for the treatment of sequential composition. It turns out that a pro gram can be described by its maximal computations in the metric approach whereas the partial order approach is suitable to describe a program by all its partial computations.

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“…e.g. the sequence operator on prime event structures [1]). vVe do not see a way to formalize the 'maximal computations' of the elements in branching time models.…”

Section: Resultsmentioning

confidence: 99%

Section: A Denotationallinear Time Semantics On Pco(m)mentioning

confidence: 99%

“…• there is a binary non-distance-increasing operator + on P*(M) As shown in [1]: Under the assumptions of above there is a unique meaning function which satisfies:…”

Section: (M)mentioning

confidence: 99%

“…• Mecms(P I ; P 2 ) = Mecms(Pd~Me cms (p 2 ) • Mecms(P I + P 2 ) = Mecms(P I ) + Me crns (p 2 ) • lV1e cms (w(P I , ... , P k )) = w(Mecms(P I ), ..…”

Section: (M)mentioning

confidence: 99%

“…As shown in [1]: Under these assumptions there is aleast meaning function • MeCPO(P[; P 2 ) = MeCPO(Pt};-Me CP O(P 2 )…”

Section: P (D)mentioning

confidence: 99%

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Denotational linear time semantics and sequential composition

Baier

Majster-Cederbaum

1996

Information Processing Letters

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Modeling Timed Concurrent Systems

Liu

Matsikoudis

Lee

2006

CONCUR 2006 – Concurrency Theory

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Timed concurrent systems are widely used in concurrent and distributed real-time software, modeling of hybrid systems, design of hardware systems (using hardware description languages), discrete-event simulation, and modeling of communication networks. They consist of concurrent components that communicate using timed signals, that is, sets of (semantically) time-stamped events. The denotational semantics of such systems is traditionally formulated in a metric space, wherein causal components are modeled as contracting functions. We show that this formulation excessively restricts the models of time that can be used. In particular, it cannot handle super-dense time, commonly used in hardware description languages and hybrid systems modeling, finite time lines, and time with no origin. Moreover, if we admit continuoustime and mixed signals (essential for hybrid systems modeling) or certain Zeno signals, then causality is no longer equivalent to its formalization in terms of contracting functions. In this paper, we offer an alternative semantic framework using a generalized ultrametric that overcomes these limitations.

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Concurrent Semantics Without the Notions of State or State Transitions

Lee

2006

Lecture Notes in Computer Science

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This paper argues that basing the semantics of concurrent systems on the notions of state and state transitions is neither advisable nor necessary. The tendency to do this is deeply rooted in our notions of computation, but these roots have proved problematic in concurrent software in general, where they have led to such poor programming practice as threads. I review approaches (some of which have been around for some time) to the semantics of concurrent programs that rely on neither state nor state transitions. Specifically, these approaches rely on a broadened notion of computation consisting of interacting components. The semantics of a concurrent compositions of such components generally reduces to a fixed point problem. Two families of fixed point problems have emerged, one based on metric spaces and their generalizations, and the other based on domain theories. The purpose of this paper is to argue for these approaches over those based on transition systems, which require the notion of state.

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Denotational semantics in the cpo and metric approach

Cited by 32 publications

References 4 publications

Denotational linear time semantics and sequential composition

Denotational linear time semantics and sequential composition

Modeling Timed Concurrent Systems

Concurrent Semantics Without the Notions of State or State Transitions

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