A Dynamic Approach to Timed Behaviour

Gunawardena, Jeremy

doi:10.1007/978-3-540-48654-1_17

Cited by 9 publications

(7 citation statements)

References 9 publications

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“…The results described in this section include some powerful applications of topology in distributed computing, particularly for proving impossibility results. Other connections between topology and distributed computing have been discussed in the literature (see [152,157,204,268]). …”

Section: Topologymentioning

confidence: 99%

Hundreds of impossibility results for distributed computing

Fich

Ruppert

2003

Distributed Computing

124

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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing. There is a strong emphasis in our presentation on explaining the wide variety of techniques that are used to obtain the results described.

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Section: Topologymentioning

confidence: 99%

Hundreds of impossibility results for distributed computing

Fich

Ruppert

2003

Distributed Computing

124

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“…As the sequence i k À k is increasing, there exists t 2 ½0, s such that i k ¼ k for all k4t and i k 5k þ 1 for all k > t. Note that y i 5a ii x i 5x i =K for all i. Combining this with inequality (27), we obtain By the Hardy-Littlewood-Polya theorem, these inequalities, combined with (26), show that y is indeed in P N ðK Þ. oe…”

Section: Stochastic Products Of Max-plus Functionsmentioning

confidence: 81%

“…ð f Þ is a lattice morphism from UTpðR S , RÞ to R S . This statement is essentially equivalent to the 'duality theorem' by Gaubert and Gunawardena about 'rectangular' families of min-max-plus functions [10,25,26].…”

Section: The Selection Principlementioning

confidence: 82%

Finite-range topical functions and uniformly topical functions

Bousch

Mairesse

2006

Dynamical Systems

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We introduce a remarkable subclass of the class of topical functions, the class of uniformly topical functions, whose dynamical behaviour is investigated. Every uniformly topical endofunction has a spectral vector, related to some special fixed points (possibly at infinity), about which we establish various properties. In the stochastic case, we prove a multiplicative ergodic theorem, asserting that the stochastic spectral vector exists in all cases.

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“…Timed extensions of partial-order models have received scant attention in the literature. Extensions of pomsets [12], configurations [26], event structures [29], posets [18], {and, or}-automata [16] and higher-dimensional automata [15] are known to us. Our approach resembles that of [14].…”

Section: Related Workmentioning

confidence: 99%

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Katoen

Langerak

Brinksma

et al. 1998

Formal Methods in System Design

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This paper discusses a timed variant of a process algebra akin to LOTOS, baptized UPA, in a causalitybased setting. Two timed features are incorporated-a delay function which constrains the occurrence time of atomic actions and an urgency operator that forces (local or synchronized) actions to happen urgently. Timeouts are typical urgent phenomena. A novel timed extension of event structures is introduced and used as a vehicle to provide a denotational causality-based semantics for UPA. Recursion is dealt with by using standard fixpoint theory. In addition, an operational semantics is presented based on separate time-and action-transitions that is shown to be consistent with the event structure semantics. An interleaving semantics for UPA is immediately obtained from the operational semantics. By adopting this dual approach the well-developed timed interleaving view is extended with a consistent timed partial order view and a comparison is facilitated of the partial order model and the variety of existing (interleaved) timed process algebras.

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A Dynamic Approach to Timed Behaviour

Cited by 9 publications

References 9 publications

Hundreds of impossibility results for distributed computing

Hundreds of impossibility results for distributed computing

Finite-range topical functions and uniformly topical functions

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