On Transfinite Hybrid Automata

Nakamura, Katsunori; Fusaoka, Akira

doi:10.1007/978-3-540-31954-2_32

Cited by 8 publications

(3 citation statements)

References 14 publications

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“…This requires infinitely many iterations, but the process is finite in terms of physical time, because each iteration gets progressively shorter. This yields an example of Zeno behaviour [16,23,32], which is often dismissed in the hybrid systems literature, as justified by the fact that such behaviour is on the one hand not computationally realisable, and on the other hand notoriously difficult to analyse. Here, we commit ourselves to the task of faithful modelling Zeno behaviour as an inherent feature of physical, biological and other systems.…”

Section: A While-language For Hybrid Computationmentioning

confidence: 99%

An Adequate While-Language for Hybrid Computation

Goncharov

Neves

2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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Hybrid computation harbours discrete and continuous dynamics in the form of an entangled mixture, inherently present in various natural phenomena and in applications ranging from control theory to microbiology. The emergent behaviours bear signs of both computational and physical processes, and thus present difficulties not only in their analysis, but also in describing them adequately in a structural, well-founded way.In order to tackle these issues and, more generally, to investigate hybridness as a dedicated computational phenomenon, we introduce a while-language for hybrid computation inspired by the fine-grain call-by-value paradigm. We equip it with operational and computationally adequate denotational semantics. The latter crucially relies on a hybrid monad supporting an (Elgot) iteration operator that we developed elsewhere. As an intermediate step, we introduce a more lightweight duration semantics furnished with analogous results and based on a new duration monad that we introduce as a lightweight counterpart to the hybrid monad. CCS CONCEPTS• Theory of computation → Timed and hybrid models.

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Section: A While-language For Hybrid Computationmentioning

confidence: 99%

An Adequate While-Language for Hybrid Computation

Goncharov

Neves

2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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“…In this context, hybrid computations can be seen as computations extended in time. might produce open trajectories r0, dq Ñ X that we cannot sensibly extend into r0, ds Ñ X without assuming some structure on X [17,18,23]. Furthermore, we introduce a variant of H `, which we call H and which extends the facilities of H `even further by including the empty trajectory r0, 0q Ñ X which will be used to accommodate non-progressive divergent computation (see Remark 11).…”

Section: A Fistful Of Hybrid Monadsmentioning

confidence: 99%

A Semantics for Hybrid Iteration

Goncharov,

Jakob,

Neves

2018

Preprint

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The recently introduced notions of guarded traced (monoidal) category and guarded (pre-)iterative monad aim at unifying different instances of partial iteration whilst keeping in touch with the established theory of total iteration and preserving its merits. In this paper we use these notions and the corresponding stock of results to examine different types of iteration for hybrid computation. As a starting point we use an available notion of hybrid monad restricted to the category of sets, and modify it in order to obtain a suitable notion of guarded iteration with guardedness interpreted as progressiveness in time -we motivate this modification by our intention to capture Zeno behaviour in an arguably general and feasible way. We illustrate our results with a simple programming language for hybrid computation which is interpreted over the developed semantic foundations.

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“…Hence A ω = A ω • reflects the fact that, operationally, after a Zeno gap the behaviour doesn't matter, since the gap cannot be "crossed" anyway. For a discussion of these phenomena in the context of hybrid automata see [44].…”

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confidence: 99%