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Modelling cooperating failure-resilient Processes

Rüdiger Valk

TL;DR

The subclass of regular cycloids describes cooperating sequential processes, and such cycloids are extended to cover failure resilience.

Abstract

Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and elementary information processing gates to the modelling of interacting sequential processes. The subclass of regular cycloids describes cooperating sequential processes. Such cycloids are extended to cover failure resilience.

Modelling cooperating failure-resilient Processes

TL;DR

The subclass of regular cycloids describes cooperating sequential processes, and such cycloids are extended to cover failure resilience.

Abstract

Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and elementary information processing gates to the modelling of interacting sequential processes. The subclass of regular cycloids describes cooperating sequential processes. Such cycloids are extended to cover failure resilience.
Paper Structure (5 sections, 18 theorems, 5 equations, 10 figures, 1 table)

This paper contains 5 sections, 18 theorems, 5 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Petri Space and Cycloids
  3. Regular Cycloids
  4. Stop-resilient Cycloids
  5. Conclusion

Key Result

theorem thmcountertheorem

The following cycloids are isomorphicBy a net isomorphism Reisig-Smith-87. to $\mathcal{C}(\alpha,\beta,\gamma,\delta)$: $\;\;\;$ a) $\mathcal{C}(\beta,\alpha,\delta,\gamma)$, $\;\;\;\;\;\;\;\;\;\;\;($The dual cycloid of $\mathcal{C}(\alpha,\beta,\gamma,\delta).)$$\;\;\;$ b) $\mathcal{C}(\alpha,\bet

Figures (10)

  • Figure 1: Three sequential processes synchronized by single-bit channels,
  • Figure 2: a) Petri space, b) circular traffic queue and c) time orthoid.
  • Figure 3: a) Fundamental parallelogram of $\mathcal{C}(4,2,2,3)$ and b) Petri space.
  • Figure 4: Cycloid $\mathcal{C}(4,3,3,3)$ in a) and with regular coordinates in b).
  • Figure 5: The regular cycloid system $\mathcal{C}( 3,2,1,4,M_0 ).$
  • ...and 5 more figures

Theorems & Definitions (42)

  • definition thmcounterdefinition: Valk-2019
  • definition thmcounterdefinition: Valk-2019
  • definition thmcounterdefinition: Valk-2019
  • theorem thmcountertheorem
  • theorem thmcountertheorem: Valk-2020valk-arXiv-algebra-2024
  • lemma thmcounterlemma: Valk-2019
  • theorem thmcountertheorem
  • proof
  • definition thmcounterdefinition: Valk-2019
  • definition thmcounterdefinition
  • ...and 32 more