Abstract

Event structures are a prominent model for non-interleaving concurrency. The use of event structures for providing a compositional non-interleaving semantics to LOTOS without data is studied. In particular, several quantitative extensions of event structures are proposed that incorporate notions like time – both of deterministic and stochastic nature – and probability. The suitability of these models for giving a non-interleaving semantics to a timed, stochastic and probabilistic extension of LOTOS is investigated. Consistency between the event structure semantics and an (event-based) operational semantics is addressed for the different quantitative variants of LOTOS and is worked out for the timed case in more detail. These consistency results facilitate the coherent use of an interleaving and a non-interleaving semantic view in a single design trajectory and provide a justification for the event structure semantics. As a running example an infinite buffer is used in which gradually timing constraints on latency and rates of accepting and producing data and the probability of loss of messages are incorporated.

Author Keywords: Deterministic time; Event structures; Probability; Process algebra; Semantics; Stochastic time; True concurrency

Article Outline

1. Introduction

2. Basic LOTOS and event structures

2.1. Basic LOTOS

2.2. Event structures

2.3. Non-interleaving semantics for Basic LOTOS

3. Adding time to event structures

3.1. A simple operator: timed action-prefix

3.2. Timed event structures

3.3. A non-interleaving timed semantics

3.4. Timed event-based operational semantics

3.5. Other timed operators

4. Stochastic timing

5. Probabilistic behaviours

6. Related work

6.1. Partial-order models for LOTOS

6.2. Other brands of event structures

6.3. Time in partial-order models

6.4. Timed process algebras

6.5. Stochastic process algebras

6.6. Probabilistic process algebras

6.7. Consistency of semantics

7. Conclusions

Acknowledgements

References

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