# Relational Concurrent Refinement: Timed Refinement

Derrick, John and Boiten, Eerke Albert (2011) Relational Concurrent Refinement: Timed Refinement. In: Bruni, Roberto and Dingel, Juergen, eds. Formal Techniques for Distributed Systems Joint 13th IFIP WG 6.1 International Conference. Lecture Notes in Computer Science . Springer, Berlin, Germany, pp. 121-137. ISBN 978-3-642-21460-8. E-ISBN 978-3-642-21461-5. (doi:10.1007/978-3-642-21461-5_8)

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## Abstract

Data refinement in a state-based language such as Z is defined using a relational model in terms of the behaviour of abstract programs. Downward and upward simulation conditions form a sound and jointly complete methodology to verify relational data refinements, which can be checked on an event-by-event basis rather than per trace. In models of concurrency, refinement is often defined in terms of sets of observations, which can include the events a system is prepared to accept or refuse, or depend on explicit properties of states and transitions. By embedding such concurrent semantics into a relational one, eventwise verification methods for such refinement relations can be derived. In this paper we continue our program of deriving simulation conditions for process algebraic refinement by considering how notions of time should be embedded into a relational model, and thereby deriving relational notions of timed refinement.

Item Type: Book section 10.1007/978-3-642-21461-5_8 Data refinement, Z, simulations, timed-refinement Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming, Faculties > Sciences > School of Computing > Programming Languages and Systems Group E. Boiten 21 Sep 2012 09:49 UTC 29 May 2019 09:24 UTC https://kar.kent.ac.uk/id/eprint/30757 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-9184-8968