Abstract
Action systems are a framework for reasoning about discrete reactive systems. Back, Petre and Porres have extended these action systems to continuous action systems, which can be used to model hybrid systems. In this paper we define a refinement relation, and develop practical data refinement rules for continuous action systems.
The meaning of continuous action systems is expressed in terms of a mapping from continuous action systems to action systems. First, we present a new mapping from continuous action systems to action systems, such that Back’s definition of trace refinement is correct with respect to it. Second, we present a stream semantics that is compatible with the trace semantics, but is preferable to it because it is more general. Although action system trace refinement rules are applicable to continuous action systems with a stream semantics, they are not complete. Finally, we introduce a new data refinement rule that is valid with respect to the stream semantics and can be used to prove refinements that are not possible in the trace semantics, and we analyse the completeness of our new rule in conjunction with the existing trace refinement rules.
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Back, R.-J., Petre, L., Porres, I.: Generalizing action systems to hybrid systems. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 202–213. Springer, Heidelberg (2000)
Back, R.-J., von Wright, J.: Trace refinement of action systems. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 367–384. Springer, Heidelberg (1994)
Back, R.-J., von Wright, J.: Refinement Calculus: A Systematic Introduction. Springer, Heidelberg (1998)
Back, R.-J., Kurki-Suonio, R.: Decentralization of process nets with centralized control. In: Proc. of 2nd ACM SIGACT-SIGOPS Symp. on Principles of Distributed Computing, PODC 1983, pp. 131–142. ACM Press, New York (1983)
Back, R.-J., Kurki-Suonio, R.: Distributed cooperation with action systems. ACM Trans. on Program. Lang. and Syst. 10(4), 513–554 (1988)
Back, R.-J., von Wright, J.: Reasoning algebraically about loops. Acta Inform. 36(4), 295–334 (1999)
Cohen, E.: Hypotheses in Kleene algebra. Techn. Report TM-ARH-023814. Belcore (1994)
Cohen, E.: Separation and reduction. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837. Springer, Heidelberg (2000)
Dijkstra, E.W.: A Discipline of Programming. Prentice Hall, Englewood Cliffs (1976)
Hayes, I.J.: Reasoning about real-time repetitions: Terminating and non-terminating. Sci. of Comput. Program. 43(2-3), 161–192 (2002)
Hayes, I.J.: Programs as paths: An approach to timing constraint analysis. In: Dong, J.S., Woodcock, J. (eds.) ICFEM 2003. LNCS, vol. 2885, pp. 1–15. Springer, Heidelberg (2003)
Kozen, D.: Kleene algebra with tests. ACM Trans. on Program. Lang. and Syst. 19(3), 427–443 (1997)
Morgan, C.: Programming from Specifications, 2nd edn. Prentice Hall, Englewood Cliffs (1994)
von Wright, J.: From Kleene algebra to refinement algebra. In: Boiten, E.A., Möller, B. (eds.) MPC 2002. LNCS, vol. 2386, pp. 233–262. Springer, Heidelberg (2002)
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Meinicke, L., Hayes, I.J. (2006). Continuous Action System Refinement. In: Uustalu, T. (eds) Mathematics of Program Construction. MPC 2006. Lecture Notes in Computer Science, vol 4014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11783596_19
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DOI: https://doi.org/10.1007/11783596_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35631-8
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