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Using logic to solve the submodule construction problem

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Abstract

Submodule construction is the problem of finding a new submodule which, together with a given submodule, provides a behavior that conforms to a given desired global behavior. A new formulation of this problem and its solution in first-order logic is presented, and it is shown how the known solutions to this problem in the context of various communication paradigms and specification formalisms can be derived. Communication paradigms are: synchronous rendezvous at several interfaces; interleaved rendezvous; input/output automata with complete or partial behavior specifications and with synchronous or interleaved communication. A new algorithm for deriving a progressive solution is also presented.

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Acknowledgements

I would like to thank the late Philip Merlin with whom I started my work in the area of submodule construction. I would also like to thank Nina Yevtushenko (Tomsk University, Russia) for many discussions about submodule construction algorithms and the idea that a generalization of the concept could be found for different specification formalisms. I would also like to thank Bassel Daou for many inspiring discussions on the topic, and finally would like to mention that the work of my former PhD students Z.P. Tao and Jawad Drissi also contributed to my understanding of this problem.

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  1. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Ave (room 5082; delivery: room 5105), PO.Box 450, Stn A, Ottawa, ON, K1N 6N5, Canada

    Gregor v. Bochmann

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  1. Gregor v. Bochmann
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Correspondence to Gregor v. Bochmann.

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Some very preliminary version of this paper was written in September 2001 (not published); it was completely rewritten Fall 2008 and a small subset was published in FORTE 2009 (Bochmann 2009). This paper is a largely extended version of the 2008 paper. This work was partly supported by a research grant from the Natural Sciences and Engineering Research Council of Canada.

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Bochmann, G.v. Using logic to solve the submodule construction problem. Discrete Event Dyn Syst 23, 27–59 (2013). https://doi.org/10.1007/s10626-011-0127-6

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