Discrete Event Dynamic Systems

, Volume 23, Issue 1, pp 27–59 | Cite as

Using logic to solve the submodule construction problem

  • Gregor v. Bochmann


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.


Component design Equation solving Submodule construction Derivation of component behavior State machines Labeled transition systems Input/output automata First-order logic Discrete event control systems 

Mathematics Subject Classification




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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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceUniversity of OttawaOttawaCanada

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