Abstract
Regions, as introduced by Ehrenfeucht and Rozenberg more than thirty years ago, have been used as a fundamental tool in synthesis problems, where a Petri net of a specific type must be built from a specification given in terms of a transition system. Some topics emerged in the research on regions are discussed, and a few open problems are stated. In particular, the paper focuses on three areas: (1) the notion of ‘type of nets’ as a tool for unifying the theory of regions, and as a notion leading to new variants of Petri nets; (2) the algebraic aspects of region theory; (3) the proposal of a new type of regions, inspired by reaction systems, and the potential for studying problems of synthesis of reaction systems.
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Acknowledgments
Many colleagues and friends have contributed to shape my views on concurrency theory and on region theory during more than twenty-five years. I gratefully acknowledge the pleasure I took working with them, even if they are too many to mention. I feel I can make an exception for Philippe Darondeau, who will not be able to apply his rigour and scientific perspicacity to comment on these pages.
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Bernardinello, L. (2021). Topics in Region Theory and Synthesis Problems. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_1
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DOI: https://doi.org/10.1007/978-3-030-76983-3_1
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