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.
Bernardinello, L. (2021). Topics in Region Theory and Synthesis Problems. In Application and Theory of Petri Nets and Concurrency 42nd International Conference, PETRI NETS 2021, Virtual Event, June 23–25, 2021, Proceedings (pp.3-16). Springer Science and Business Media Deutschland GmbH [10.1007/978-3-030-76983-3_1].
Topics in Region Theory and Synthesis Problems
Bernardinello, L
2021
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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