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Transition systems without transitions

Borzyszkowski A. M., Darondeau P.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

2003

Nr 964

1-7

We study the problem of embedding partial 2-structures into set 2-structures such that the target substructure is full and forward closed and it is minimal w.r.t. these properties.

Badamy problem takiego zanurzenia częściowej 2-struktury w 2-strukturę zbiorową, by docelowa 2-struktura była pełna, domknięta w przód i minimalna względem tych własności.

Finite completeness of categories of Petri nets

Bednarczyk M.A., Borzyszkowski A.M., Somla R.

Fundamenta Informaticae

2000

Vol. 43, Nr 1-4

21-48

The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equaliz-ers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. The main positive result of the paper states that reachable Petri nets with multiplica-tive morphisms form a finitely complete category. As an application of this result, some well-known categories are shown to be finitely complete. For instance, since all morphisms between reachable safe Petri nets are multiplicative, it follows that the category of reachable safe Petri nets is finitely complete.