Concurrent Computing: from Petri Nets to Graph Grammars

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Functorial Semantics for Petri Nets under the Individual Token Philosophy

Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of net

Nondeterminism and Guarded Commands

The purpose of this paper is to discuss the relevance of nondeterminism in computer science, with a special emphasis on Dijkstra's guarded commands language.Comment: 34 pages. This is authors' version of Chapter 8 of the book K.R. Apt and C.A.R. Hoare (editors), Edsger Wybe Dijkstra: His Life, Work, and Legacy, volume 45 of ACM Books. ACM/Morgan & Claypool, 202

Complexity analysis of reactive graph grammars

The aim of this paper is to present a way to calculate a complexity measurement of graph grammar specifications of reactive systems. The basic operation that describe the behavior of a graph grammar is a rule application. Therefore, this operation will be used to characterize the tasks to be performed within a system. The complexity measurement defined here ,vill give us the minimum numbei:· of steps that must be present in a computation that performs a desir_ed task