Language-based comparison of petri nets with black tokens, pure names and ordered data

  • Authors:
  • Fernando Rosa-Velardo;Giorgio Delzanno

  • Affiliations:
  • Universidad Complutense de Madrid, Spain;Università di Genova, Italy

  • Venue:
  • LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
  • Year:
  • 2010

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Abstract

We apply language theory to compare the expressive power of models that extend Petri nets with features like colored tokens and/or whole place operations. Specifically, we consider extensions of Petri nets with transfer and reset operations defined for black indistinguishable tokens (Affine Well-Structured Nets), extensions in which tokens carry pure names dynamically generated with special ν-transitions (ν-APN), and extensions in which tokens carry data taken from a linearly ordered domain (Data nets and CMRS). These models are well-structured transitions systems. In order to compare these models we consider the families of languages they recognize, using coverability as accepting condition. With this criterion, we prove that ν-APNs are in between AWNs and Data Nets/CMRS. Moreover, we prove that the family of languages recognized by ν-APNs satisfies a good number of closure properties, being a semi-full AFL. These results extend the currently known classification of the expressive power of well-structured transition systems with new closure properties and new relations between extensions of Petri nets.