Petri Nets with Structured Data

Abstract

Abstract. This paper proposes Structured Data Nets (StDN), a Petri net extension that describes transactional systems with data. In StDNs, tokens are structured documents. Each transition is attached to a query, guarded by patterns, (logical assertions on the contents of its preset) and transforms tokens. We define StDNs and their semantics. We then consider their formal properties: coverability of a marking, termination and soundness of transactions. Unrestricted StDNs are Turing complete, so these properties are undecidable. We thus use an order on documents, and show that under reasonable restrictions on documents and on the expressiveness of patterns and queries, StDNs are well-structured transition systems, for which coverability, termination and soundness are decidable.

DB-Nets: On the Marriage of Colored Petri Nets and Relational Databases

“…In their original formulation, though, CPNs must be severely restricted when it comes to their formal analysis, in particular requiring color domains to be finite, and in principle allowing one to get rid of the data via propositionalization. Several data-aware fragments of high-level Petri nets that are amenable to formal analysis even in the case of infinite color domains have consequently been studied, ranging from nets where tokens carry single data values (as in data-and ν-nets [23,30]), to nets where tokens are associated to more complex data structures such as nested relations [18], nested terms [32], or XML documents [8]. The common, main issue of al such approaches is that data are still subsidiary to the control-flow dimension: data elements "locally" attached to tokens, without being connected to each other by a global, end-to-end data model.…”