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A Language-Based Comparison of Extensions of Petri Nets with and without Whole-Place Operations
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
On the efficient computation of the minimal coverability set for Petri nets
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
A classification of the expressive power of well-structured transition systems
Information and Computation
Ordinal theory for expressiveness of well structured transition systems
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Forward analysis and model checking for trace bounded WSTS
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
Language-based comparison of petri nets with black tokens, pure names and ordered data
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
The Ordinal-Recursive Complexity of Timed-arc Petri Nets, Data Nets, and Other Enriched Nets
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
The theory of WSTS: the case of complete WSTS
PETRI NETS'12 Proceedings of the 33rd international conference on Application and Theory of Petri Nets
On the coverability and reachability languages of monotonic extensions of Petri nets
Theoretical Computer Science
Ordinal theory for expressiveness of well-structured transition systems
Information and Computation
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This paper introduces the notion of well-structured language. A well-structured language can be defined by a labelled well-structured transition system, equipped with an upward-closed set of accepting states. That peculiar class of transition systems has been extensively studied in the field of computer-aided verification, where it has direct an important applications. Petri nets, and their monotonic extensions (like Petri nets with non-blocking arcs or Petri nets with transfer arcs), for instance, are special subclasses of well-structured transition systems. We show that the class of well-structured languages enjoy several important closure properties. We propose several pumping lemmata that are applicable respectively to the whole class of well-structured languages and to the classes of languages recognized by Petri nets or Petri nets with non-blocking arcs. These pumping lemmata allow us to characterize the limits in the expressiveness of these classes of language. Furthermore, we exploit the pumping lemmata to strictly separate the expressive power of Petri nets, Petri nets with non-blocking arcs and Petri nets with transfer arcs.