Non-atomic Transition Firing in Contextual Nets

Abstract

The firing rule for Petri nets assumes instantaneous and simultaneous consumption and creation of tokens. In the context of ordinary Petri nets, this poses no particular problem because of the system's asynchronicity, even if token creation occurs later than token consumption in the firing. With read arcs, the situation changes, and several different choices of semantics are possible. The step semantics introduced by Janicki and Koutny can be seen as imposing a two-phase firing scheme: first, the presence of the required tokens is checked, then consumption and production of tokens happens. Pursuing this approach further, we develop a more general framework based on explicitly splitting the phases of firing, allowing to synthesize coherent steps. This turns out to define a more general non-atomic semantics, which has important potential for safety as it allows to detect errors that were missed by the previous semantics. Then we study the characterization of partial-order processes feasible under one or the other semantics.

Learning any memory-less discrete semantics for dynamical systems represented by logic programs

“…Meanwhile, the respective merits of existing synchronous, asynchronous and generalized semantics for the study of dynamic behaviors has been discussed by Chatain and Paulevé in a series of recent papers. In [7], they introduced a new semantics for Petri nets with read arcs, called the interval semantics. Then they adapted this semantics in the context of Boolean net-works [8], and showed in [6] how the interval semantics can capture additional behaviors with regard to the already existing semantics.…”

Non-deterministic updates of Boolean networks

“…From the concurrency theory, it is known that the execution of 1-bounded contextual Petri nets corresponding to the asynchronous updating mode (known as steps semantics) may miss some transitions that can be triggered when considering certain delay of state change [6,5].…”

Concurrency in Boolean networks

“…Interestingly, the introduction of read arcs in Petri nets has also led to several variants of the semantics. In this section, we present some of them, mainly taken from [14]. Next, relying on a natural encoding of BNs in RPNs (Sect.…”

“…Intuitively, the step semantics is somehow similar to the general asynchronous updating as it considers any set of fireable transitions; whereas the maximal step semantics which considers only maximal sets of fireable transitions is analoguous to the synchronous updating. We then recall the interval semantics introduced in [14], which allows a more liberal choice of checking and firing transitions in a set.…”