Token Multiplicity in Reversing Petri Nets Under the Individual Token Interpretation

TL;DR

This paper extends Reversing Petri Nets to allow multiple tokens of the same type distinguished by causal paths, developing a causal semantics and proving their expressive equivalence to single-token RPNs.

Contribution

It introduces multiple tokens in RPNs under the individual token interpretation and establishes their expressive power equivalence to single-token RPNs.

Findings

Developed a causal semantics for multi-token RPNs

Proved isomorphism between multi-token and single-token RPNs' LTSs

Showed expressive power equivalence of both models

Abstract

Reversing Petri nets (RPNs) have recently been proposed as a net-basedapproach to model causal and out-of-causal order reversibility. They are based on the notion of individual tokens that can be connected together via bonds. In this paper we extend RPNs by allowing multiple tokens of the same type to exist within a net based on the individual token interpretation of Petri nets. According to this interpretation, tokens of the same type are distinguished via their causal path. We develop a causal semantics of the model and we prove that the expressive power of RPNs with multiple tokens is equivalent to that of RPNs with single tokens by establishing an isomporphism between the Labelled Transition Systems (LTSs) capturing the reachable parts of the respective RPN models.