Reversible Computation in Petri Nets

Abstract: Reversible computation is an unconventional form of computing that extends the standard forward-only mode of computation with the ability to execute a sequence of operations in reverse at any point during computation. As such, in this thesis we propose a reversible approach to Petri nets by introducing machinery and associated operational semantics to tackle the challenges of the main forms of reversibility. Our proposal concerns a variation of cyclic Petri nets, called Reversing Petri Nets (RPNs) where tokens are persistent and distinguished from each other by an identity. An immediate extension of the original model includes allowing multiple tokens of the same base/type to occur in a model. Specifically, we explore the individual token interpretation where one distinguishes different tokens residing in the same place by keeping track of where they come from. We also propose the collective token interpretation, as the opposite approach to token ambiguity, which considers all tokens of a certain type to be identical, disregarding their history during execution. Both of the proposed models of RPNs (with single or multi tokens) implement the notion of uncontrolled reversibility, meaning that it specifies how to reverse an execution and allows to do so freely, yet it places no restrictions as to when and whether to prefer backward execution over forward execution or vice versa. In this respect, a further aim is to control reversibility by extending our formal semantics where transitions are associated with conditions whose satisfaction allows the execution of transitions in the forward/reversed direction.