Acyclic and Cyclic Reversing Computations in Petri Nets

Reversible computations constitute an unconventional form of computing where any sequence of performed operations can be undone by executing in reverse order at any point during a computation. It has been attracting increasing attention as it provides opportunities for low-power computation, being at the same time essential or eligible in various applications. In recent work, we have proposed a structural way of translating Reversing Petri Nets (RPNs) - a type of Petri nets that embeds reversible computation, to bounded Coloured Petri Nets (CPNs) - an extension of traditional Petri Nets, where tokens carry data values. Three reversing semantics are possible in RPNs: backtracking (reversing of the lately executed action), causal reversing (action can be reversed only when all its effects have been undone) and out of causal reversing (any previously performed action can be reversed). In this paper, we extend the RPN to CPN translation with formal proofs of correctness. Moreover, the possibility of introduction of cycles to RPNs is discussed. We analyze which type of cycles could be allowed in RPNs to ensure consistency with the current semantics. It emerged that the most interesting case related to cycles in RPNs occurs in causal semantics, where various interpretations of dependency result in different net's behaviour during reversing. Three definitions of dependence are presented and discussed.