  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.
