May 10, 2021

Amélia Durbec (LIS, Aix Marseille University)

Consider a network that evolves reversibly, according to
nearest neighbours interactions. Can its dynamics create/destroy nodes?
On the one hand, since the nodes are the principal carriers of information,
it seems that they cannot be destroyed without jeopardising bijectivity.
On the other hand, there are plenty of global functions from graphs to
graphs that are non-vertex-preserving and bijective. The question has
been answered negatively—in three different ways. Yet, in this paper we
do obtain reversible local node creation/destruction—in three relaxed
settings, whose equivalence we prove for robustness. We motivate our
work both by theoretical computer science considerations (reversible
computing, cellular automata extensions) and theoretical physics concerns
(basic formalisms towards discrete quantum gravity).