Inheritance of sufficient conditions for full consistency to the inverse

Ascertain whether the sufficient local conditions for full consistency of a forward commutative local rule in space-time deterministic graph rewriting—such as the privacy condition—are inherited by its commutative inverse local rule when the forward rule is space-time reversible.

Background

The authors prove that full consistency is inherited from a reversible, commutative forward local rule to its commutative inverse at the level of outcomes. They then ask whether the known sufficient conditions ensuring full consistency for forward rules, notably the 'privacy' condition from prior work, also carry over to the inverse rule itself.

Clarifying this would strengthen the structural understanding of reversibility by tying concrete forward-side design constraints directly to properties of the inverse operator.