Relaxing the past-to-future requirement in space-time reversibility

Determine whether the formal definition of space-time reversibility for local operators in space-time deterministic graph rewriting can be weakened so that an operator applied at position x does not necessarily map a past vertex at position x to a future vertex at the same position, while still admitting a backwards local inverse and preserving the locality axioms.

Background

The paper formalizes space-time reversibility for local operators within the framework of space-time deterministic graph rewriting. Under this definition, a reversible local operator necessarily transforms the positions of past vertices into those of future vertices, a property highlighted earlier in the text. The authors explicitly pose whether this requirement can be relaxed without breaking the notion of reversibility and its local inverse.

Relaxing this constraint would broaden the class of reversible rules and could impact how reversibility interacts with scheduling non-determinism and space-time determinism in asynchronous settings.