Develop probabilistic and information-theoretic formulations for extent actions

Develop probabilistic and information-theoretic formulations for extent actions of entities represented as spatiotemporal patterns in multivariate Markov chains, where actions at time t+1 differ in the set of occupied variables rather than only in their values, analogous to the existing formulations for value actions.

Background

The paper distinguishes between value actions (where entities differ only in their values at the next time-slice) and extent actions (where entities differ in the set of variables they occupy). While probabilistic and information-theoretic expressions are available for value actions, the authors note that no corresponding formulations have been developed for extent actions.

Providing such formulations would extend the analytical toolkit for STP-based entities and enable richer comparisons with PA-loop agents, which are limited to value actions.