Spatial complexity of reversibly computable DAG

Abstract

In this paper we address the issue of making a program reversible in terms of spatial complexity. Spatial complexity is the amount of memory/register locations required for performing the computation in both forward and backward directions. Spatial complexity has important relationship with the intrinsics power consumption required at run time; this was our primary motivation. But it has also important relationship with the trade off between storing or recomputing reused intermediate values, also known as the rematerialization problem in the context of compiler register allocation, or the checkpointing issue in the general case. We present a lower bound of the spatial complexity of a DAG (directed acyclic graph) with reversible operations, as well as a heuristic aimed at finding the minimum number of registers required for a forward and backward execution of a DAG . We define energetic garbage as the additional number of registers needed for the reversible computation with respect to the original computation. We have run experiments that suggest that the garbage size is never more than 50% of the DAG size for DAGs with unary/binary operations.