Computational spacetimes

Abstract

The execution of an algorithm is limited by physical constraints rooted in the finite speed of signal propagation. To optimize the usage of the physical degrees of freedom provided by a computational engine, one must apply all relevant technological and physical constraints to the temporal and spatial structure of a computational procedure. Computational spacetimes make explicit both technological and physical constraints, and facilitate reasoning about the relative efficiency of parallel algorithms through explicit physical complexity measures. Similar to Minkowski spacetime being the world model for physical events, computational spacetimes are the world model for computational events. Algorithms are specified in a spatial single-assignment form, which makes all assignments spatially explicit. The computational spacetime and the spatial single-assignment form provide the framework for the design, analysis and execution of fine-grain parallel algorithms.<>