Complexity and mission computability of adaptive computing systems

Abstract

There is a subset of computational problems that existing algorithms may not complete due to a lack of adequate computational resources on tactical edge computing platforms. Although this subset is computable in polynomial time, many polynomial problems are not computable in mission time. Here, we define a subclass of deterministic polynomial time complexity called mission class, wherein the computations must complete in mission time. By focusing on this subclass of languages in the context of successful military applications, we discuss their computational and network constraints. We investigate feasible (non)linear models that will minimize energy and maximize memory, efficiency, and computational power, and also provide an approximate solution obtained within a pre-determined length of computation time using limited resources so that an optimal solution to a language could be determined.