Complexity Models for Incremental Computation \Lambda

Abstract We present a new complexity theoretic approach to incremental computation. We define complexity classes that capture the intuitive notion of incremental efficiency and study their relation to existing complexity classes. We show that problems that have small sequential space complexity also have small incremental time complexity. We show that all common LOGSPACE-complete problems for P are also incr-POLYLOGTIME-complete for P. We introduce a restricted notion of completeness called NRP-completeness and show that problems which are NRP-complete for P are also incr-POLYLOGTIME-complete for P. We also give incrementally complete problems for NLOGSPACE, LOGSPACE, and non-uniform NC1. We show that under certain restrictions problems which have efficient dynamic solutions also have efficient parallel solutions. We also consider a non-uniform model of incremental computation and show that in this model most problems have almost linear complexity. In addition, we present some techniques for lower bounding the complexity of explicitly defined problems