Abstract
Reversal complexity has been studied as a fundamental computational resource along with time and space complexity. We revisit it by contrasting with access complexity which we introduce in this study. First, we study the structure of space bounded reversal and access complexity classes. We characterize the complexity classes L, P and PSPACE in terms of space bounded reversal and access complexity classes. We also show that the difference between polynomial space bounded reversal and access complexity is related with the L versus P problem. Moreover, we introduce a theory of memory access patterns, which is an abstracted structure of the order of memory accesses during a random access computation, and extend the notion of reversal and access complexity for general random access computational models. Then, we give probabilistic analyses of reversal and access complexity for almost all memory access patterns. In particular, we prove that almost all memory access patterns have ω(log n) reversal complexity while all languages in L are computable within O(log n) reversal complexity.
