Computational Complexity of Random Access Models

摘要

The relative power of several computational models is considered in this thesis.These models are the Turning machine and its multidimensional variant, the random access machine (RAM), the tree machine, and the pointer machine. The basic computational properties of the pointer machine are examined in more detail. For example, time and space hierarchy theorems for pointer machines are presented. Every Turning machine of time complexity t and space complexity s can be simulated by a pointer machine of time complexity O(t) using O(s/log s) nodes. This strengthens a similar result by van Emde Boas (1989). Every alternating pointer machine of time complexity t can be simulated by a deterministic pointer machine using O(t/log t) nodes. Other results concerning nondeterministic and alternating pointer machines are presented. Every tree machine of time complexity t can be simulated on-line by a log-cost RAM of time complexity O((t log t)/log log t). (KR)