Searching constant width mazes captures the AC0 hierarchy
We show that searching a width k maze is complete for Πk, i.e., for the k'th level of the AC0 hierarchy. Equivalently, st-connectivity for width k grid graphs is complete for Πk. As an application, we show that there is a data structure solving dynamic st-connectivity for con stant width grid graphs with time bound O(log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools.
Unable to display preview. Download preview PDF.
- 1.D. A. M. Barrington, N. Immerman and H. Straubing. On uniformity within NC 1 Journal of Computer and System Sciences, 4(3):274–306.Google Scholar
- 3.P. Beame and F. Fich. On searching sorted lists: A near-optimal lower bound. Manuscript, 1997.Google Scholar
- 4.M. Blum and D. Kozen. On the power of the compass (or why mazes are easier to search than graphs). In 19th Annual Symposium on the Foundations of Computer Science, pages 132–142, October 1978.Google Scholar
- 5.D. Eppstein. Dynamic connectivity in digital images. Technical Report 96-13, Univ. of California, Irvine, Department of Information and Computer Science, 1996.Google Scholar
- 8.T. Husfeldt and T. Rauhe. Hardness results for dynamic problems by extensions of Fredman annd Saks chronogram method.. Manuscript, 1997.Google Scholar
- 13.A. A. Razborov. Lower Bounds for deterministic and nondeterministic branching programs. In L. Budach, ed., Fundamentals of Computation Theory, 8th International Conference: FCT '91. Lecture Notes in Computer Science 529, 47–60. Berlin, Springer Verlag, 1991.Google Scholar
- 14.M. Sipser. Borel sets and circuit complexity. In Proceedings, 15th ACM Symposium on the Theory of Computing, 1983, 61–69.Google Scholar