Strict sequential P-completeness
In this paper we present a new notion of what it means for a problem in P to be inherently sequential. Informally, a problem L is strictly sequential P-complete if when the best known sequential algorithm for L has polynomial speedup by parallelization, this implies that all problems in P have a polynomial speedup in the parallel setting. The motivation for defining this class of problems is to try and capture the problems in P that axe truly inherently sequential. Our work extends the results of Condon who exhibited problems such that if a polynomial speedup of their best known parallel algorithms could be achieved, then all problems in P would have polynomial speedup. We demonstrate one such natural problem, namely the Multiplex-select Circuit Problem (MCP). MCP has one of the highest degrees of sequentiality of any problem yet defined. On the way to proving MCP is strictly sequential P-complete, we define an interesting model, the register stack machine, that appears to be of independent interest for exploring pure sequentiality.
Unable to display preview. Download preview PDF.
- [Con92]A. Condon. A theory of strict P-completeness. In Proceedings of the 9th Symposium on Theoretical Aspects of Computer Science, number 577 in Lecture Notes in Computer Science, pages 33–44. Springer-Verlag, 1992.Google Scholar
- [FLR96]H. Fernau, K.-J. Lange, and K. Reinhardt. Advocating ownership. In V. Chandra, editor, Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science, volume 1180 of Lecture Notes in Computer Science, pages 286–297. Springer, December 1996.Google Scholar
- [GHR95]R. Greenlaw, H. J. Hoover, and W. L. Ruzzo. Limits to parallel computation: P-completeness theory. New York u.a., Oxford Univ. Pr., 1995.Google Scholar
- [HU79]J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.Google Scholar
- [LN93]K.-J. Lange and R. Niedermeier. Data-independences of parallel random access machines. In R. K. Shyamasundar, editor, Proceedings of the 13th Conference on Foundations of Software Technology and Theory of Computer Science, number 761 in Lecture Notes in Computer Science, pages 104–113, Bombay, India, December 1993. Springer-Verlag.Google Scholar
- [VS86]J. S. Vitter and R. A. Simons. New classes for parallel complexity: A study of unification and other complete problems for P. IEEE Transactions on Computers, C-35(5):403–418, 1986.Google Scholar
- [Wie90]J. Wiedermann. Normalizing and accelerating RAM computations and the problem of reasonable space measures. In M.S. Paterson, editor, Proceedings of the 17th ICALP (Warwick University, England, July 1990), LNCS 443, pages 125–138. EATCS, Springer-Verlag, 1990.Google Scholar