Abstract
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.
This research has been supported by the DFG Project La 618/3-1 KOMET.
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Reinhardt, K. (1997). Strict sequential P-completeness. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023470
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DOI: https://doi.org/10.1007/BFb0023470
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