Measure on P: Robustness of the Notion

In AS , we de ned a notion of measure on the complexity class P in the spirit of the work of Lutz L92 that provides a notion of measure on complexity classes at least as large as E, and the work of Mayordomo M that provides a measure on PSPACE. In this paper, we show that several other ways of de ning measure in terms of covers and martingalesyield precisely the samenotion as in AS . Similar robustness" results have been obtained previously for the notions of measure de ned by L92 and M , but for reasons that will become apparent below di erent proofs are required in our setting. To our surprise, and in contrast to the measures of Lutz L92 and Mayordomo M , one obtains strictly more measurable sets if one considers nonconservative" martingales that succeed merely in the limsup rather than having a limitof in nity. For example, it is shown in AS that the class of sparse sets does not have measure zero in P, whereas here we show that using the nonconservative" measure...

• Type: Conference
• Year: 1995
• Where: MFCS
• Authors: Eric Allender, Martin Strauss
• Keywords: Complexity Class, Lutz L92, Measure Zero, MFCS 1995, Theoretical Computer Science