A generalization of resource-bounded measure, with application to the BPP vs. EXP problem

H Buhrman, D Van Melkebeek, KW Regan… - SIAM Journal on …, 2000 - SIAM
We introduce resource-bounded betting games and propose a generalization of Lutz's
resource-bounded measure in which the choice of the next string to bet on is fully adaptive.
Lutz's martingales are equivalent to betting games constrained to bet on strings in
lexicographic order. We show that if strong pseudorandom number generators exist, then
betting games are equivalent to martingales for measure on E and EXP. However, we
construct betting games that succeed on certain classes whose Lutz measures are important …

[PDF][PDF] A GENERALIZATION OF RESOURCE-BOUNDED MEASURE, WITH APPLICATION TO THE BPP VS. EXP PROBLEM

H Bl'HHl, AND VAN, KWR IELKEBEEKt - 2000 - core.ac.uk
\Ye introduce resource-hounded betting games and propose a gm: 1eralizatio: 1 of Lutz:
sn·,; oarc,•-bounded measure in which the choice of the next string to bet on is fully adaptive.
Lutz s! llart ingales an• equivalent to betting games constrained to bet on string~ in
lexicographic~ rder. We slio\\· that if strong pseudorandom number generators exist, then
betting games are eqmvalent to martiugalt's for measure on E and EXP. However, we
construct betting gan1es that su. ccee. d on certam class<'S whos<'Lutz mea-, ures are …
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