RELATIONSHIPS AMONG PL, #L, AND THE DETERMINANT

摘要

Nous donnons une épreuve très simple d'un résultat de Jung; ceci montre que la classe PL ne change pas, même si l'on impose la condition que les machines n'utilisent que de temps polynomial. Nous recherchons aussi les relations entre PL, #L, et le déterminant, sous les notions de réducibilité diverses.%Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the determinant is characterized by the complexity of counting the number of accepting computations of a nondeterministic logspace-bounded machine. (This class of functions is known as #L.) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of a theorem of Jung, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.