The PL Hierarchy Collapses

Mitsunori Ogihara

Abstract: It is shown that the PL hierarchy PLH = PL,\bigcup\limits\, PLPL,\bigcup\limits\, PLPLPL,\bigcup\limits\, \cdots$, defined in terms of the Ruzzo--Simon--Tompa relativization, collapses to PL. MSC codes 68Q05 68Q10 68Q15 Keywords probabilistic complexity classes nondeterministic complexity classes logspace reducibility constant-depth circuits relativization