Inductive counting below LOGSPACE

We apply inductive counting to nondeterministic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. We obtain for arbitrary space bounds s(n) that the alternation hierarchy of nonuniform O(s(n)) space bounded Turing machines collapses to its first level. This improves the previously known result of Immermann and Szelepcsenyi to space bounds of order o(logn) in the nonuniform setting. This reveals a strong difference to the relations between the corresponding uniform complexity classes, since very recently it has been proved that in the uniform case the alternating space hierarchy does not collapse for sublogarithmic space bounds. (orig.)Available from TIB Hannover: RR 1843(94-12) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman