The Resolution of a Hartmanis Conjecture
نویسندگان
چکیده
Building on the recent breakthrough by Ogihara, we resolve a conjecture made by Hartmanis in 1978 regarding the (non) existence of sparse sets complete for P under logspace many-one reductions. We show that if there exists a sparse hard set for P under logspace many-one reductions, then P = LOGSPACE. We further prove that if P has a sparse hard set under many-one reductions computable in NC1, then P collapses to NC1.
منابع مشابه
Resolution of Hartmanis' Conjecture for NL-Hard Sparse Sets
We resolve a conjecture of Hartmanis from 1978 about sparse hard sets for nonde-terministic logspace (NL). We show that there exists a sparse hard set S for NL under logspace many-one reductions if and only if NL = L (deterministic logspace).
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