The resolution of a Hartmanis conjecture

J. Hartmanis (1978) conjectured that there exist no sparse complete sets for P under logspace many-one reductions. In this paper, in support of the conjecture, it is shown that if P has sparse hard sets under logspace many-one reductions, then P/spl ...

Let $\Sigma $ be a finite alphabet. A set $S \subset \Sigma ^ * $ is called sparse if the number of members of S having length at most n is bounded above by a polynomial in n. Let $ \leqq _m^P $ denote polynomial-time many-one reducibility, and let $ \...

Let $A$ be a language and $C$ be a class of languages. $A$ is said to be s-C-close (s-C-outside-close) if there exists $B \in C$ such that $\parallel (A \bigtriangleup B)^{\leq n}\parallel \leq s(n)$ (and $A \subseteq B $). If $A$ is q-C-close (q-C-...