Observations on complete sets between linear time and polynomial time

Polynomial-Time Isomorphism of 1-L-Complete Sets

Let C be any complexity class closed under log-lin reductions. We show that all sets complete for C under 1-L reductions are polynomialtime isomorphic to each other. We also generalize the result to reductions computed by finite-crossing machines. As a corollary, we show that all sets complete for C under 2-way DFA reductions are polynomial-time isomorphic to each other.

Sets Computable in Polynomial Time on Average

In this paper, we discuss the complexity and properties of the sets which are computable in polynomial-time on average. This study is motivated by Levin's question of whether all sets in NP are solvable in polynomial-time on average for every reasonable (i.e., polynomial-time computable) distribution on the instances. Let PP-comp denote the class of all those sets which are computable in polyno...

On Elementary Linear Logic and polynomial time

Linear logic (LL) [Gir87] has been used in implicit computational complexity to characterize various complexity classes within the proofs-as-programs approach. This can then be the basis of type systems to guarantee complexity properties on lambda-calculus. As duplication is controlled in LL by the connective ! the key idea of this line of work is to consider variants of this system with a weak...

Polynomial-Time Membership Comparable Sets

This paper studies a notion called polynomial-time membership comparable sets. For a function g, a set A is polynomial-time g-membership comparable if there is a polynomialtime computable function f such that for any x1; ; xm with m g(maxfjx1j; ; jxmjg), outputs b 2 f0; 1gm such that (A(x1); ; A(xm)) 6= b. The following is a list of major results proven in the paper. 1. Polynomial-time membersh...

Relations between Sets of Time Points and Quasi-linear Orderings