The relative power of logspace and polynomial time reductions

Abstract

There exist many different formalisms to model the notion of resource bounded ‘truth-table’ reduction. Most papers in which truthtable reductions appear refer to the seminal paper of Ladner, Lynch and Selman for a definition. The definition of truth-table reductions given there however, pertains to only one of the possible incarnations of the notion. For larger resource bounds, this definition often coincides with other-often implicitly used-definitions of the notion. In this paper we focus our attention on resource bounds for which the various definitions probably donot pertain to the same notion. In particular, we show that coincidence of different notions implies coincidence of complexity classes likeNC1,LOG, andP, which are widely believed to be different.