Characterizing NC with tier 0 pointers

Abstract

A two-sorted term system characterizing NC implicitly is described. The term system is defined over the tree algebra T, the free algebra generated by 0, 1 and * , and the recursion scheme uses pointers over tier 0. This differs from previous characterizations of NC, where tier 1 pointers were used or full parameter substitution over tier 0 was allowed.

Logspace without Bounds

“…Different techniques to implement an intrinsic growth-control have been developed and with them characterizations without explicit bounds in the recursion schemes have been achieved. Besides others, we mention: for the class of polytime functions [3], [10], [14]; for the class of polyspace functions [15], [17]; for NC [11], [5], [16], [4]. The aim of the present paper is to provide such a characterization for the logspace functions.…”

Implicit characterizations of FPTIME and NC revisited

“…In implicit computational complexity, much attention has been payed to the complexity classes FPTIME and NC, e.g. see [2,4,6,7,9,10,15,18,19,24,26].…”

Characterizing PSPACE with pointers

“…The characterization given in [4] is established in a two-sorted context and, just like the one we give here, the pointers are in the highest tier, meaning that one can recurse on the pointers. Recent work showed that for NC we can avoid to recurse on the pointers, see [10].…”