Abstract

We show that a form of divide and conquer recursion on sets together with the relational algebra expresses exactly the queries over ordered relational databases which are NC -computable. At a finer level, we relate k nested uses of recursion exactly to AC k , k 1. We also give corresponding results for complex objects. 1 Introduction NC is the complexity class of functions that are computable in poly-logarithmic time with polynomially many processors on a parallel random access machine (PRAM). The query language for NC discussed here is centered around a form of divide and conquer recursion (dcr ) on finite sets which has obvious potential for parallel evaluation and can easily express, for example, transitive closure and parity. Divide and conquer with parameters e; f; u defines the unique function ', notation dcr (e; f; u), taking finite sets as arguments, such that: '(;) def = e '(fyg) def = f(y) '(s 1 [ s 2 ) def = u('(s 1 ); '(s 2 )) when s 1 " s 2 = ; For parity, we t...

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