Reflective Relational Machines

Abstract

We propose a model of database programming with reflection (dynamic generation of queries within the host programming language), called the reflective relational machine , and characterize the power of this machine in terms of known complexity classes. In particular, the polynomial time restriction of the reflective relational machine is shown to express PSPACE, and to correspond precisely to uniform circuits of polynomial depth and exponential size. This provides an alternative, logic based formulation of the uniform circuit model, which may be more convenient for problems naturally formulated in logic terms, and establishes that reflection allows for more “intense” parallelism, which is not attainable otherwise (unless P=PSPACE). We also explore the power of the reflective relational machine subject to restrictions on the number of variables used, emphasizing the case of sublinear bounds.