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# A note on first-order projections and games.

Arratia, A. A. and Stewart, I. A. (2003) 'A note on first-order projections and games.', Theoretical computer science., 290 (3). pp. 2085-2093.

## Abstract

We show how the fact that there is a first-order projection from the problem TC (transitive closure) to some other problem $\Omega$ enables us to automatically deduce that a natural game problem, $\mathcal{LG}(\Omega)$, whose instances are labelled instances of $\Omega$, is complete for PSPACE (via log-space reductions). Our analysis is strongly dependent upon the reduction from TC to $\Omega$ being a logical projection in that it fails should the reduction be, for example, a log-space reduction or a quantifier-free first-order translation.

Item Type: Article Descriptive complexity, Finite model theory, Quantifier-free projections. PDF - Accepted Version (185Kb) Peer-reviewed http://dx.doi.org/10.1016/S0304-3975(02)00491-7 29 Jun 2009 15:35 10 Nov 2011 11:06

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