We show how the fact that there is a first-order projection with successor from the problem TC (transitive clousure) to some other problem Ω enables us to automatically deduce that a natural game problem, LGΩ, whose instances are labelled instances of Ω is complete for PSPACE (via log-space reductions). Our analysis is strongly dependent upon the reduction from TC to Ω 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 with successor.
CitationArratia, A.; Stewart, I. A note on first-order projections and games. "Theoretical computer science (Berlin, west)", 2003, vol. 290, núm. 3, p. 2085-2093.
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