A note on first-order projections and games

Authors:
Argimiro A. Arratia;Iain A. Stewart
Affiliations:
Departmento de Matemáticas, Universidad Simón Bolivar, Apartado 89000, Caracas 1080-A, Venezuela;Department of Mathematics and Computer Science, University of Leicester, Leicester LE1 7RH, UK
Venue:
Theoretical Computer Science
Year:
2003

Citing 4
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Abstract

We show how the fact that there is a first-order projection from the problem transitive closure (TC) to some other problem Ω enables us to automatically deduce that a natural game problem, LG(Ω), 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.