Spira's Theorems on Complete Linear Proofs of Systems of Linear Inequalities.

摘要

Motivated by questions of computational complexity, M. Rabin introduced the notion of a complete proof of a system of inequalities. The theorems of Rabin and P. Spira concerning that notion can all be interpreted as statements about partial coverings of convex polyhedra. Both papers are interesting and treat questions of fundamental importance for the study of computational complexity, but only Rabin's paper is correct in all respects. The present note contains counterexamples to some of Spira's results and establishes a correct version of one of them.