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A second step towards circuit complexity-theoretic analogs of Rice's theorem

  • Lane A. Hemaspaandra
  • Jörg RotheEmail author
Contributed Papers Circuit Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)

Abstract

Rice's Theorem states that every nontrivial language property of the recursively enumerable sets is undecidable. Borchert and Stephan [BS97] initiated the search for circuit complexity-theoretic analogs of Rice's Theorem. In particular, they proved that every nontrivial counting property of circuits is UP-hard, and that a number of closely related problems are SPP-hard.

The present paper studies whether their UP-hardness result itself can be improved to SPP-hardness. We show that their UP-hardness result cannot be strengthened to SPP-hardness unless unlikely complexity class containments hold. Nonetheless, we prove that every P-constructibly bi-infinite counting property of circuits is SPP-hard. We also raise their general lower bound from unambiguous nondeterminism to constant-ambiguity nondeterminism.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  1. 1.Dept. of Computer ScienceUniversity of RochesterRochesterUSA
  2. 2.Inst. für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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